As you may know if you follow me on Facebook, I pretty much hate, with a capital H-A-T-E, this “new common core” math being taught. Every day it’s a massive struggle for Chris and me, him with a Masters Degree and myself with a Bachelors, to teach 3rd grade homework to our daughter.

Putting aside that we work for hours past an *already* 8 hour school day, ignoring that we are provided no text books to learn about the material, and sweeping under the rug that they send home homework on things they have yet to even teach yet, we are doing our best.

But we are lost.

**LOST. **

And I am a bit angry to tell you the truth.

Today was just another example of “fuzzy” math.

This is on Charlotte’s homework:

All her problems have to be done this way.

Under what math EVER would 291 be “estimated” or “rounded off” to 200? Am I missing something? And this is the example for her to base all her other math homework on.

I can tell you that if I estimated or rounded off my bills from $291 to $200, I would get a notice of an unpaid bill. I am not sure my mortgage or car payment would agree with that.

And let’s jump to the answer. The estimated sum ‘500’ is *considered reasonable* with ‘645’?

Is 5 million the same as 6.5 million? Ask an accountant that. Ask a corporation that.

I can’t help but wanting to refuse to teach Charlotte something that I find completely and utterly wrong.

~trisha

### Free Printables Monthly!

Get FOUR FREE Child Friendly Printables, perfect for home decor, nursery, or childs bedroom. Just print and frame for instant art- FREE! When you join my mailing list, you will be updated any time I have a new printable so you can be first to download!

Momma says

I personally think that both math curriculum is flawed. Math that is taught in our schools should be math that is used in everyday life, Ratios, multiplication, division, percentages,area, volume, fractions etc. is what’s important. Unless you’re going to be an engineer, physicist, astronomer or some kind of math based profession continue the extensive knowledge at college. But to teach children things that they’ll never utilize unless going into those math intensive professions is a waste of their brain space.

Portia says

Wow, there are a lot of arrogant people on here. For those of you that get Common Core and feel it’s valuable great for you, but for those of us that live in the real world, this is horrible. I have a 2nd grader that is learning Common Core they want to retain my daughter because although she can arrive a the answer the standard way, she is confused by having to use a different strategy every single time. As a parent, you know what your kid is learning is bad when their own teacher flat out tells you that she thinks it is so wrong to teach them this and for their team to agree to not include test grades involving Common Core for the first 3 terms of the year for all 2nd graders. Sorry, but that speaks volumes to me. If you had to figure out what 37+10 is, it is a absolute fact that not one parent here would use Common Core to arrive at the answer. We have to be honest with ourselves here. The premise behind Common Core is to provide evidence of arriving at the answer. The problem with that is if you don’t know how to add and subtract ANYWAY, it doesn’t make one difference what kind of evidence you are trying to provide. If you don’t know what 3+1 is, Common Core is not going to help you.I am livid that they are playing around with the education of children just to receive grant money. This whole thing is about grant money and in the process they are confusing the crap out of these kids. It just really shouldn’t matter how one arrives at the answer as long as it is the right answer. This is ridiculous.

Marie says

Here’s the thing… anyone who learned estimating and rounding in the past learned anything past half of the amount is rounded UP not down. So it would be 400 + 300, an estimate of 700, which would be reasonable. Teaching them not to round up if it’s closer to the next hundred is stupid. Teaching them to place more value on the first number and ignore the others is foolish.

Amelina says

I think common core is just another advancement in the education world that parents are against because they do not understand and they do not want to change their way of seeing things.

– 17 year old high school student with two younger brothers who are both in elementary school

Mitch says

I feel as though it is you that doesn’t see the problem. They did assume 1 significant figure in the math, which would be unnecessary as addition wouldn’t change the significant figures in this problem, but they rounded down when the obviously should have rounded up. In my intended major of Chemical Engineering an answer being off by 55 (400+300=700) is acceptable but 145 (300+200=500) is way to far off and would be wrong. If I were calculating the amount of force, hopefully in Newtons, that a bridge must be able to hold I doubt you would want me to be off by much if at all, and in the real world and college you would be penalized, with the respective punishment, for not having the correct answer because close doesn’t always count. — 18 year old College student

Ted says

The more I look at people’s reactions to Common Core math problems, the more I am convinced that these adults lack basic understanding in elementary mathematical notions and concepts. And frankly, to those of us who have an understanding of mathematics, you are making fools of yourselves.

First of all, this is a practice problem in a technique. Mathematics training, at all levels including the most advanced, has been doing this for ever. Practice problems are often simplified illustrations of a concept, given for learning purposes. The goal, is for the student to grasp the underlying principle. It is not necessary that the problem reflect anything immediately useful.

What I find most striking about people who criticize common core by picking on math problem examples, is not even that they are ignorant of the elementary mathematical concepts being illustrated. It is the arrogance with which they proclaim their ignorance as knowledge. People, the problem isn’t with the Common Core … it’s with you and your level of understanding… and the fact that most of these elementary concepts are lost on you.

However, for all of those too dull witted to be unable to contrive a example for this particular problem where this estimation technique would be both useful and valid, let me do it for you — A ballroom has a capacity of 700 people. We are having a party where two classes are invited. The first has around 354 students and the other no more than 291 students. Is the room large enough? Using the estimation technique above, we estimate 500. The real number has to be within 200 of that estimate (why?), so yes, the room is large enough.

The problem is you. Not Common Core.

your mother says

This reply is the stupidest ever! Its insulting. The way we learned math when we were kids worked for us and now they are doing it a longer harder way. I think your smarter if you can do math in your head rather than have to write out a huge problem that can be done faster the old way. Common core sucks and I think you suck too.

Amelina says

Have you learned the math or just memorized a line of math facts and spent your entire life quoting a text book?

Lloyd A Dale says

What an imbecile! The problem is people lime you who don’t care about the correct answer. The correct answer is not an estimation. I am completely with Trisha. According to your mentality, 1 + 1 = Could be 1 or three because the estimation is close. You are a nut job.

Cathy says

Just exactly where are these kids gonna be using this Common Core Math at in life? Explain that to me. All they are doing is putting more stress on our students.

Marie says

Your example is flawed. You would round up to 300 for the 291, and you’d probably round up for the second since it’s past the 50 mark, making it 400, so the answer would be 700. You’d know that the number is actually less than that because you rounded up. To use your example, how about if the room can hold no more than 550. According to this and your rounding estimates you would be under the mark, when in actuality you’re more than a hundred over it. Terrible estimation, terrible rounding.

Teaching students to ignore the math to the right and focus on the largest number is a recipe for disaster. When you use rounding and estimates you round up if it’s past the half mark, round down if it’s under the half mark, there is a huge difference between 200 and 291, it’s asking them to ignore even earlier information on the number line. (Is it closer to 300? Or 200? If you were to estimate where it was, would you pick 200 or 300? Shouldn’t we be building on this information they get in common core in the first grade? Can you begin to see how a child may think “how can 291 be more like 200 than 300?”)

The parents are just stupid is a foolish ‘sticking my head in the sand’ comment. It’s an excuse to ignore real issues that are cropping up. Most parents can and do understand estimation and rounding. This is simple, and still used in real world and much higher math. But 291 is never going to be closer to 200 than 300.

Linda says

Common core is terrible. There is no reason for 6th graders to cite text evidence on a classic fiction story.

Amelina says

TO answer your question of when they will use this information: when have yo9u ever used Latin? or trig? or calculus? or any of that information you learned in high school? You have not used half of it so why can we not teach kids with this new way

Jackie says

I HATE common core! How can I help my 6th graders with homework when I don’t understand it myself??!! My son asks his teacher for help and she tells him to try and figure it out by himself! They have no books with references or examples for educated parents to look at. My son use to get great grades in math, now he gets frustrated and feels stupid because he can’t solve simple problems that should take a few steps instead of 30 steps. Common core is the most ridiculous thing! I don’t understand how my 11 year old is suppose to learn something when there is no one or no book to help him! It’s incredibly frustrating and and demeaning. Teachers expect these kids to understand the concept they day they teach it and then to move on to the next concept, when they can’t understand any of it.

Anu says

My daughter and I struggle through her homework, which calls for diagrammatic representation, explanations, and justifications to explain the most basic concepts. Did we really pay millions of dollars for this? And the educators are now blaming the schools, the teachers, & (are you kidding me), the parents! Do the parents need to go to school again to help their kids with the homework?

Amelina says

Would you rather your daughter grow up and struggle through classes not having full understanding of math and chemistry and other classes in school or her job and career, or would you rather go and ask her teacher to explain how to do this math to you and be able to help her and support your daughters learning career?

Teresa says

I 100% agree with you. As for the person commenting without kids – his opinion is null and void!!! I have no idea how to teach my daughter how to do her 4th grade homework. I don’t see how this is going to help her in the real world – you cannot estimate that the pineapple in the grocery store is $1.00 if the price tag is $1.69. Sorry. They wouldn’t sell it to you.

Rant says

Ummm, have you read the Common Core Standard (CC)? So I just saw this example and yes, I agree, it is wonky. So then I did a little research (very little) and read the entire 3rd grade CC. It doesn’t take long, it’s just some achievement standards. So all these ridiculous examples I keep seeing friends posting or reposting have nothing to do with common core and everything to do with your state implementation, the teachers, and probably most importantly, whoever is writing the textbooks. I don’t have kids, so I really don’t care all that much. But I do not like misinformation so guess what, the common core is not the problem. Read it then point your laser cats at the right target.

trisha haas says

Since the books have this stamped on them….. (and this came directly out of my daughters desk)

rant says

I can see where people would be confused but it seems the makers/authors of the textbooks are to blame, not the standards. What does the inside cover show I wonder. And seriously, you should read the common core guidelines if you haven’t. If everybody start directing the problems at the right source, maybe something can be done.

Stephen Spencer says

It is obviously clear this program called Common Core is nothing but a design to instill futility in thinking among young students, make it near impossible to learn, and deliberately dumb down the nation. I haven’t heard of any other nation accepting this. I wouldn’t teach my kids this way. Here is what happens. Very few, if any pass, they are all given an IEP, a learning disabled designation, then put on some drug, which makes it worse. Schools should outright refuse, regardless of federal or state funds, to teach this complete nonsense. As a teacher myself, I won’t teach it. Okay school, do something about it. My kids are going to excel.

Shari says

Are you sure this is related to Common Core? I have a teacher friend who struggles with math and teaches her struggling learners to break down the problems in a non-traditional way – but they arrive at the correct answer in the end! (She would also have them add 50 and 90 and 4 and 1 in your example problem.) Although I am not a fan of CC, I thought it was more about scope and sequence than actual techniques. Is it possible that curriculum publishers are using this time to push their own agendas?

Chris says

This Common Core is ridiculous. It’s all about not ‘offending people’ if they are wrong. In maths there is either a right answer or a wrong answer. But officer I was only going about 100km which is reasonably close to 60kmh!! What happened to learning times tables as we all had to do at primary school. Yes the whole class would be heard singing along 2×4’s are 8 3×4’s are 12 etc but it stuck in our memory and to this day I can walk around a supermarket and be within a few cents when we get to the check out. As a Professional Quantity Surveyor, my clients want to know exactly what their project is going to cost, not something reasonably close. I totally agree with draagydragoon re paying teachers something reasonably close to their expected pay. And I’m on the Board of a very large educational facility so mix with these people regularly.

PC says

This is a very poor example of estimation. The proper way is to round to the nearest 50, not round down to the lower 100. They should have: rounded 354 to 350 and 291 to 300. This would give you an est of 650, much closer to the correct answer. I have a degree in Apllied Math and I was an navigation instructor for the Air Force for 20 years. We taught our students to do rounding estimates because you need to think on your feet. I have taught my kids and many of there friends this and it has help them with there math courses. It is also used by most people in life (when you add up the items in your shopping cart, you always us this to estimate). Don’t get me wrong, I hate the common core. Most of the way they are trying to teach solving math problems is STUPID!!!! But this is a great way to teach kids how to confirm there answer and will help later in life.

Mr. facepalm says

Seriously? First of all, “(when you add up the items in your shopping cart, you always use this to estimate)”? I always use a calculator to find the exact total so I don’t go over budget and pretty much everyone else I know either does this or doesn’t add up the items in their cart at all. I’m in Calculus now and you don’t estimate to confirm your answer, you check it using another method of solving it or reversing the problem (i.e. subtracting 354 from 645 and seeing if that equals 291. Sure, In the Air Force or some other quick-reflex situation you might need to use this, but for most everything else, you need to be exact whilst confirming your answer.

geekymom says

I always estimate in the grocery store. That way I don’t have to carry a calculator or fumble around with my phone. $1.99 rounds to $2.00. $2.09 becomes $2.00. You can come reasonably close to the cost without having to take out a calculator. If you are worried about going over your budget round up to the nearest 50 cents. IE $2.09 would be $2.50. By rounding up, you will save yourself some money, coming in under budget each time. 😉

Livinginbrooklyn says

34,000 New York children refused to take the ELA state tests. Many more will choose to refuse the math, especially now that principals and educators are speaking up. Watch and spread the video. Parents have a right to refuse!

http://youtu.be/2ayYajsQjg8

James says

WTF???? Has anybody stopped to think that this is 3rd grade math, not college level calculus? Who dreams up this s**t? As a holder of two masters degrees and a professional accountant by trade, I can tell you that estimation is a good skill, but the analysis done by some of the people on here makes my head hurt. The problem is wrong. Anyone who can tell me otherwise in 2500 unintelligible words needs a hobby.

Debbie McCormick says

Completely ridiculous. One thing I do want to repeat that was mentioned earlier – teachers are not to blame. They have to teach this by law and a vast percentage of them hate it as much as parents do.

Jburd says

My daughter is in 8th grade and hates CC!!! Because of it, her grades are going down and she was an honor roll student!!! Even the state tests she took in the past was above average until last year, with CC BS test it was lower. I have opt out my child from ELA CC test in April and going to do it for Math which is held this week (4/30-5/2)you as a parent have a right to refuse your child to take these tests! I’m worried about when she goes to high school because its going there!!!!

draggydragoon says

That’s ok, we can just pay the teachers that use this method of teaching math with the same method. If their monthly paycheck is supposed to be $4,798, I think $4.000 is reasonable.

t c says

Teachers did not come up with this. Why do you want to take it out on them???

Jane McGonnigle says

Teaching this concept to 3rd graders is not only useless, I bet it hinders them as well.

Kuildeous says

Seems like she is asked to provide the actual sum, so it’s not like they’re skimping on that.

I can see the value in estimation to ensure you’re in the ballpark even if you’re not right, but I have to agree that rounding off 291 to 200 is sloppy. At the very least, it should round to 300 and 300. I would actually round to 350 and 300, but I will not fault someone for choosing to round only to the nearest hundred.

Michelle says

This type of teaching has nothing to do with Common Core. This is about your child’s school curriculum choices. Common Core has nothing to do with curriculum. I am a teacher. I can tell you first hand that Common Core is nothing but a list of standards students are required to meet. How the school chooses to teach them is up to each individual school district. I am not necessarily in favor of CC, but I am getting sick and tired of folks who aren’t in education and have not been through the training blaming everything they don’t like or understand about what their child is being taught on CC. If someone at your child’s school is telling you that this is Common Core Math they are either lying or they themselves have not been educated about what Common Core is.

Michelle says

By the way, I just looked up and read the Alabama Common Core State Standards for 3rd grade math and no where does it mention front-end estimation as a standard. I repeat, this math has NOTHING to do with Common Core.

Jon says

So I’ve spent some more time thinking about this, and I think my position is that on the one hand, the technique is of highly dubious value and there’s an argument that time shouldn’t be spent teaching it, but on the other I maintain that it’s alarming that neither you nor your husband could understand the technique.

First, the technique itself. On three-digit summands it catches errors outside of a range of 200, and where that range is centered relative to the correct value varies based on the second and third digits of the summands. I’ll admit that I no longer have any but the vaguest memory of what it’s like to have a third-grader’s understanding of math (or a sixth-grader’s, for that matter), but my guess is that most errors on these problems are likely to be small relative to 200—forgetting to carry, or double-carrying, or incorrectly performing addition on two single-digit numbers. Since you have to be able to add the leading digits correctly to get the estimate correct, it effectively only works for errors that make the result too large. It looks like it’s really mostly useful when the last two digits of both numbers are relatively large—which admittedly is probably the circumstance in which elementary schoolers would most likely be making mistakes, but since it has so little value the student won’t have a good reason to use it for its own sake, which means it will quickly be forgotten. Unless the entire point of teaching this is to reinforce principles like two two-digit numbers summing to less than 200, I can’t see any point to it.

That said, on to understanding:

“Under what math EVER would 291 be “estimated” or “rounded off” to 200?”

Well, let’s look at what happens when you make different rounding/truncation choices. You seem to want to use the standard unqualified “rounding” rules ( 0, ≥5 –> 10); the third option is to always round up (we’ll ignore other options like round-to-even). Since the given example makes standard rounding and rounding up the same, we’ll instead use 344 and 291.

If you round down, you get an estimate of 500, so you know the answer is between 500 and 700.

If you round up, you get an estimate of 700, so you know the answer is between 700 and 500.

If you round-on-5s, you get an estimate of 600. What’s the answer between? There are ways of recovering the interval, but I’m pretty sure they’re all more difficult than simply adding the original two sums, which entirely defeats the purpose.

So that’s why we don’t want to round-on-5s. As we see, rounding up and down are in one sense equivalent, but keeping in mind that we’re talking about third-graders the fact that rounding down simply involves taking the first digit is pretty compelling. Then the upper bound is calculated with addition instead of subtraction, which I seem to remember as being easier at that age.

The question then is why you two didn’t see this. In the post, you repeatedly conflate the estimate with the result despite the problem clearly saying that the estimate is “to check that each answer is reasonable”. Although my initial reaction was to question your math ability, and I still think that’s part of the issue, I wonder now if the problem isn’t your assumptions going into the worksheet. Given your stated strong negative views on the current math curriculum, I’m thinking that when you encountered something that at first glance seemed counterintuitive or nonsensical you concluded that it was nonsense rather than examining it further to see if your conclusion was justified and maybe running some numbers.

Anyway, I can’t say I know enough about the Common Core to have an opinion on it (I don’t have a dog in the fight, as it were), but it seems to me that by failing to understand the technique being taught you weaken your criticism—instead of a strong argument that time and effort is being wasted on an unenlightening and marginally-useful technique that will probably never be used again and will be promptly forgotten, you have an easily-rebuttable argument that the technique is “fuzzy math” and “completely and utterly wrong”.

LinLafayette says

Um, Common Core is one Evil indoctrination by Commies, and should be rejected outright! If the idiotic public schools insist on this garbage, take your children OUT of these Marxist day care centers, and teach them at home. Anyone who cannot see through this BS..is either a flaming “progressive” or a complete moron.

Harry says

Appears in order to explain and defend this assignment example is to have a background in applied logic and congnitive reasoning to get into the mechanics within the methodology. An adventure in descriptive sequence and pathway search.

A fair assumption if you are already grounded in formuli calculus in order to have to provide such a lengthy explanation which would cause a 3rd grader to skip school… forever. As well, not to have to impress anyone with an already college level, masters degree in math.

There is too much suggestion of redundancy, wasted exercise and weak provision of true or even practical, if not useful direction, to simpler problem solving.

Just to get to the truth and final solution.

A problem, of any variety, needs not to be treated with such useless abuse.

Drick says

Here’s some info on front end estimation. It is an actual math concept to help add large numbers together quickly: http://www.basic-mathematics.com/front-end-estimation.html. That being said the numbers should be rounded up to the nearest hundredth. 400 and 300. Should be added together according to this site. . Fun note: once you have 700 you can then subtract in your head what you added to the two numbers to get the correct summation of the original numbers.

Ralph Hogav says

I am as retired teacher. I have seen many so-called education gurus come and go with all their BS on how to teach kids. Most of these idiots have never been in the classroom. Someone in education needs to wake up and tell the powers in charge that we need to go back to the basics.. Memorizing the multiplication tables, learning how to diagram sentences, and learning correct grammar must be put back into schools. The educational BS of No Child Left Behind and Common Core are just more ways that somebody is making big money. We are falling further behind the world in educating our youth because we will not return to the basics. Kids cannot even make change anymore. We are graduating students with no work skills. They cannot be successful in the job market in America. You see more Asians in the top jobs because our kids are not being prepared properly for today’s jobs. We must stand up and stop these worthless education programs before the only jobs our youth will be able to do will be minimum wage employment.

th

until

Doug Hensley says

Well, there’s all sorts of ways to check “reasonable”. One of my rules is that if two odd numbers are multiplied, the answer, whatever it is, has to be odd. Any even answer is unreasonable, in the sense that you ought to know that it has to be wrong.

Flying Tiger Comics says

It isn’t about mathematics. It’s about marxism and destroying western civilisation. The last enemy of marxism on the planet is American freedom.

Lawrence Myers says

For a look at Common Core and other problems caused by No Child Left Behind and Race to the Top I suggest parents read Reign of Error – The Hoax of the Privatization Movement and the Danger to America’s Public Schools by Diane Ravitch.

Emily Haraldson says

My son is also in 3rd grade and I’m finding the Common Core math infuriating as well. However, the above example seems like a typo. We’re doing the same thing right now in math and it’s never asked us to round a number above 50 downwards. I would ask the teacher about that, if s/he even knows. My son’s teacher admitted to me that the teachers at his school haven’t even received the proper training in Common Core yet! Unreal. So, the next time I get a progress report saying my son has an issue with explaining why/how he got to the answer of the simple math problem, I’m going to throw it in the trash.

Krista says

That’s why it’s called front end estimation. You just look at the first number and throw out the rest regardless of whether it’s over or under the halfway point. I didn’t know about this either and thought it was a mistake. Nope! I first saw this a couple years ago when my high school aged sister in law was living with us and i was like seriously? I have a bachelor’s, masters and doctorate and couldn’t believe this was how they were teaching math now. My kids weren’t school age yet and this scared me and now my girls are in first grade and I’m already frustrated with the way they are being taught. In first grade!! We do our own math studies at home which go well but I’m afraid i could be confusing them even more.

Linda says

Can you please send me the publisher of that math assignment? I have a group in CT that has formed in response to CC and we are looking for lots of info.

Thanks!

trisha haas says

I cannot tell you the last time my daughter brought home a book…we dont get books in our elementary school. They come home w/ these sheets. This article was written in November I believe so this paper is long turned in.

C Woelm says

When I was a young child in the 60’s & 70’s they taught us rounding down and rounding up. It hindered my Math growth all of my life. It took playing Domino’s to help me add faster and get the right answer. I hope don’t cause the problem for them as it did for me.

Tracie says

Everyone is getting caught up on the word “estimation”. There is a difference between estimating and front end estimation. They are two different concepts. Personally I do not think front end estimation has much use due to the fact that you can get an answer that is vastly different than the correct answer. I also dislike what I have seen of the common core math. I think kids should just have to memorize their math facts like we did as children.

Bob says

We are dumbing down all the children who are taught this crap. No wonder the Asian children are the most advanced,they find “the answer” not some estimate. Build a house with this math and let me know how it works for you.

Charice Early says

http://www.youtube.com/watch?v=c4GSf5u80S4 this will help you understand what front-end estimation is and since they want you to find the Sum, that means addition. Hope this help you understand better. I had to look up what front-end estimation was, because that did confuse me.

Claudja says

I sometimes have to Google what specific terms are for helping my son with his homework. I didn’t know what a t-chart or a Venn diagram looked like until I saw pictures of them. As for front-end estimation, I suspect they teach this skill so students have a way to quickly double check their work, a skill they need for the grueling amount of testing they undergo.

MO says

In the ball park? 145 off? Off by almost 1/4? All this is teaching is that everybody gets a good grade even if you’re NOT EVEN IN THE BALL PARK. A low IQ student can be taught to use a calculator with real results but this rewards failure.

ardith says

this is DC math, right?

Angela says

Let me first say – Sam, for your judgements and correcting someone “with master’s and bachelor’s degrees” on their math skills, you leave a bit to be desired on the spelling and language end of things.

That being said, do you yourself, have a grade school child that you are helping with homework each night? The problem is not being able to do the work. The problem is knowing the CORRECT way the “standards” expect your child to do the work. Personally, had my daughter come home with this same problem and estimated it the way she had been taught two years ago, as in rounding to the next hundred (which, by the way, they spend more than half the year learning how to correctly estimate…) she would have been marked wrong. They are changing concepts almost by the minute, and not giving the students, let alone the parents, sufficient instruction as to HOW they want these things done. Once they get to the testing, they are being tested on things they haven’t even learned yet and brought to tears over it.

JaxFL says

Is the teacher telling them they can’t “estimate” up to 400 and 300? What would be wrong with that??

Joannah says

I disagree with Sam. As a teacher with 18 years of experience in 4th and 5th grades, rounding is the strategy used for estimating problems like this. We still teach students to “stay the same” when the digit to the right of the place to be rounded is 0-4, and “round up” when that digit is 5 or more. This is a terrible example to give to students. Were I to model solving this problem for my students, 354 would have been rounded to 400, and 291 would have been rounded to 300 using the rules I stated above. Therefore, my estimate would have been 700.

Trisha, you are right to be frustrated with this homework assignment.

David says

These are the same students who are now sitting in my college classes and cannot place into college level math because college placement tests do not care about ‘methods.’ It is not useful in the least for anyone and not only frustrates the students in my college classes but also my own children who get marked wrong because they did not use the ‘correct’ method (even though their answer is correct). Three cheers for the uncommon core.

pat says

Who cares what the estimated number is. The problem is 354 + 291. An estimation was not asked for. The answer, the only correct answer is 645. It’s not a reasonable answer, it’s THE answer. And if you want to check your answer add it up again, for cryin out loud. Round 291 to 200? Really? What planet are these people from who decided this was the way to teach our kids.

rhonda guinn says

I am so angry and frustrated about this crap I can barely see straight. My 5th grade boy is bringing home assignments that no one I know, many teachers as well, can’t comprehend. What the hell can we do about this?

Sam says

It’s an estimate, not rounding. Anything within an order of magnitude is generally acceptable. Though, 700 would be a better estimate, that ‘s not the point. The point is to use easily calculated estimates too help assure that you ‘re in the ball park and not making some simple foundational error. And if you have master’s and bachelor’s degrees, nothing in primary, or even secondary school mathematics should be be a cakewalk for you and books should be unnecessary. I not recall bringing home a math book until algebra.

Shannon M. says

Yes, front end estimating is different from estimating by rounding. This particular skill is not Common Core, as I have been teaching it for many years in 4th grade. That being said, I do not like Common Core math because I don’t feel it is developmentally appropriate for much of the elementary grades!

Derek Donoghue says

Sam, It’s a long time since I was at school but if I estimated a 145 difference between my estimate and the answer, I would be wondering where my error was – I would not be even in the same street as the ball park!!! Maths is an exact science not an estimate and I feel should be taught as such!!

Larry says

I was taught that 354+291=X

(round354 to 350)+(round 291 to 300)=X

350+300=X

X=650

X=645

Andrew Marlow says

I teach my grand children to do it correct and accurate. Then dare the school to hold them back. K – 5 requires the parent or guardian’s permission to hold a student back. They get to sit back and laugh at the other kids in 6th grade who have to learn the correct way. For some reason when they get to middle school all this junk goes out the window.

Matt says

It is helping them check their work. They use the first number in the integers (2 and 3) to come to a quick check about the answer (must be greater than 500). They still have to know how to add it up, but it can be a skill to make them faster at an aptitude style test that has way too many questions than can be answered in the time allotted if the work is done full length.

Kathie says

I don’t have any children but if I did I would be so frustrated. I think it is wonderful that the “actual” answer is reasonable.

Sybil says

How ironic! I’m getting ready to draft a letter to my son’s 4th grade teacher to let her know we will no longer do their ridiculous “SMART Goal,” common core, standardized test prep nightly math problem that sometimes takes up to 20 minutes to complete and teaches my son nothing but frustration.

kenny komodo says

This new common core math problem isn’t about the traditional method of rounding to the nearest hundredth or tenth; it’s more about breaking down a problem into ten’s or hundreds, adding those values to get the “reasonable” answer and then adding up what’s left over to the reasonable answer to obtain the correct answer. Kind of a stupid way to do math but at least I can understand it enough to explain it to my grandkids.

Chris says

I’m 30 years old and I had to look up what “front-end” estimation was. I was never taught this when I was in school. I don’t think I was even taught estimation till we learned to add subract multiply and divide. Even then we were taught to look at the whole number and go from there. To teach kids estimating is good but only using the first number. This looks to be a very bad system, we keep using this and well people thought our education system was in the toilet now. We should let things go back to the way things were. Before 5th grade I think we didn’t have all these standereds to meet, teachers were allowed to teach and we learned.

Machado says

My highschool experience a half century ago (I don’t recall grade school addition) was that we were required to prove answers we’d mathematically derived. Came in very handy on the SAT – just pick the most probable answer and prove it, much faster than working out the problem – and, if you guessed wrong, the “proof” gave you a very good idea of what answer was right.

Fred Matsch says

this common core is put together by high school drop outs, that want to bring down every body to there level.

Chris B. says

I’ll probably get a lot of hate for this, but what this is attempting to teach is actually very useful. However they execution is all off. If they actually rounded before doing the front-end estimation like how it is supposed to be done with would be an effective strategy. Those who say that math needs to be exact are not getting the point of the exercise. This is to teach kids a way to check themselves quickly NOT TO BE USED AS THE FINAL ANSWER. However I also feel that adding is not the best place for this sort of exercise. This idea meshes a lot better with multiplication.

For example say i have 99 *97 and I forget to put the 0 in front when multiplying through the 9 and get 1584. I mean we all know it looks wrong but sometimes when taking a test you might not notice the dumb mistake. You could do a quick check of 100*100 = 10000 and realize, holy crap I’m not even close. and then you can do it again. then when you do it correctly and get 9603 you can say to yourself that that is reasonably close to 10000 and can be confident in your answer.

In summary this technique is not meant to be some new way to do math, but a quick way to check if your answer is reasonable. however it should be rounded not just taking the first digit.

Cindy says

And the larger the number the more off the actual answer is with ‘front-end estimation. Another term for this type of math is ‘truncation’ which is by no means true math or a true estimation. Teach the kids how to do the math the first time and don’t teach them ‘methods’ to supposedly help them. If they learn it ‘wrong’ it will mean they still have to learn how to actually do the math and relearning how to do something once you have leaned it wrong and cemented it in your brain is many times harder than just spending a little extra time and learning it correctly the first time.

John Street says

America was built on the 3 R’s, memorization. Students never needed “front end estimation.” Liberals bring all these new-fangled ideas that are unproven, untested outside of their ivory towers. American students continue to fall behind other nations in math. How is 500 even close to 645? 700 is closer and more reasonable. This is a complete joke. Keep America dumb.

Vicki says

According to this, your daughter’s textbook example was done incorrectly anyway: http://www.basic-mathematics.com/front-end-estimation.html

And since when is the correct sum deemed “reasonable”? A math sum is either right or wrong. 🙂 Was the book translated poorly from another language?

Jan says

Try paying your taxes that way…

cherykie says

If some of these common core advocates ever need brain surgery, I do hope a common core graduate is their surgeon…

jwb7605 says

I’m seeing a ton of ludicrous examples (especially concerning math) lately.

My daughter is a math teacher, and says “Any publisher is allowed to put the common core stamp on their curriculum if they use the common core as a “guide” for their design. However, that does not mean their material is fully approved.”

That said, she & I fundamentally disagree on several education related topics.

Can you supply the book title (and perhaps author) this came from?

Apparently some school systems are using “unapproved” material.

Thanks!

Mary says

Speaking as a teacher and a former educational publishing company editor: There is no such thing as “approved” or “unapproved” common core material because there is nobody to approve it. If you want to write a math textbook based on your interpretation of the common core, you are free to do so. You don’t have to get it approved by anybody but the publishing company (or you can self publish it… smaller market, but it’s an option).

Furthermore, the only entity that approves or disapproves of a textbook purchase is the school’s board of education.

So if you have a problem with a text, the problem is with the publisher, not the school and not the state and certainly not the core, which is not alive and cannot approve a thing.

Jeanie Papiernik says

This looks like Singapore Math and not necessarily the Common Core. I know it’s a different approach than most of us learned it as kids, but I teach 3rd grade and I really think it makes a lot more sense then just teaching abstract algorithms. Front end estimation is actually a different thing than rounding so you aren’t understanding the problem, but it’s not wrong. I get that this can be confusing, but look into Singapore Math instead of the Common Core to help answer your questions and it might help you make sense of it. And then if you still don’t like it, you can say you don’t like Singapore Math instead of saying you don’t like the Common Core. Not everyone is using Singapore Math, but it’s researched-based and that’s why lots of schools are moving to it. Singapore Math is separate from the Common Core. They aren’t one and the same.

Isaac Walker says

The question clearly says to find the sum first. This use this technique to see if you have a reasonable answer. This concept has been taught for years in engineering schools. For a simple math problem like this, it seems ridiculous. But the exercise is intended to get students to consider how to CHECK there answers. You learn on simple example so you can profit on harder problems. When the math problem isn’t so simple, using these techniques will help you check your answer. If the problem were 354 X 291, that could easily be miscalculated. The answer would be 103014 but the student could easily miss carrying a digit and get something like 10314. Using this technique they can multiply simpler numbers 300 X 200 = 60000 and realize 10314 is well below what the answer should be. Then they can rework the problem. I understand it seeming ridiculous but the this is learning how to use other techniques to verify your work.

Chris says

Speaking as an engineer, I can assure you that this is nonsense. Nobody ‘checks’ their answers by rounding down. You would check your answer by rounding upward. The very concept is horribly wrong.

No engineers learned mathematics this way. You learn by practicing actual computation, not these dumb ways to ‘check’ your answer.

John Street says

The previous method of checking our work was fine. This is crap.

A Silver says

500 is 22% off of the correct answer, and that’s supposed to give the children an idea of what would be a reasonably correct answer? By your example, it would be alright for the engineering students to think that 78,000 would be in the right range when the real answer is 103,014. In the real world, being off by a fraction of an inch resulted in a space shuttle exploding and *killing* people. In engineering in the real world, if you don’t have exactly the right numbers, your building falls down, your bridge collapses, your drug kills the person it was supposed to help. And saying the correct answer was only 22% off really doesn’t cover the real extent of how wrong that answer is. If the true answer lies within 146 units of 500, then wouldn’t it be possible that the real answer could be 146 below 500? They could have added and come up with a total of 356, and by this questions definition of reasonable, that would have been a reasonable answer to the question of what 354+291 equals. That’s off by nearly half! But according to the margin for error in this question, they could feel confident that it’s right. You could say that due to the nature of the way they’ve rounded, any answer below 500 should be immediately discarded as incorrect, but if a person is so mathematically illiterate that they can’t round up from 291 to 300 and come up with a much more reasonable estimate of 600 – then do we really trust them to follow that rule? And what if they ended up adding and coming up with 746 by accident? How does this question show that 746 is unreasonable? Apparantly the rule is that anything over 500 has a good chance of being the correct answer. Can we honestly expect that standard to rule out answers like 6450? I’d like to think so, but given that this level of math assumes children are incapable of rounding up to 300 from 291 (200 is nearly 33% off from 291 – in what area of science is a 33% margin of error acceptable?!), then I really don’t think we can safely consider any possible error outside the realm of possibility.

Donna says

My son is taking 4th grade common core math for the first time(school did traditional math in 3rd grade). I absolutely hate it and I totally agree with you! The nature of math is that it is exact! I have a B.S. and a minor in math….and I’m having trouble helping him with homework! You can’t “estimate” when measuring for new kitchen cabinets, or paying bills, or anything else! We’re 4 months into the school year and most of what they have learned is estimation! My son has 2 books which are extremely confusing and don’t fully explain the lessons. The lessons are done in class with the teacher’s book – which you do not have available when doing homework! I also find it insulting! We’re going to teach you how to estimate because we figure you’re too stupid to get the exact answer! I’m considering homeschooling to get away from this very bad idea!

Ben says

Would some one mind explaining this concept of “front end estimation” to me? I’m a high school junior currently taking calculus and my fifth grade brother has brought home problems involving this concept. Never before in my high school career have I even heard of “front end estimation”. I’ve been taught how to do basic rounding, how to take significant digits, estimation via powers of ten, but never this. Could some one please explain?

mary lou endres says

Front end estimating only looks at the ‘front’ digit. If the number is 299, you look at the ‘front’ number which is ‘2’. That means you would estimate 200. It is a first step in learning to estimate. Later you learn about rounding.

Lisa L. says

I’m sorry but this fuzzy math does not give me the warm and fuzzies at all. Want to know what a reasonable estimate of that number is? If it’s rounded properly, it would be 700. The question example is wrong.

noel p says

Let me start by sharing that I am a dad and a high school chemistry teacher. I absolutely want my son to learn how to estimate when he is in elementary school. I observe that many of my GT high school chemistry students have not learned how to estimate. They often miss questions because they don’t realize that the answer from their calculator is not a reasonable answer because it is off by several powers of ten. Imagine that your pay check was supposed to be for $1500.00, but you were only paid $150.00, that’s only off by one power of ten. Common Core has its issues, but the goal to teach children better skills of estimation is not one of them. If a child entered numbers incorrectly into their calculator or accidentally multiplies rather than adds the two values, this technique would help them to identify that something had gone wrong and that they should re-work the problem. Estimation is a valuable tool that all children should learn, and children who don’t learn it are at a distinct disadvantage.

April says

The idea that they are wasting time teaching children to find a reasonable answer is absolutely ridiculous. I would love to know exactly when in life my child is going to have someone come and ask them “could you tell me a reasonable answer to 354 + 291???” No. They are going to want to know the exact number. Oh wait! I know I’m sure the banks they try to get car loans and mortgages from will accept a “reasonable” debt to income ratio. I’m sure the stores where the buy groceries and clothing will look over everything they want to purchase and accept a sum of money for it that is “reasonable” vs. what is actually owed.

RB says

Thank you for this post, it really hit home. I am a high school math teacher (about to hit the 10 year mark) and during a recent summer, I tutored 5th graders in math during summer school. I was HORRIFIED when I saw how this concept was being built as a foundation to number sense. I might be old school as well, but the part of me that is passionate about mathematics died a little bit knowing that so called “reasonable estimations” of answers to basic arithmetic problems were being called accepted or even worse, CORRECT!. This is utterly confusing to growing minds. Why would we show our kids a bunch wrong answers to heighten number sense? Wouldn’t knowing how to get exact right answers help better to strengthen mathematical skills? Wouldn’t it be better to observe correct sums and differences in relation to their added or subtracted parts? Is this why students are entering high school thinking that they are always right because their answers are always this preconceived notion of “close enough to being correct.”

Instead of teaching estimation (which is bologna and should really be called guessing), there are other far superior mathematical strategies that build number sense in addition and subtraction and mental math. Take this example of 354 + 291; the student should be taught to round each term to “easier number facts”, and then account for extra or missing units to still arrive at an exact answer. The student can be trained to think that 354 is 4 more than 350, and that 291 is really 9 less than 300. So 350 + 300 is 650, but we still have to add that 4, and minus that 9 since these are estimations, thus getting an exact answer of 645. (And this mental math can be built up more using easier number facts first). The point is, we have to teach students to be original thinkers, by providing them tools first on how to think and then letting them develop their own strategies. We should not be teaching them to be guessers.

Ben Brink says

Love your answer. As a recovering mathematician (two math degrees from Stanford) now doing other things, I share your love for numbers and computational tricks and shortcuts. Adding/subtracting the easy numbers and then making up the difference (your great example); checking by 9s; modulo 3; the 11 rule; forgotten what it’s called but multiplying by easy numbers and then adding/subtracting the extras (like 399X401=400*400+399-400= 159,999; and many other cool, easy ways to do things.

Miriam Dunn says

The issue here is that you are confusing two different processes and terms. You want to “round up” or “round down” but that is not the skill that is being taught here. This is, explicitly, “front end estimation” which helps in the development of number sense. They will ALSO do work that require them to “round” and add as a way to estimate. THIS IS NOT THAT DAY

Ed Fackler says

Miriam, can I have some the Kool-Aid that you’re drinking. Because you are being sucked into the No one wins and no one losses world of socialism and where all is the same. I never was availed of the blessed gift of front end estimation and my math skills kick a$$. 645 is 645. Not 619 or 500 or 600 or 701. They are not at all the same. And this “skill” is confusing kids.

Karla says

I am actually all for my kids learning to do mental math – and this is an example of a way to do math easier in your head. And yes, estimation is needed sometimes. However, I also think kids need to memorize their facts and I don’t believe some of what the common core math is teaching is developmentally appropriate. They are teaching things at the wrong age on many cases. You get children can do some of this mental math but really need manipulatives – they aren’t able to do think abstractly like this. I also think the problems are coming in because the teachers were dumped in this with very little training and of course they also can’t help parents. Lastly I believe math and reading both need to be taught in groups to a accommodate children of different levels.

Lisa says

And….THIS is why I home school my kids. Two with scholarships to top universities in Texas and three well on their way. Don’t just complain about this…DO something! Scale down tighten the belt and live on one income and YOU teach your kids! When you rely on someone else (I.E. our inept government system) to teach your children anything this is what you are going to get. It’s like walking into a thrift store and complaining that everything is cheap and used. If you want quality make it yourself! If you want well educated children…TEACH them yourself and stop complaining! We seem to do a lot of that lately….complain, whine, moan… but we never really want to make the sacrifices that it takes to actually DO something to change it. I know there will be A LOT of excuses as to why you can’t home school your kids but please save your breath…I have lived most of them and overcome most of them.

Trish says

For what it’s worth…I believe that all children learn at different rates by using a variety of methods. I am opposed to the Common Core State Standards for a multitude of reasons but the bottom line is there are some kids who will actually excel using this method. If they can’t get it using the traditional (and in my opinion, the easiest) way then I think this is a good method for them. I am completely opposed to making all children learn the same way. This just frustrates and beats down the child and does not foster a love of learning. Unfortunately, the CCSS does not allow teachers to teach to groups of students independently; it’s a one size fits all approach. That in itself is a disaster. For those of you opposed to the standards and are on FaceBook, search for the page “Parents and Educators Against Common Core”.

SM says

Oh c’mon, why is this problem so hard to understand? In the example above, “The estimated sum is 500. The answer 645 is reasonable.” Therefore, the mathematic formula that applies here is 354 + 291 = 501~700. 645 was the correct answer yesterday. Today, it is 678. Tomorrow it will be 621, unless the moon is full and it’s Tuesday, in which case the answer is 688. I’m sorry, what did you say? That’s ridiculous? No it’s not! Look at the example! They’re all correct! YAY! We learned nothing, but hey, we all passed the test, so the national average will go up! I’m told that fact even benefits us all, somehow! Go new math (and please stay the hell away from my child).

JV says

I stare at my son’s 5th grade homework like an idiot. Just wait till you model draw it all out!

Ron says

As a former high school math teacher and now a college math professor this is unacceptable. 645 is exact, and estimates are evaluated as reasonable or not reasonable by their proximity to the exact answer. I left high school math teaching because of this kind of fuzzy thinking.

Patricia R. Lang says

Common Core is a massive disaster. It wants to destroy independent, creative thought. It makes things so difficult and convoluted, that kids Hate it. You wonder why kids hate school, look at Common Core. I have been int the classroom for 25+ years, and left because of the system. I love teaching, love kids, but the system is a disaster.

Lawrence 1st grade teacher says

Calm down everybody, it looks like a straight up typo in the textbook, which were hastily manufactured to cashed in on the new standards. They are not trying to teach some kind of ‘new’ math. It’s just sub-par ‘for profit’ product with lax quality control on the part of the publisher.

SadieA says

No, Lawrence, it’s not a typo, it’s ‘front end estimation’. I think that it’s fairly useless but it’s another gift of Common Core Math.

Tricia McMasters says

My son is in third grade also and they are doing multiplication. It is the biggest waste of time I’ve ever seen. He’s lucky because math comes easy to him, but now I feel like he’s penalized because of it. He has to draw out and very laboriously explain everything he can easily do in his head. I understand that this method helps kids who don’t have such an easy time with the concepts, but it is pure unnecessary torture for him and others in his advanced mat class.

He missed a point on a test the other day because he didn’t draw 18 little circles to represent the “rolls that Melanie baked.” They were supposed to be divided into 2 groups. He wrote 9-9 instead. It was the correct answer and he totally got the concept, but he missed points because he didn’t draw the 18 little circles.

Are you kidding me? I hate busy work more than anything, and that’s what this is. My 1st grade son is even better at math, and I honestly shudder to think about him going through this. If this math curriculum is still in place when he gets to third grade, I will seriously consider pulling him out of public school.

patti says

Sorry to tell you, but your first grader is already going through this! I retired last year after teaching for ten years, partly because of Common Core. In the years I taught my kids loved math UNTIL last year! A new concept is taught every day, leaving no time for mastery. Even bright children, who catch the concept immediately, are frustrated with it. Brilliant kids sit and wait while the teacher tries to help struggling students understand…or end up doing busy work to occupy them…while the teacher beats herself up trying to help EVERY child learn what’s being presented. Even brilliant children can be “burned out” when learning isn’t fun.

crunchymama says

OMG, I am so sick of the little drawn arrays this year I could scream (Grade 3 as well). Add to that a kid who desperately wants all her circles to align nicely and you have a recipe for over an hour of math homework that could otherwise have been done in 15 minutes.

I can hardly wait till they start the Fractions unit; I think it’s 10-12 WEEKS of fractions. 🙁 Can hardly wait to see with what fresh hell of a time-consuming draw-and-explain procedure they will insist our kids demonstrate understanding. *facepalm*

Michael Paul Goldenberg says

@crunchy: you know you should know better.

crunchymama says

You’re right – I should. *sigh*

But I gotta say, I hate seeing the changes in my little one. She was always the one her teachers used to describe as “a smile with feet” – not so much now. And she was always the one about whom people would always say confidently, “She’ll bloom wherever she’s planted, that one.”

She’s not blooming this year. She’s shriveling. With every fresh math assignment in which she’s supposed to create and/or solve a problem to a prescribed rubric, using prescribed vocabulary, and with every one that comes back marked down because we ran out of time to do one more array because it was pushing 9PM and it was time for the 8YO to go to BED already, she shrivels a little more. And it kills me.

And the big kid, even though she’s settling in socially better than I ever imagined she would, is bored out of her skull in math with the non-content that’s still piling up with busy-work that doesn’t show much more but takes 2-3 times the time. She’s like her mom in that only chorus and orchestra and English – and science, to a point – are giving her enough motivation to care about getting on the bus in the morning. That’s only half the day.

Hence all the questions about finding new math resources so we can go homeschool. *grin*

Rachel says

I took one look at this and knew exactly what it was. It is a type of math called partial sums, and it helps people add large numbers without the aid of calculators. The principle is to keep the numbers at their actual place values. Traditional math would have us adding 354+291 this way: 1+4=5, 9+5=14, carry the one….this is where I am going to stop. This is false math because it is not 9+5, they are not in the ones place. It is 90+50. That is what partial sums is, and it doesn’t matter which end you start from because there is none of that carrying ones crap. Here is how partial sums, would do the problem…and I will be working from left to right just to show you it makes no difference. So, let’s look at the hundreds place, what do we have there…well we have 200 + 300, that’s easy, it’s 500. Actually, now lets skip a bit and look at the ones place…we have 1 +4, that one is super easy, 5. Ok, so now lets look at the tens place…90 + 50= 140. Again, pretty simple. So, now we have 500 + 140 + 5. We could get this answer in our heads no problem but lets break it down just one more time. See, we have two numbers in the hundreds place 500 + 100, well we know that is 600. So whats left: 600 + 40 + 5= 645. It may seem like more steps but if you teach kids to break it down like this they will have a much, much easier time adding…and subtracting…large sums in their heads and do so accurately.

Apart from that, front end estimation has been around a long, long time. So you have a problem, you add it up and get 645. Ok, but do you have the right answer…mmm, well 200 + 300 is 500 so we know the correct answer HAS to be above 500. Thus, 645 is a reasonable answer. Front end estimation is used to check your answer, not to come up with the answer.

Traditional front end estimation would have given you 400 + 300 because both numbers are at the point where you round up…but in partial sums there is no rounding, you get the whole number. The traditional way would have given you an estimate of 700 and still would have made 645 reasonable. But in using partial sums, you simply add up the place values. They didn’t round down to 200, because the hundreds place was 200. Instead of rounding up or down look at the number. I know 200 + 300 is 500, therefore I know 354 + 291 HAS to be greater than 500. So a given answer of 645, is reasonable based on the estimation that I have.

It is a much simpler way to do math, and more accurate. I honestly wish someone had taught this to me in school because then I might not have been so dependent on my calculator for all those years. Now, I can add larger numbers much, much faster. For example: 1859 + 5671. 5000+1000=6000 (so my answer has to be above that) 800+600=1400 50+70= 120 9+1=10…now, lets break it down again…6000+1000=7000 100+400=500 10+20=30….so the correct answer is 7530. Go ahead, use a calculator to check.

Jan says

With all due respect and what the author of the article ALREADY stated, if we did this with our bills we would be in deep doo doo. Do you use this type of “fuzzy” feelgood “math” any time you shop and buy anything? Good in THEORY, NOT IN REALITY.

Michael Paul Goldenberg says

@Jan: do you understand the difference between calculation and estimation? Do you understand why it makes sense to estimate in the real world? If I look at a bunch of numbers and quickly ascertain that the sum is approximately $600, I’m not asserting that the EXACT sum is $600. But if the sales clerk tells me I owe $6000, I know something is wrong. And I know it without needing to add the pennies or the single dollars or even the ten dollars together.

I realize that everyone is up in arms about the Common Core. But first of all, this isn’t something that was invented for the Common Core. Or for NCTM’s standards in 1992.

Insisting that an estimate is worthless because it isn’t the exact sum is like refusing to look at an estimate from an auto-mechanic before deciding whether to authorize the work, because you only want “the exact total.” I suspect you and the rest of the people yelling here don’t do that. And if you do, you’d best learn to do “home auto-mechanics,” and “home” a lot else. Because estimation is a key piece of how the sane people in the real world operate.

Jan says

The word “sane” is subjective. Spare me the hystrionics and the blah, blah, blah. The “best” we can do and you say we don’t live in the real world. (eye roll)

Beth says

This is why it is NOT developmentally appropriate to teach 3rd graders this way. Does anyone here understand that many steps is beyond an 8 years old’s attention capacity? Mutliple step math problems at this age spells disaster. These people need to take a child development or a developmental psychology class.

SadieA says

My goodness, are you serious? It’s front end estimation. Anything in the 300’s is rounded to 300 and anything in the 200’s is rounded to 200. Is not really very useful or accurate at all and in MHO a total waste of time.

Stephanie says

As a teacher and understanding a bit about CC, your explanation is spot on!!! They are teaching this so the student has NUMBER SENSE!! Did you ever really understand why you carried the one when adding? This shows how to break it down and exactly how you get what you get when you “carry” over the old fashioned way. Like many of you, I was not thrilled about the change in teaching, but I can see a difference in understanding in my students. As for the laborious explanations that have to be written out, it’s for the student to explain the process and show the fully understand.

Elisabeth says

“Did you ever really understand why you carried the one when adding?” – Why, yes, yes I did… my first grade teacher made sure that we did. I then passed that along to my own (homeschooled) children, all of whom have excelled in mathematics way beyond their traditionally schooled peers (because they have avoided all of this garbage). In fact, my 17 year old son is heading down to college in the fall to begin his degree in engineering.

How idiotic that you would assume that other people don’t understand the very basic principle of why the one is carried in addition. I can explain it to any 4 year old in about 5 minutes using basic manipulatives (money works VERY well.) Then again, 4 year olds are generally far more intelligent than what comes out of most colleges of education these days.

Amber says

if i’m bad at math and get 545 and 500 is the reasonable answer then i’m going to assume i’m correct even if i am 100 off. and yes i know you carry the one or any number bc of place value.

Tab says

Using the “one’s crap”, I was able to calculate the answer significantly faster and without a calculator. Imagine that. I agree with Beth, multiple step math problems, where you take the scenic route to get an answer, is not age appropriate for third grade kids. Also in this time is money world, no employer is going to tolerate someone taking 15 minutes to do a few seconds worth of work.

Taz Osgood says

no offense, but this is how i do math in my head. when i see 34+56 i can immediately get the answer. but having to show the work for higher problems, especially later on, made me stop doing it. i’m not gonna take a half a page to get to an answer when i already know what it is, and that’s what it gets to in high school. what they’re saying is let the kid do it their way, whether it’s in their head or not, and they’ll continue improving. but when you give busy work, they’re going to just not do the work eventually. i know i didn’t. and i know my grammar ain’t all that good, but this should still make sense.

Jane says

…and I thought Math Superstars was a challenge. It sounds as though Common Core lacks Common Sense, so at least we’ll raise children who won’t scratch their head at the way government operates…and they’ll be using the same math. Sure glad our kids are in college.

J. Knight says

I assure you I am no fan of Common Core. Having said that, let me give my take. I worked in engineering for over 25 years and the taught 5th grade math for another 16. While in engineering I had the occasion to estimate many jobs. Later, while teaching, I stressed the importance of being able to estimate sums, differences, and products. My reasoning was that in this age of technology ( eg, calculators) a “target answer” was extremely helpful as one couldn’t say for sure if he/she pressed the correct calculator keys! Anyway, I informed the students that a front end estimated answer was not the most desirable as it tended to always be low. Rounding is much better. In fact, in my previous work, I combined both methods and got really close and it still was fast. In the referenced problem: 354 + 291 the child correctly used front end estimation arriving at a very low estimate of 300 + 200 = 500 — a 145 difference from the calculated answer. If one rounded, the estimate would be 400 + 300 = 700 — an only 55 difference from the calculated answer. if one combined the two and then averaged them (easy to do mentally) one would have 500 + 700 = 1200. Dividing by 2 to obtain an average would yield 600 — an only 45 difference. The point? Front end estimation should be learned as a strategy but not encouraged to use as the results tend to be not very reasonable. Stress rounding for a more reasonable estimate. A problem with Common Core is that the teacher must do some reasoning on their part and many just won’t or can’t. Notice this is just one reason; there are many. (Just sayin’)

Jessie Prince says

While I agree that most 3rd graders wouldn’t go as in depth with their thinking as we adults have on these problems. I can tell you that my current 4th graders JUST worked with both rounding and FEE (front end estimation). They understand it WAY better than we do as adults because their minds are WAY more adaptable if we let them be. My 4th graders know that we use estimation and rounding at DIFFERENT times! We know that rounding the usual way is a better and more accurate representation BUT we also know that when I need to QUICKLY figure out if my answer is correct, FEE is much faster. if we were working with the problem: There are 194 students in one school and another school as 321 students, how many students are there altogether? We would find the CORRECT answer 515. then we would use FEE to estimate to see if our answer is correct. 100+300 (you keep the leading digit and the rest turn to zeros) well that tells me 400. My 4th graders know that because we are rounding down (always down with FEE) that our estimate will be less than the actual answer. and they also know that it if we round down by a lot (like with the 194) that our answers might be pretty far away. all it FEE is supposed to do is to let our students say well i got 892 and my estimate is only 400, i must have done something wrong! it is just a quick check not a totally different thing to do!

Kimberly Griffith says

This is just awful! We are active duty military and are living in NJ and this is the first year it was fully implemented. We are now pulling my daughter out of 1st grade and homeschooling her because of it. This is ridiculous and is dumbing down our kids. I started her on Professor B math and its amazing!!!!!! It is basically “unschooling” her and teaching her Math the right way. I highly recommend it!

bob says

I understand the comments and have gone through this with my son in the past. But I also understand the point they are trying to make. One should know what a “reasonable” answer would be. In other words know “that can’t be right” when they make a mistake. For example the cashier that tried to give me $30 + in change when I only gave her a twenty in the first place – she entered in the register that I gave her $50 instead of $20 so the register said I was owed more. She should have realized something wasn’t right. Of course the example given wasn’t that hard, so why not just teach them to add correctly. But with so many using a calculator it is nice to have some concept of what the answer should be so if you made a mistake entering the numbers you know the answer you got doesn’t seem correct. Trust me as a professor I have adults giving me answers that common sense should tell them there is no way that could be the answer.

Kira says

My daughter is in 2nd grade and this is the first time, I’m hearing about this. I agree with you though, the concept doesn’t make sense and is realistic.

Scott Brandt says

My wife and I had similar experiences at our old childrens’ school. They had so many convoluted ways to try to “teach” the students math that we could not understand. We could get the math correct, but the additional parts that apparently were there to help kids understand made no sense to us. Of course, the right answer was not good enough you needed to get something that had nothing to do with the math right, too. Things that were never taught to 2 college grads, one an MBA.

Douglas J. Bender says

Using the pattern of the example, the following would be considered correct:

Find 399 + 299.

399 + 299 = 698.

300 + 200 = 500.

The estimated sum is 500.

The answer, 698, is reasonable.

698 is almost 700. 700 is 40% more than 500. From this perspective, the answer, 698 is NOT “reasonable”. (Of course, the term, “reasonable”, was not defined in the Example.)

Or what if there are more than just 3-digit numbers being used? Or two numbers of differing numbers of digits? For example, how would Common Core handle something like, “12,749 + 421”? Or “18,783 + 39,446”? Or even “8423 + 581”?

Jacob says

12,749 + 421 = 13,100

18,783 + 39,446 = 57,000

8423 + 581 = 8900

Michael Paul Goldenberg says

No, it’s not a matter of what is correct if by that word you mean “exact.” But when has the word “estimate” EVER meant the same thing as “exact”? On what planet, in what language?

Shell says

My son’s third grade teacher taught the kids that they could do subtraction problems starting from the left and going to the right(and yes, this is how he teaches it, not my son being confused). Or starting wherever they want and then if they need to borrow, they can do it from the answer, instead of the traditional way. It is the stupidest thing I’ve ever heard of. WHY not just teach them right to left? It’s how they’ll do it for the rest of their lives. I have a big list of questions for our conference this week.

trisha haas says

WHAT? LEFT TO RIGHT?

Heide says

Trisha… What is the math curriculum your child is using and who is the publisher?

Anna Webb says

My kids were taught that as well. Subtract any direction you want! STUPID! No more public/government school for us.

Michael Paul Goldenberg says

I have done subtraction from both directions. I know mathematicians who do so as well. It works and it’s trivially easy to show that it is mathematically sound. I’ve also seen children come up with that idea on their own. Oh, you didn’t learn it that way? Well, “no more government schools for” YOU! You do have a legal right to make your children as narrow-minded, dense, and ultimately ignorant as yourselves. That’s part of the glory of a democratic society. Enjoy the dumbth and whatever you do, DON’T LEARN ANYTHING NEW!!!

Stina says

Okay, for all those defending this method… how does it help kids determine a result is reasonable if the margin of error is greater than the place value rounded (in this case more than 100)?

500 is not only not the nearest hundred, it is 145 away from the answer… a kid looking at 645 who would expect the boundary numbers to be 600 and 700, would be bothered by their math–expect an error, second guess things–if they thought it was supposed to near be 500. If you aren’t going to round to the closest something how can it be at all helpful in the second step of evaluating the reasonableness of a number? Even using the ‘front end’ mentality won’t the kid be expecting 645 to be near 600 rather than 500?

My big questions: a) How is this helping kids that are struggling with math become more able to understand and perform?, b) Is it just confusing kids who were previously fluent in math until they too think it is too hard?, and c) Are we only encouraging further dependence on calculators?

Jeff Porter says

Math is math right ? It would appear Al Gore has been teaching science like this for years , ” it doesn’t matter that their isn’t global warming , only that you care about the earth with your heart . “

Angela says

Stina, first of all I want to say that this new Math is ignorant. I was not top of my class, nor was I at the bottom of my class. I graduated with almost 500 seniors. But, in my elementary career I was very good at math. Recently, my fourth grader had a tonsillectomy and missed a week and a half of school. When I picked up her make-up work from the teacher, she tried to go over some of her math with me. I told the teacher if I had any questions I would call her. She said not to bother, because without looking at it, she couldn’t help me over the phone. Their lies the problem. Most of our teachers didn’t learn through common core, in fact, none of them did. My mom is a retired 4th grade teacher. I called her, no help. She was more confused than me and my child. When I told my daughter to just work the problem, she was fine with that. She could work the problem, and got the correct answer. I’m not sure what this new math is trying to achieve, but I totally agree, it is dumbing our kids down. To answer your questions, yes, yes and yes! Frustrating!

Michael Paul Goldenberg says

For a couple of decades, I tried to figure out how to dumb kids up. I couldn’t come up with anything good, so I and my co-conspirator mathematics educators agreed that dumbing kids down was the best we could do. 🙁

Tim says

IMO, the challenge is NOT to teach kids how to think. They do that every day. Just look at them with their cell phones, video game and computers. The real challenge to all of us as parents and educators is to teach them to REFOCUS the energy elsewhere.

Beth says

The question is what do you mean by think? Some kids certainly do think in complex, analytical ways with their video games etc. But a part of what I want my kids to know is how to adapt that thinking to different scenarios. And I surely want them to know more than a kid who plays Angry Birds and watches TV all day, about analytical thinking. Kids certainly think. But some think in more sophisticated ways than others, and some are more adaptable. So I would conclude that it’s important to teach kids to improve their thinking skills.

Sheri says

Of course, one step an educated parent might take is to do some research into the background and purpose of what is being taught. I did some checking, and FEE (front end estimation) has been a strategy recognized by educators since at least 1986. Part of the rationalization is that the leftmost digit in a number is going to be the most significant in many real world situations. I spent hideous numbers of hours when I gather information for my son’s income taxes (he is self-employed and lousy at keeping records) and my own (I have income from a variety of arcane sources with equally arcane deductible expenditures, and our tax preparer is a maniac for precision). On the other hand, if I am doing rough budgeting to prepare for the humongous heating bills my old house racks up in the winter, I don’t have to be so particular. For information about FEE, try this link: http://dimacs.rutgers.edu/nj_math_coalition/framework/ch10/ch10_03-04.html. It might be helpful to try to reinforce to your kiddo that numbers are useful in lots of ways, many of which don’t require precision–and in many cases precision is actually misleading (because people don’t account for loss of significance as the precision increases–precise and accurate are NOT the same thing).

Stina says

To me, it seems less about the FEE existing or being taught as a strategy period and more about how it was used and what we’re teaching kids about what is “reasonable.” Teaching a child that a margin of error of 20, 200, or 2000 (depending on place value in question) or less is “reasonable” is much more of the issue/problem than FEE itself. This use of front end estimation to determine if the answer is reasonable is prime to create nightmare situations with wrong answers being validated and correct answers being second guessed… why? Not to improve math skill, nor to improve understanding but to check off a list that one of the techniques under 3.OA.8 (using FEE to check for reasonableness) was taught and collect pieces for the portfolio as proof.

Approaching things differently is fine, good even when it actually helps a struggling child overcome a sticking point and propels him into success… but while this is a poor example of using FEE, it was an excellent example of using the wrong tool for the job at hand. Had the goal been to teach checking there are a great many ways that could be achieved… had the goal been to use mental math to check there are still stronger methods (estimation or compensation for example–compensation even allows for precise answers quickly and mentally in add’n, sub’n, mult’n, and div’n) that would cause less confusion within the students about what is reasonable and held the “reasonable answer” standard in a better light… but sadly, neither the child nor the child’s understanding or fluency is particularly a factor of importance in the common core equation. *This* is the issue, not FEE or any specific strategy for that matter… ability to perform math functions correctly should be the end goal of math education. Using new strategies to facilitate reaching a correct answer is great, but the situation in question in this post was the use of this strategy make a child second guess a correct answer because of its questionable reasonableness given the front end estimate… which is truly a foreseeable issue (as is the flip side of feeling more justified in the reasonableness of incorrect answers) especially for a seasoned teacher, hence the problem.

As for the purpose of what is being taught, I guess I’ll just happily be the ‘uneducated’ parent not buying into the PR spin of the usefulness of bad logic being taught in math. I agree precision is not always necessary, but that doesn’t make *this* application a good idea.

Sheri says

Well, what you provided was a problem without context, so it’s hard to tell whether the material was being taught using good methods or not. In terms of math concepts, there are myriad situations in which order of magnitude is much more important than whether the leading digit is 2 or 5 or 9 or whatever. I do have some misgivings about focusing on estimation techniques in grades 3-4, since estimation involves “meta” concepts being the concrete basics which do require a great deal of drill and practice, and in that regard I agree that the teaching itself could make for confusion–as opposed to the content per se.

Sheri says

I just took a quick look at the common core standards for grade 3 math. Keep in mind, standards are not the same as teaching methods. For example, the standards for grade 3 include knowing all products of one digit numbers and being able to add any numbers that are under 1000. There’s actually nothing in the common core standards about teaching front end estimation. I looked at the implementation for my state and didn’t see anything there either. Which means this has more to do with thing like textbook selection and curricula in your local district (or, depending on how your state works) at the state level–not with common core. Your state education department website most likely has your state’s interpretation of common core.

steve says

Do you think we would have landed on the moon using this nonsense. Best to go back to the basics.

Chuck XProf says

Of course we landed on the moon using such methods. The scientists and engineers involved were quite competent, and knew very well that as they did their complex, precise calculations, they needed to check to be sure that their answer was in the right ballpark. They would even do similar estimates before bothering with the full-blown calculations–these were called “back-of-the-envelope” calculations, since they might actually be tossed off on whatever piece of paper was handy.

Sheri says

Although we did lose a Mars landing vehicle due to someone forgetting to convert English measurements to metric.

We could go back to the basics–like the Indiana state legislature, which a century ago tried to legislate the value of pi as 3.

Michael Paul Goldenberg says

I can readily see support for pi = 3 from the Teabillies. Don’t the communists use the mathematical definition? If so, it must be un-American. See how simple math can be when you use politics!

Paul says

My local superintendent said that it seems that Common Core Standards are being used as an excuse by some schools to spend money on new text books that come with a “Common Core” seal approval. He said in some cases they are the same old text book with a new cover! If you don’t like what is being taught, I would go after the school’s choice of text books first, not Common Core Standards, which are pretty open-ended.

Leigh says

A message to the teachers who are defending this method: you have increased my respect for your profession exponentially. When I first saw the example, my knee-jerk reaction was similar to many others’. I thought, “How stupid is that, how can that possibly be a real example?” But then I did something crazy: I read your responses with an OPEN MIND. And you convinced me. This is a useful way to help kids learn how to think, to determine at a glance whether something makes sense. In a day and age where I carry a calculator with me at all times (on my phone), this is nearly as important a skill as being able to add numbers together with precision. Thank you for teaching me something today. As a homeschooling mom, I’m often too quick to make judgmental assumptions about schoolteachers. I walk away from this conversation with a lot more appreciation than I came with.

Michael Paul Goldenberg says

Congratulations, Leigh: you’ve restored my faith in the possibility that not ALL Americans are complete dunderheads when it comes to mathematics education. I was starting to feel like I’d woken up in one of those bizarre countries Gulliver visited in his travels. Jonathan Swift would have a field day reading most of the closed-minded, intentionally dense comments here.

Amy Magnus says

As an instructor of physics, I L-O-V-E that we are teaching our students how to analyze their results.

To check your work, you might be tempted to round 354 and 291 up and say “Yeah, 700 is close to 645 so 645 is a reasonable answer.” Here’s the thing though…. The sum of two numbers on in the 200s and one in the 300s is going to be in the 500s or 600s, never in the 700s.

This method generalizes well. Let’s add the numbers 587+129+399 and check our results as we go.

First, 500+100+300=900, so I can conclude that the solution is in the 900s, 1000s, or 1100s. I know this because I am adding three numbers. By inspection the tens and ones column, I can assume most probably in the low 1100s or perhaps the high 1000s.

Next, 80+20+90=190. Ok, the answer is definitely low 1100s then because the ones column adds to more than 10.

Finally, 7+9+9=25.

Altogether, 900+190+25=1115 so 1115 is my answer and, from the first step, a reasonable one.

Note, I add the “estimates” of each column value to get to the correct solution. I could have rounded 587 and 399 up, yes, but then I’d have to subtract somewhere.

The cool thing is that I knew my approximate solution (low 1100s) by simply adding the hundreds column and glancing at the remaining columns. I could assume most probably low 1100s because 587 is in the high 500s, 129 is in the low 100s, and 399 is almost 400.

I use this technique in the grocery store when I have to keep my bill under say the $10 bill that I am carrying. I can keep track in my head the number of items I can pick up before I max out.

Will Seaton says

Thank you very much for explaining Front-end Estimation. My son is in the third grade. When he first brought this homework home, I had to look it up on the internet. I thought it was all pretty pointless until I read your awesomely worded response. Thanks also for being a physics instructor. Physics is my favorite course of study.

Amy Magnus says

You’re welcome. I’m glad it was helpful.

Barbie says

OR, you could just add the whole damn thing together like any normal person would do and TADA! you have the answer!!

Why do we teach to round up & now we are teaching to round down? AND, why are we adding extra steps to EVERYTHING? I thought in this day & age (and most days & ages, including 30 years ago when I was in school), the biggest thing was to simplify? Make less work for ourselves? So now we are adding all these extra steps? Lets add the first columns together & then the second column & then the third column… OR, Round like we always do. 587 = 600, 129 = 100, 399 = 400. Oh look, 1100!! In ten seconds flat we got that answer!

Amy Magnus says

The technique I describe is a way to add the numbers all together. I’m just working from left to right. It’s a more natural way to go…like the way we read words…and the way that the digits are arranged from most significant digit to least significant digit.

Michael Paul Goldenberg says

Ann, you’ve done a fine job of explaining front-end estimation. You’ve even reached a couple of people. But those who are arguing that this must be ridiculous because: a) it’s not how they were taught estimation (no kidding, folks: it’s called “learning ANOTHER way – quicker, easier, not intended to be the SAME as the way you learned, which hasn’t been thrown out, just given a ‘partner'”); and b) you can’t buy goods with an estimated amount – are being pointedly stubborn and/or dense.

Calling this “dumbing down” is indicative of narrow-mindedness. There’s nothing shocking in noting how pervasive that mind set is in America, but it’s nonetheless sad and disappointing. And very common when it comes to mathematics education.

For those who’ve missed it: front-end estimation has been around a long time. It wasn’t commonly taught 50 years ago, at least not in elementary school, but then, neither were a lot of things that kids learn today. Civilization didn’t grind to a halt in the ’30s, and fortunately, my parents didn’t decry things they taught me and my brothers in the ’50s & ’60s. But somehow, recent generations of parents seem more conservative than my own GRANDparents. Anything they don’t recognize from their children’s homework in math must be “stupid,” “dumbing down,” etc., not merely “another way.” Could it be that many of these folks are afraid to look stupid in front of their own children? Or are they simply unwilling to see anything new?

Michael Paul Goldenberg says

Ooops, sorry. That should be “Amy,” not “Ann.”

Queen of the Pen says

The day I can walk into a grocery store, find an item that’s $5.49, walk up to the cashier, thrown down a $5 bill and tell them that’s all I’m going to pay because although $5.49 is reasonable, the estimated sum is $5 is the day I’ll have to find another planet to live on. For a physics instructor, you have shown why it’s best to homeschool our children.

There are many ways to teach our children how to think analytically without dumbing them down into mindless mush-heads. By the way, at which university or college do you teach? I want to ensure I let my readers, radio show listeners, family, friends, acquaintances, and foes know so they can avoid that institution like the plague.

Chuck XProf says

Working with your example, I guess I’d love to have you come into a store that I owned. You could select an item for $2.79 and another for $1.19. I could then crunch the numbers, badly, and tell you that, withy 7% sales tax, you owned $42.59. You would, apparently, pay, that without question, since you violently object to comparing this outrageous price to the $3 you would estimate by rounding down, or the $4 you would estimate by rounding off, or even the $5 you would estimate by rounding up. By all appearneces, you would literally pull your children out of school, and urge others to d the same, to prevent them from learning to think this sensibly, and to avoid being taken advantage of.

Adding two items under $5 is simple enough that we can all tell that the answer cannot be over $40. It’s simple enough to use to teach 3rd-graders. But it doesn’t have to get much more complicated for adults to get confused. If you drove a normal automobile from Atlanta to San Diego and back, what would you pay for fuel? $75? $2500? Something else? Many readers could get an estimate in their heads–a starting point, that you can use to check your work later. If you calculate your fuel costs as $14.25, or as $14,250, your answer may be precise, with no roundoff error, but your answer is also wildy wrong. Being able to do a reality check is an important skill, and a brief introduction to it in 3rd grade will help them build that skill later.

Of course, it seems likely that you just missed the point of using the estimation to check the exact calculuation, and not as a check on it. I hope that’s the mistake that you were making.

Chuck XProf says

Last paragraph should read: “Of course, it seems likely that you just missed the point of using the estimation to check the exact calculuation, and not as a REPLACEMENT FOR THE CALCULATION. I hope that’s the mistake that you were making.”

Proofreading is another important way to check one’s work, that should not be neglected… 😛

Michael Paul Goldenberg says

;^) Well, Chuck, it’s easy to miss things when your blood is boiling. And some of the absolutely closed-mind comments here, the repeated insistence that estimation is “dumbing down” and similar idiocy, has my blood pressure rising precipitously, as well as my temperature.

I’m sure anyone who has taught math or science knows how bloody difficult it is to get students to estimate (as well as to check their work). And so much problem solving (not doing donkey arithmetic, but actually solving problems) requires being able to make seat-of-the-pants estimates so as to avoid going down blind alleys needlessly. I know for certain that every donkey-headed person who has decried estimation here in fact uses it in the real world and doesn’t misunderstand the issue. But this is not about reason: it’s about politics. Folks’ political dander has been raised by math education issues repeatedly in the last couple of decades, generally in ways quite similar to what we’re seeing here. And when that happens, even the best explanations, like those you and Amy have offered, become useless. You can lead a fanatic to reason, but you can’t make him (or her) think.

Amy Magnus says

Exactly. The whole point of going from left to right is to understand that, for the shopping example that Chuck XProf gives, the total including tax must be less than $5.35 and enough less that I can pay with my fiver.

First the subtotal must be greater than $3 and less than $5.

$2.79 + $1.19=$3.00+0.80+0.18=$3.98

Now, for the final calculation, I’d use a different approach. I’d use distribution since $4 is so very close to $3.98.

($2.79 + $1.19)*1.07=$3.98*(1+0.07) =3.98+0.28 =$3.98+0.02+0.26=$4.26

Queen of the Pen says

@Chuck and Amy:

Per your examples, I guess a 3rd grader would sincerely understand being that all 3rd graders are mathematical genius from birth? What you two have illustrated is where YOU currently are mathematically and not where a 1st, 2nd, or 3rd grader is or will be during their elementary school days.

I remain steadfast in my opinion (yes, my opinion) that those parents who are concerned about Common Core should homeschool. Also, if you were to communicate your examples to your 1st, 2nd, or 3rd grade child (that’s if you have children), will they sincerely have a ‘reality check’? It’s bad enough the majority of American school children can barely at 2+2 correctly without them being forced to totally give up on academic rigor that is age appropriate.

My suggestion is this: leave your examples for high school and college age students because that’s where your examples fit best. I’ve taught elementary through college and am saddened that some cannot do basic mathematics without a calculator.

By the way, Chuck, I wouldn’t shop at your store because your example asserts that only STUPID people can shop there. :-/

Queen of the Pen says

Correction to paragraph 2. It should read, “. . . It’s bad enough the majority of American school children can barely able to add 2+2 correctly without them being forced to totally give up on academic rigor that is age appropriate.”

Chuck XProf says

Your Majesty,

Our examples are given for adults, in an effort to explain to them why someone would want to use an estimate to check the exact calculation. If I were dropped in front of a 3rd-grade class doing sums, then of course I would speak very differently. I’d be saying things like, “Now, about how big should this be?” “Oops, that looks like it’s wrong. Let’s check!” Given the choice, I would never say “front-end estimation” to third-graders, it just makes it sound like it must be difficult and makes the whole thing harder than it really is. Really, if a child can laugh at a cartoon of an elephant riding a child’s tricycle, then that child gets the ideo of something being is truly the wrong size. That’s all the conceptual understanding they need before they BEGIN to grasp the way that this works with numbers, too.

If a child turned in an assignment to you, with 53 + 22 equalling 750, would you just mark it wrong or explain it? If they asked you why it was wrong, what would you say? If several students kept making such mistakes, wouldn’t you try to tell the class how to fix this?

We’ve always taught children to check whether their answers made sense. In the bad old days, this might have involved a stool in the corner and dunce’s cap for those who made mistakes. Nowadays, they are making this systematic, which is good. What’s not so good is giving it a clunky name like “front-end estimation,” that confuses everyone.

BTW, if I actually ran a store, I’d do everything I could to prevent overcharges, and make every effort refund them if they occurred anyway. Cheating people is bad business as well as bad karma.

Anyone can homeschool, for whatever reason, if they can afford the time. But this is one of many issues that gets a lot of people riled up, and for many of them, they feel a lot better once they find out what”s really going on.

Queen of the Pen says

@Chuck:

I’m not interested in your explaining to adults. I’m interested in the author’s concern that this concept is being taught to our elementary school children. My entire dialogue has been based on that premise. There isn’t a need to ‘educate’ me as I am already educated. I will not lose focus here. If you want to really be helpful, then explain to us adults how you would explain your aforementioned concepts to a 1st, 2nd, or 3rd grader? Thanks in advance.

Chuck XProf says

I’d be happy to toss around ideas about how to teach this, but since I’m not an elementary school teacher, it would only be my impressions. I’ve already said some general things: keep it brief (a few days at most), keep it simple, don’t use unnecessarily technical names. And don’t introduce this method right after doing rounding; that’s confusing.

But, the biggest frustrations I’ve seen seem to come from those who see no sense in the method at any level, because they are trying to use it for an estimate of a number, rather than as a check on a calculation. This is where I feel I can be the most useful, since I use that general type of estimate a lot, and I have seen many students who didn’t know how to do any sort of reality check. Their answers were off by factors of 10, 100, or 1000 or more.

And yes, Ms. Queen of the Pen, you did come across as one of the people who didn’t get the point of the method, given your grocery shopping example. My aplogies if that was wrong. But, the mere fact that we are talking about how to teach the method, and at what level, is, to me, a tremendous improvement over dismissing the method entirely.

Queen of the Pen says

@Chuck:

Thank you. Although I already knew you had answered my question in your original post, I’m confident I understand better. You are not an elementary school teacher. Therefore, your continual hammering of your adult mathematical concepts are truly irrelevant for this author’s article. She was addressing her concerns about Common Core standards being taught to her 3rd grader. As another person noted, what has been illustrated here is not MATH. It is a concept.

Anyway, my original response was from an elementary point of view. That’s why I chose to use such a ‘small’ dollar amount so that a 3rd grader could understand should he or she be presented with such a situation. Again, I’m focused our elementary school children and not adults, unless they have not learned basic mathematics.

Chris Miller says

The problem is, which is closer, 700 or 500 to 645? That is terrible to teach such poor precision in physics, let alone basic math. Saying that 145 off is better than 55 off destroys the value of math and the level of precision science (not even advanced science) requires. Your examples make a bit more sense than the one given in the original post, but add needless steps for reduction and increase cycle times to just add the numbers together. While you are trying to make math fit English rules (left to right vs right to left), the fact is that you still ultimately are processing the information left to right. I’m still adding the ones digit to the tens digit to the hundreds, ad infinitum.

Chuck XProf provides an example that fails the precision test. If l have $4 it is still reasonable to assume that I have enough money. Based on the method suggestion understanding that I have $4 is enough to make that purchase in which solid math disproves. The example becomes more apparent when it is $2.79 + $1.79.

This does children a disservice when they are learning advanced math later as their foundation has been compromised.

Chuck XProf says

Estimating that $4 is enough money is a misuse of the method. What it is supposed to do is to let you add $2.79 and $1.79 and get $4.58, then note that this is fairly close to $4, and see that the answer is reasonable. If you accidentally added $2.79 to $179 (easy enough to do with a calculator), you’d get $181.79, which is nowhere near $4. This example is so easy that you wouldn’t need the estimate to check it, but if you add a couple more numbers in, or just drop a digit (entering 104.50 as 14.50 for example) the errors soon get harder to see without the estimate. In teaching this, it would be important to give a few examples of why you DON’T use this method to as an estimate for adding prices, but only as a check on the answer you get when you to the calculation.

Sheri says

Some mathematical musings. . . I always wanted to tell my remedial algebra students (college kids who couldn’t pass the screening test to take college math) that there really is no such thing as subtraction (or division, for than matter) in algebra–only adding (or multiplying) the inverse. Conceptually that’s a much simpler way to go and eliminates all those idiotic conditions elementary algebra textbooks tend to provide for adding and subtracting positive and negative values. I think this approach should be introduced early in the k-12 curriculum. But I know that would send some people into a tailspin, just as this “front-end” estimation seems to do now. And I can’t imagine the parental horror that would ensue with k-12 kids. Here’s some more goodies for you–it is often useful in math to use these sort of pseudo number we call Big Oh and Little oh. In an equation, they simply mean something way bigger (or smaller) than any quantity that might be used in a calculation.

Joe White says

I can’t tell you how much I agree with your statements. I was one of those remedial math students, not because I was incapable of understanding higher math, but because I was bored and frustrated. Every year math was the same thing. We never seemed to learn anything new. Consequently I refused to do the work, received low grades, and was put in the remedial classes. Now years later, having taught myself algebra, linear algebra, trigonometry, calculus, and 6 computer languages I realize that if they had taught algebra in grade school instead of repeating the same old basic arithmetic day after day, I would have gone on to college instead of having to teach myself. I could possibly have had a career in theoretical physics, a subject I find to be fascinating, and I wouldn’t feel completely intellectually wasted because I am stuck in a dead end job selling cell phones.

Sheri says

Joe, thanks for your comments. I graduated high school in 1972, when help wanted ads still were divided up between men and women, and it took me many years to discover my love for math. And, given my age by then and life events, the “might have been” was also not what was to be. I hope you can find some way to use your gifts and ability to learn where they are recognized.

Joe White says

Actually this is being taken way out of context. To explain the background of the lessen being taught here put yourself in the position of the teacher. Little johnny brings in his homework, There is a math problem 354+291. Little Johnny makes a mistake in his math, and his answer is 147 (yes this kind of thing actually happens) The teacher looks at Johnny and says “How can you even think that could be right? 147 is less than both of the numbers before you added them?” Little Johnny looks at his teacher and says “I dunno.” This is what teachers face on a daily basis. This lesson is not teaching a new method of math, it is teaching kids to have an expectation before doing the math and to be able to compare their answer to those expectations. It is simply trying to get the kids to think, only for a second, about the problem outside of the procedure. It is trying to teach common sense.

Kat says

There is more to teaching math than just numbers, algorithms etc. Part of it is teaching you how to think – this core method seems to encourage mental math. I know that when I add large numbers in my head I round down or up – so for example 243+ 139 – for me I add 240+140 = 380, then I add 3 and take away 1 equaling 382. We all learn and think differently people, there is no right or wrong way. At the end of the day as teachers we hope our students develop an understanding of how they learn. I rememeber being taught certain ways of dng things and I hated it, I was uncomfortable. Sure there was some frustration and tears, and my parents probably were all worried too. Then over time I was taught a different way and that worked for me. Through this I learned about myself as a learner. So worry not parents, your kids will be ok.

Bridgette says

Thank you. Yes it’s different and FEE isn’t how we were taught, but we also didn’t get to use calculators in 3rd grade. It’s one technique for kids to learn to check their work. Please quit taking it out on the teachers who are busting tail to teach what used to be Jr High material to much lower grades. CCSS pushed nearly everything down a grade at least. It will be a learning curve for a couple years but we will be better for it in the end.

Me says

How can you all not look at this and get it? It is FRONT END estimation. That means you take the number in the ones place and determine whether it should be rounded up or down. Estimation is an important mathematical skill. Just because it is different from the way you were taught doesn’t make it wrong. Our country is trying to teach math more like it is taught in Asian countries so that we will have adults that can keep up in a global marketplace.

Jenny says

I couldn’t tell you what this is, I failed math every year I was in high school. They’re teaching stuff like this to MY kid now too. You know, getting all sophisticated and weird… it just makes me go (o.O) This stuff isn’t what I learned in school. Maybe they’re trying to teach american kids the way that the japanese do? xD Calculus in Kindergarten!!

Jenny says

Correct that… failed constantly after they started teaching division!

Sheri says

Did anyone notice that the person who wrote this wrote “for Chris and I” instead of “for Chris and me”?

trisha haas says

That is the correct form.

I is the first person singular subject pronoun, which means that it refers to the person performing the action of a verb.

Me is an object pronoun, which means that it refers to the person that the action of a verb is being done to, or to which a preposition refers.

The easy way to decide whether to use I or me: try out the sentence with just I or me (or if you need a plural, we or us – “we” is equivalent to “I” and “us” is equivalent to “me.”).

In this case, the sentence: “Every day it’s a massive struggle for Chris and me, him with a Masters Degree and myself with a Bachelors, to teach 3rd grade homework to our daughter” would be “Every day it’s a massive struggle for Chris, him with a Masters Degree and myself with a Bachelors, to teach 3rd grade homework to our daughter” or “”Every day it’s a massive struggle for me, him with a Masters Degree and myself with a Bachelors, to teach 3rd grade homework to our daughter” therefore the correct grammar is “and me” and not “and I”.

The article does say “for Chris and me”, however it was originally saved as “Chris and I” on the sentence when I first published 3 days ago. It was corrected within the hour of publication. The reason you see it on the shares is due to how Facebook pulls a cached form.

If publishing a grammar rule is the worst thing that happens to me all week, I am doing OK in this world.

Sheri says

And so, even people who know the rules–of grammar or addition–make careless mistakes sometimes. This is why it is good to have simple strategies for checking one’s work. . . like front-end multiplication or grammar-check.

trisha haas says

The issue for me (and I replied in another comment, so I am going to cut and paste that here) is that its not checking. Its causing confusion. See below:

——————–

As an update to this blog post, I wanted to say that they sent home another work sheet of “front end estimation.”

It is sitting on my desk.

It says 260 + 350 =

_______ + ________ =

The estimated sum is ___________.

Is the answer reasonable? ___________

My daughter has answered:

260 + 350 = 610

___200____ + _300_______ = 500

The estimated sum is _____500______.

Is the answer reasonable? ____ no_______

I can see where she wrote yes first and then erased it and wrote no. She did this exercise in class.

However the answer based on the assignment lesson would technically be yes. The front end estimation is supposed to show her that her answer of 610 is reasonable based on this method of “checking”. This is what they taught her last week and the article stemmed from.

All it really did was make her second guess if she got it right.

*head bang*

calvin pauley says

The grammar isn’t the issue. How can stem work when the kids can’t do basic math in high school? But on the grammar thing I have heard that schools are doing away with spelling and such. Then no one has to worry about grammar or speelcheck. Get it?

Ali says

I did notice because people rarely get this right! Good job, Tricia.

trisha haas says

I have had about 25 people come in and try to tell me which way is wrong or right the past few days. Seems like no one knows.

🙂

I had an editor look at it just to check and she said it is correct the way it’s currently published.

Horrified says

The horror! Learning math a different way than you were taught! I have fainted from shock.

Heather says

THIS is NOT math.

Homeschoolmom says

I agree with you this is not math.

Queen of the Pen says

Thank you, Heather! This has absolutely NOTHING to do with math. The proponents have admitted it is about ‘thinking through the process’ and it has nothing to do with adding, substracting, dividing, or multiplying. These are called ‘word problems’ which I learned in algebra. They wonder why public schools are failing? Geesh!

Infidel!! says

In what Universe did you learn Mathematics? It MUST be some parallel universe, because in this universe, you round 291 UP to 300….because it is MUCH CLOSER to 300 than it could ever be to 200.

Further, Common Core is NOT MATH. Learning how to do math differently from what we were originally taught, would me that we would come up with the same answer….not a night and day difference. Common Core is FAR FROM Common Sense!! Apparently, you lack Common Sense to do Mathematics in this universe…therefore, you are free to leave it, and pursue Common Core Math in a parallel universe!!

buddyglass says

I learned math in this universe. One thing I recall is that there are multiple methods of rounding, one of which is being employed here:

http://en.wikipedia.org/wiki/Rounding#Rounding_to_integer

Timothy53 says

It’s not about learning/teaching math in a way different from how she was taught. It’s about math being taught wrong. The given example is not much different from what I was taught 50+ years ago. Round the addends and come up with an estimate. But in this case the 291 is rounded DOWN to 200. Why? And 354 is rounded down to 300. Why? If these two were rounded up as has been taught since at least 1961, to 300 and 350 respectively, the estimated answer would have been 650. Way closer to the correct answer, 645, than 500 is.

It is simply wrong. Not different. WRONG. And that, Horrified, is the beauty of math. Answers are right or wrong. There is no ambiguity.

buddyglass says

Explain to me why this method of estimation is unequivocally “wrong”. You seem to prefer rounding to the nearest increment of 50, which gives an answer of 650, which is indeed a better estimate than 500.

You know, I prefer rounding to the nearest even number before adding, breaking ties by rounding down. That gives me 290 and 354, which sum to 644. That’s even closer than 650!!! [sarcasm]Clearly your method of rounding to the nearest increment of 50 is WRONG.[/sarcasm]

Bruce McIntyre says

There is nothing “reasonable” about the answer… even if you round off the numbers (both up) you end up with an estimate that is a LOT closer. Nothing about the reference makes ANY sense? In what bizzaro world is 200 an estimate for 291??? Anywhere? I would NEVER come up with that answer, and if anyone that worked for me came up with that answer, they would be out the door instantly.

Lisa says

…unless you’re a contestant on the Price Is Right.

And to address another comment: When shopping, I always round to the nearest dollar amount, up or down, according to the cents (.50 and above, round up: $4.51 is $5.00; .49 and below, round down: $4.38 is $4.00). If I walk into the store with $100, and I know that the sales tax is 7%, I know I can’t spend more than $93 and stay within my budget, but I may want to be careful and keep it under $90 to be on the safe side in case I want a pack of mints at the counter. This is useful estimation, common sense and math working together. Maybe I could have purchased one more item and stayed within budget, but I’ve been taught that budgeting means you set yourself a limit and spend no more.

How this applies correctly to physics, I assume, has something to do with statistics. However, I believe it would be more beneficial for students to just learn how to do the math right to left and rounding up or down in the way I’ve described. Physics and statistics aren’t really part of a child’s common sense vocabulary, but whether they have enough money to purchase two toys with their piggy bank money is.

Randy says

You call what is shown above math? Stay fainted; you’re pretty useless anyway.

Jill says

So I’ve read many comments here agreed with some, disagreed with some and ignored many. If 500 is reasonable, is 400 reasonable? Is 1000 reasonable? What do you tell the student if he is trying to get the concept and he asks where is the line drawn on what is “unreasonable?” What good is teaching a concept that only catches big mistakes? Most children should be able to just look at the numbers added and be able to say that 1000 or even 800 is unreasonable. Is the problem only reasonable because front-end estimating was lower than the correct answer? :-/

Jesse says

The problem is in two parts. 1) find the sum. which they did with 645. then 2) use front end estimation to be sure it is reasonable. Which they did. They are teaching the concept of front end estimation AND doing more math practice. Now we can question rounding 291 to 200; but, the fact is even if your estimate is 500, 645 is reasonable. It’s a concept as adults we learned and I remember thinking it was stupid. But we do in the grocery store every day. I count the estimates of the prices and am like it’ll be around 50 bucks. Sometimes its 42 and some times its 58; but it’s never 120.

G says

I think the point is that the rounding was done wrong for 291. When you’re doing your grocery store estimation for something that costs $2.91, do you count it as $2 or $3?

SE Stone says

I’m glad we didn’t have such a Progressive Math when I went to school. I probably wouldn’t have been in Honors Algebra, English, etc. I would have been trying to get the real right math and wondered how my teachers were so much smarter than myself and more than likely developed a complex of some sort and dropped out along the way.

Can parents of children that have moved beyond this proficiency, let’s say by first grade, opt their children out of this backwards program or must they sit through this remedial class and get behind to stay behind with those children that can’t learn as quickly as my child?

A Math Teacher says

This is NOT common core math. This is either an example of a teacher using poor examples to teach his or her student, or it is being used as a counterexample so students learn that there are multiple forms of estimation and it is important to know when to use each type.

The Common Core standards are publicly accessable. Go and read them and you will see that they are not some magical list of how to teach every topic in mathematics or any other content area. They are list of concepts and the thought processes that students are expected to develop. How each of those topics get taught is entrusted to the teacher to interpret and determine how best to develop the thought process in students.

Teaching is not magic. It is an art form. Teachers every day do their best to understand how the brains of the children they are entrusted with are developing and then decide on how to present information so that the children can learn to think in certain ways.

Infidel!! says

I am utterly happy that you do not teach at my son’s school!! Teaching is NOT AN ART FORM!! It is a scientific method of imparting certain facts in a manner that young students can understand. If you try to use art to pass on this knowledge, you will no doubt, make that student more confused later in his/her school career, as the information you pass on will become twisted in their minds.

If you had an ounce of brains, you would be completely against Common Core. Common Core was developed to dumb-down our children, in order to make a mindless generation that will blindly follow everything they are told. Teaching is not meant to be entrusted to a teacher to INTERPRET IT. Teaching is meant to take information, FACTS, and present them to a child so that they understand this is what it is….this is what it is not. Black and White….no grey area. Common Core lends too much license to a teacher to press his or her agenda onto our children….and not teach them what it is they need taught!!

Every child’s brain develops at about the same rate as the next. True, some develop faster/slower than others, and therefore, they are taught in a different manner than the others…however, they are to be taught the same things. Abstract thinking is not for slower children. Just as simplistic thinking is not for faster children. And teachers would do well to teach FACTS, not Artistic Interpretations of Facts.

Michelle says

I am utterly in agreement with your entire post and I felt compelled to tell you so. My daughter is in the fourth grade at a new school. Her last school was not common core. This one is. She was in advanced classes in her old school and can read adult-level books. She is a whiz at math also (unlike me). She CANNOT grasp the math at her new school and is falling behind. I have dyscalculia so I am no help at all. She is extremely detail and fact oriented and just cannot understand WHY she cannot understand. 🙁

Dr Hovatter says

You are correct this is not math it is an attempt to turn all of our children into mindless DEMOCRATS

a Teacher says

“Teaching is not meant to be entrusted to a teacher to INTERPRET IT. Teaching is meant to take information, FACTS, and present them to a child so that they understand this is what it is…this is what it is not.”

WOW. Seriously? I didn’t have much of a problem with you on the post itself — I agree that 500 is not a “reasonable estimate” in my book, nor are the Common Core elements my teaching standard of choice.

HOWEVER, you’ve completely lost me — and offended me — with this statement. If teaching is merely importing facts, what is the purpose of a teacher? Why even bother sending your child to school? Pull your child out, hand her a math book from 1950, or access to a computer and tell her to read the facts. All you want is a robot. You may be the first parent I’ve ever come across who wants your child to be UNengaged and simply receiving the “black and white facts.” What a miserable classroom.

Now I’m not a ‘long time reader’ — to be honest, I had never even heard of you until a friend linked this post — so I’m sure you don’t really give a flip what I think. I am, however a teacher, and I think it’s important to reply to your words in an effort to encourage your READERS (or whoever reads comments) to stop and think. Hating the Common Core is one thing — but to redefine teaching as merely instructing in factual information is quite another. Teaching at it’s heart is about thought. It’s about opening student’s minds to opposing views, the power of questioning, and the ability to reason for themselves (not to merely parrot either me OR their parents.) If we want a truly free society, our children MUST be truly educated — Merely filling them with facts dooms us to failure.

Feel free to ignore me, or not post this comment. I can guarantee I won’t be coming back to this blog.

Dave says

Yeeeessss! What YOU said! Couldn’t have said it better. So tired of hearing Common Core being beaten up on.

Charles Arredondo says

WOW!!! I just have to chime in here So If I got 3 apples and you owe me 4 apples that will give me a peck of apples and I make a apple pie you insist on a slice….. That will be OK but you got to give me $9.95 for it but you estimate to give me $20.00 for it and I’ll take it… So shut the Blank Blank blank blank up and pay me and teach the children readn, writn and rithmetic . And by the way you have no problem making out every word I have said here. Im just gestimating…. !

Charles Arredondo says

BTW … I do hope someone get a laugh out of this post

Heather says

your comment is ‘reasonable’ Charles. 🙂

Marie says

I saw this on fb and was intrigued as my mom and I were just discussing this the other day. She used to fight with my math teachers because I refused to do this worth of phony math when I was a kid. Of course I was the only kid in our class who could look at a math problem and tell you what the correct answer was without adding or subtracting. I could understand it if they wanted the kids to round up rather than down as that does come in handy while shopping. For example you have three items that are 1.49 2.99 and 7.50 round those up to 13 assuming its taxable that extra bit accounts for taxes. I know if I have to teach that garbage I would fight for my son too who is a perfectionist when it comes to anything school related. (Assuming of course he isn’t having a 5yr old melt down.) fight for your daughter to have a real education not that sort of dribble they try to teach. Or at least teach her the proper way to estimate. Always round up. That’s the only way I think that makes sense

AM Reina says

I know its been a long time since I was in grade school but whatever happened to the concept of checking your work. If 354 + 291 = 645, then 645 – 291 = 354. How much simpler can it get!

Jackie says

I never thought I would want to comment on something like this, especially as LON as the discussion has been. But I thought my experience might make sense here,

I graduated from High School in 1968, I hated math, I dropped it in my senior year because they let me. My dad was a math teacher, and used to try out the new “computer programs” for teaching math. That’s when I was in elementary school, in the late fifties. 25 years later I got up my courage to try college. I took the placement test. I flunked math. So I went to “Introduction to College Math” which started with addition, subtraction, multiplication, and division. Now you have to understand, I was a math-hater, 26 years away from ANY math instruction. I finished ALL of the math in THREE WEEKS except for advanced algebra, because all it was teaching me was what I had learned when I was a kid, and it was a refresher, which is what is was SUPPOSED to be! The rest took me the remainder of the semester, because I still hated math. But the kids right out of high school in class with me? They took all semester to learn the first basics, then many of them had to take the class AGAIN, and some went on to THREE semesters of BASIC math. These were not dumb kids, they were doing well in other basic classes. I came to realize after talking with many of them, and doing freshman orientation for 3 years, that these kids had never learned the basics AT ALL! And this was in the 90’s. How much worse is it now? In trying not to leave any child “behind,” we are ensuring that not many children will actually succeed!

My granddaughters are in 3 different schools. The one going into 5th grade has not yet learned basic MULTIPLICATION! The second grader has mastered addition AND basic subtraction. She is almost ready for multiplication. The big difference? Different town school systems! They actually both started in the same town, then changed last year. So far I cannot discover a difference in intelligence. The youngest, who is 3, knows how to add basic numbers, because we have TAUGHT her! My conclusion is, TEACH THE BASICS and leave the “concepts” for when they are READY for “concepts.” In third grade, even though I hated math, I knew how to multiply and divide any basic number. I would have known immediately that the problem stated at the beginning of this LONG discussion was simple! I knew how to round numbers correctly by 4th grade.

Pardon my long rant, but whoever the “government” people who decide these things must think MOST kids are dumb!

Chris says

And yet, the parent and child are stumped enough by this example to make a blog post about it, so perhaps there is something to the Common Core standards. If this was simple for the students, why are the students taking a simple class. Challenge them!

Danielle Dennis says

They’re stumped because it flies in the face of both what we were taught growing up and common sense. It is illogical to round 291 down to 200. When estimating, i think it’s reasonable to want kids to get it within 100 numbers or less. Otherwise, you aren’t estimating, you are guessing.

Alicia says

Jackie I agree with your statement: ” TEACH THE BASICS and leave the “concepts” for when they are READY for “concepts.” ” That is exactly what I was thinking. I too hate math, and beyond the basics I am not qualified to speak. 🙂 I do however believe the problem here is teaching “concepts” before basics. Do we teach kids how to read before they know the alphabet or even before phonics? No, that is ridiculous and would set a child up for failure. I can see there are many ways in Math to arrive at the same or almost the same answer. I believe we need to understand that the issue really is with teaching an uncommon concept for a child at a time when the BASICS are needed first.

Linda Edwards says

I’m truly surprised at all the uproar about this. As a former public school math/science teacher who is now teaching science to high school homeschoolers, the idea of a super quick way to find a “reasonable” answer (interpreted as “in the right ball park of magnitude”). is a great skill to have. So many times in my chemistry or physics class, a student will push the wrong button the calculator and simply write down the answer. If the student would just look at the problem and do a quick ballpark estimate, he would easily see that he’d made an error on the calculator, re-do it and correct his exact answer. So I encourage my students regularly to always do a ballpark estimate so they can catch such mistakes. Since they are in a high school science class, I don’t teach that in the class, but will help them if they don’t know how to do it

The math problem in question is in no way saying that the “reasonable” answer is the right one that should be used in a real-life situation. It just means than the correct real answer should be of the same order of magnitude as the estimate. When I do an estimate, I prefer to round the numbers properly since that gives a closer estimate, however, front-end estimation will still give the correct ball-park for checking order of magnitude and is easier for young students to learn.

There is a lot wrong with common core, but seriously this is not one of the concerns, or shouldn’t be.

James says

But that’s just it… The estimated sum (which SHOULD be considered the “Reasonable” answer) is not reasonable. On what planet, in what system is 500 comparable to 645. A BETTER and much more “reasonable” solution would have been to round to the nearest 50. 354 become 350 and 291 becomes 300, and the “Reasonable” answer (650) is now significantly (dare I say, reasonably) closer to the actual CORRECT answer of 645.

The home work lists 645 as a “Reasonable” answer when it, in fact is not reasonable at all. It’s CORRECT. This is not acceptable. Partly because it is bad math, but also because it is bad grammar. “Reasonable” and “correct” are not synonymous. To teach a child that such a thing is so is ludicrous and will only result in increased relativism and ineptitude.

LisaG says

Excellent points!!!!!

LisaG says

Are you SERIOUS???? Just add the numbers and be done with it; IF you know math, you’ll have the correct answer and won’t need a “reasonable estimate” or any such nonsense. I watched a video of this type of “math” a few months ago and it was painful – I had the correct answers within literally seconds while the kid in the video had to go through hoops and steps for many minutes. Why not just teach how to add? what is wrong with just teaching how to add? what is the point of the extra baloney? trying to make sure kids/people are slow and second-guess themselves? what are they going to do on BIG life issues, use a mobile shout-out? ask people around them if it is “reasonable” to cross the street at a given time? what drivel.

Alex F says

because you are not teaching them to think, only go through the mechanics of what technology will do for them.

Heather says

You NEVER use a calculator? LOL

Jeanne says

In rounding, I was always taught that numbers from 1-4 should be rounded down, and 5-9 should be rounded up. Therefore, 350 should be rounded to 400 (or left alone) and 290 should be rounded to 300. Though 700 is not as close to the correct answer as 500, 650 certainly WOULD be a LOT closer.

Seth says

Jeanne, so how is 700 not as close to the answer as 500?

The difference between 700 and 645 equals: 55

The difference between 654 and 500 equals: 145

55<145: Fifty five is less than one hundred and forty five. I could do this math by 3rd grade.

Seven hundred is much closer to the answer than is five hundred. Seven hundred is only fifty five digits off while five hundred is one hundred and forty five digits off. Which has less digits?

But yes 650 would be much closer.

laura says

I agree with another teacher that posted here. I have taught high school and middle school math for 10 years. By now I know that I am a good teacher and I have parents and students every year tell me that they never (or their kid never) understood math until I taught them. The skill that they are trying to teach hear is to get a quick and easy ballpark estimate. We are not saying to pay your bills like this or that it is a good way to do accounting. There are many times that I have had students put the wrong numbers into the calculator and they don’t realize it. If they had done an estimate (even one using front end estimation) they would have know that the answer should be around 500 and not 5000 or 5. One of my favorite ones was when I was teaching algebra and students had to convert feet to miles to get the correct answer to the story problem. Many students ended the problem saying that the plane was flying 2 feet above the ground when it was still 2 or 3 miles from landing! If they would have taken the time to look at the question again and do a rough estimate they would know that the answer did not make any sense! Now, I am not saying that CCSS are the best thing in the world; they have mistakes, as all systems in any business do. However, they are a step in the right direction and they focus and teaching across topics so that students can see that the material in different classes is connected. I am a huge fan of this. Finally, to put in a personal rant, when it comes to math it really shouldn’t be okay for people (especially parents) to say that they are not good with math and that is okay because it is not important or they don’t really use it. I wonder how many of them would say that about reading or using the English language. Stop accepting mediocrity when it comes to math!

Sheri says

Linda–that was my first thought, making sure the order of magnitude is right

Rhonda Martin says

I have spent most of my working adult age doing accounting work and after reading all these comments I’ve come to the conclusion that several post really have great opinions yet they are completely opposite of each other. However I have a question the reason for this math exercise is to teach our children how to quickly check their work so they can fix an outrageous math error. Ok , I get that concept but this new method is it really needed or accurate if they are still learning to do rounding???? If you think about it the child would get the answer faster and would be closer to the actual correct answer. Example

345 + 425 = 770

300 + 400 = 700

The estimated sum is 700

The actual sum is 770

The answer 770 is reasonable

ok so I used the rounding method that she was just taught days earlier so why wouldn’t this work to recognize a math error. Why would they bother to confuse children by then turning around and having them estimate a whole different way when it’s not even needed and only confusing because they were just taught differently. If they are still going to implement rounding then why not estimate using rounding to check their answers ?

Amazed says

You are thinking as an adult- not as a child. You have background information and years of experience to help you reason. A third grader is being TAUGHT how to reason. People seem to forget how they arrived at their current skills set. It is a progression of years of learning. This is a lesson in reasoning- not in rounding.

Seth says

This is a terrible way to teach a third grader how to reason. I was taught a better way how to reason, and in third grade, front end estimation was not it.

This is regression, not progression.

Chuck XProf says

Good point. Giving them rounding and then taking a step backwards to learn estimating by front-end estimation could confuse a lot of the kids. Either teach front-end estimation first, or else use rounding for estimation. (The simpler front-end method still gives a reality check, and that’s worth hearing about sometime, but don’t confuse them by taking a step backwards.)

Curiously, your example gives the same estimate either way. That will happen sometimes.

D.K. Sullivan says

. If I recall correctly, the difference between our American math system and the metric system resulted in a Mars space probe failing some years ago. In this case, where an answer is 23% less than the actual mathematical answer, that mission would have been on its way to Mercury instead.

. That being said, the child of these parents will never work in science, math, engineering, medicine…the only job I can think of where a 23% error might be acceptable is where in the dump to unload the garbage truck.

LisaG says

good point

Tracy says

How about this….just sit those kids down and teach them how to add, subtract, divide and multiply CORRECTLY. Let’s just start there and stop trying to make all of this harder than it has to be.

Just teach!! Simple as that!!!

Christie says

“Order of magnitude” approximations are very important in engineering to check if you are in the right ballpark. In this instance, 500 is a reasonable ballpark for 645 – versus if your quick front-end rounding gave you an answer of 50 or 5,000.

Kile says

500 is nowhere near a reasonable approximation for 645. If you were to describe a criminal to a cop as 5 feet tall but he was really 6 and a half feet tall, would that be “good enough”? If I was teaching a child how to calculate this quickly, I’d say just add 300 and 350. You get 650 which is almost EXACTLY 645. Much easier to do and much closer to the correct answer. There is only ONE correct answer. Why not just teach the kid to freaking add? I believe they are intentionally teaching these kids to be stupid so that they will vote Democrat for the rest of their lives.

Chris says

Kile: You miss that this was a 2 part question. Part 2 was a sanity check (The Front end estimation). They’ve already done the math, this is to make sure they didn’t do something silly like make the number 6450. It is teaching the kid to do a quick and dirty Estimation as a DOUBLE CHECK to make sure the answer to the actual math is close to what the estimation answer is. I’m not sure when this will be better than rounding, but this isn’t rounding and learning another way of doing things isn’t bad, as long as they are taught WHEN to use each type.

Jason says

And right there is why I’d find this useless. When I was in school YEARS back… A double check of your work meant you DOUBLE CHECKED your work. You checked to make sure you added (subtracted, multiplied…) things properly. If you wanted a quick and lazy way to make sure you were in the ballpark you rounded your numbers but that only works on simple addition and subtraction. And with rounding, my numbers were never WAY out of the ballpark like that one above. That is nowhere a REASONABLE answer. I would have failed math had I been taught that way. I’m sorry but some teachers are just getting lazy and don’t want to put the time in to teach kids properly. Case in point… I know a lot of kids these days that have trouble reading an analogue clock. If it’s not a digital clock they really have a hard time trying to figure out the time. Teachers don’t seem to find it important these days even though they are still widely used. I sure hope none of these kids plan on becoming doctors or anything more than a politician. 🙁

Hannah says

Kile: Probably will :P. Everyone else: If I had been taught to use that dumb ‘front-end estimation’ I would have taken seven hours on each of my short math assignments in fourth grade because I would have thought since 645 is CLEARLY not in the range of 500, so i would have tried maybe subtracting because it was a typo? Or maybe division? or maybe divide it by 3.14 to get the circumfrence of a circle? (yes, I learned that in fourth grade. I remember) All to only finally figure out the thing that’s supposed to help me find the right answer is the thing that’s screwing me! At the ABSOLUTE LEAST you could round to the nearest hundred (up in this case, but sometimes you have to round down. like 201 or 530 should be rounded down or it’s unreasonable. adds an extra thousand,) so you would get 700 which would still be kinda close but it’s better for younger children who like lots of zeros, and It’s only about 50 numbers away rather that 150, but I still prefer by 50s.

Hannah says

(For that sign i made in my last comment, it’s supposed to say 🙁

Chris says

I wish it were so simple Jason. For parents like you and I, we can help your kids with double checking. WAY too many parents don’t make their kids do the homework, let alone spend the time to make sure the kids are getting it. So by doing Front end Estimation the school is giving those kids without parental involvement a tool to do quick estimation. It is also the first step on the path to rounding. Once you teach this, you can show how far off it is, and show how rounding is better. Learning is a series of steps. If you miss a step, it’s hard to skip it to get to the next. Some kids don’t need this step, others are greatly assisted by it. If your child doesn’t need this step, then get them in a higher math class. PARENTAL INVOLVEMENT IS KEY.

Jason says

My apologies Chris. If your a teacher I didn’t mean that as an offense to all teachers. I do understand there are good teachers. I have had some AWESOME teachers when I was in high school but unfortunately had some really useless and LAZY ones. Unfortunately the good teachers seem harder and harder to come by these days. I’m just not sure why they wouldn’t just teach rounding right off the bat (Like I was taught). It’s not that hard to pick up and less confusing then learning one way of estimating a problem then suddenly being taught a different way. Rounding is only very slightly more complex then this front end estimation stuff for young kids but gets you way closer to the answer. I’m just not sure why they would teach something less effective and just cloud the waters. And yes. I do totally agree that parental involvement is key. That’s the other part of the problem. Too many parents that are content to let their kids play video games all afternoon rather than make them do homework. Back in my day your parent was your PARENT. Not like today’s parent’s where most of them are too busy trying to be their kids “friend” rather than the authority figure kids need. 🙂

LisaG says

If the child is SO bad at math that they cannot add the actual two numbers together, then why in heaven’s name is it assumed that they will be adding together the two “estimated” or “rounded” numbers in any sort of a fashion as to make the resulting answer any sort of a “reality check”???? I don’t understand this “logic” at all – – either they can add, or they cannot. Teaching a fuzzy interim will only create fuzzy thinking, teach fuzzy confidence. Testing is where they learn if their answer is reasonable or not – if necessary, do more testing, quizzes, more homework until they trust their abilities, but don’t do them the lifetime of disservice of teaching fuzziness.

Chris says

Why do you assume this is taught before they have mastered addition? This is the first step in teaching rounding. Or do you believe rounding has no place in math and life?

LisaG says

what BALONEY!!!! check back to the box with the example to which we are all referring: “Find” the sun; the answer they found is “reasonable” – the emphasis is on what is the answer to the two numbers added together, nowhere does it say “is 300 a reasonable rounding for 345?” nor does it specify rounding up or rounding down, so this is NOT a rounding exercise, this is an addition exercise, with the attempt to each a “reality check” for is your answer the correct one, or in this case, even reasonable. Had they mastered addition and this were merely a rounding exercise, that is where the emphasis would be. and stop with the classic condescension tactic of asking a snotty question with an assumption front-loaded into it? thanks for the laugh!!!

Chris says

Lisa: This isn’t a rounding exercise. Did you read the problem?

LisaG says

I’m not the one trying to say it is a rounding problem, you are, go back and read your own comment: “Why do you assume this is taught before they have mastered addition? This is the first step in teaching rounding. Or do you believe rounding has no place in math and life?” that was your comment. My original comment was on the entire thing, not the ’rounding” part. Don’t put words in my mouth. And there you go with the condescension again. Keep making my point for me, makes things easier.

Jason says

Wow. Take a chill pill LisaG. Your the one making it easy. Chris was in no way being condescending. Just asked a simple question as to why you assume something. Chris also never told you that you were commenting on only the “rounding” part. And I in no way see words being put in your mouth. When someone is trying to explain something or offer a different point of view… My advice.. Quit treating it like an attack and flying off the handle. Honestly Lisa. Learn how to READ what others say. You offend WAY to easily. Listening and patience seem to be a virtue and unfortunately not a skill these days. 🙂

LisaG says

Jason, thank you for this laugh, maybe take your own advice, I am well aware that there are different points of view, doesn’t seem to me that you are aware though by how I am at some sort of fault in this, it is all my misreading, attacking, etc. Am not offended – listen to your own advice about listening and patience. Am not going to waste any more time on this, therapy from an obtuse stranger isn’t worth the time. Smiley face? seriously?? !!!!!

Jason says

I just find it funny LisaG that you attack others for their point of view yet can’t take it when someone gives theirs. Interesting. And by the way I wasn’t offering therapy. However now that you mention you wouldn’t take if from strangers anyways… I agree. Perhaps you should seek professional help? Oh and just as a heads up… Suddenly using fancy words in your posts in no way makes you sound more intelligent. How long did it take you to look that up BTW? 🙂

Joe says

Christie,

If you are an engineer, you should be fired. As both an ABET accredited Computer Engineer and Civil Engineer PE, I am disgusted by this method of teaching. If you want children to understand order of magnitude, you teach them how to use a slide rule, not how to see if math is “reasonable.”

Mark says

Individuals aren’t accredited by ABET. Do you make a habit out of falsifying your credentials?

If one gives slide rules to children this age, one will soon have a bunch of broken slide rules. You have to remember that schools don’t have the unlimited budgets of civil engineers.

Chris says

Trisha:

The biggest problem I see with this article is that you do not seem to understand the differences between the term ESTIMATING and the term ROUNDING. These are 2 DIFFERENT concepts. You’re right. If this were a rounding problem you run into issues with the math. This is ESTIMATION through, which is different. This is more of a “parents needs to learn it” issue than a “OMG They’re TEACHING THIS WRONG” issue.

First: The assignment has your child get the real answer.

Second: The assignment asks you to do FRONT END ESTIMATION to CHECK your answer. Front end estimation is to do QUICK and SIMPLE math to CHECK your answer is reasonable (So you don’t accidentally say 6450 for example). You do the math for the answer. That answer is 645 in this. Then, you CHECK your math using estimation, if you ignore the rest and just use the FRONT of the numbers (FRONT END ESTIMATION) you find that the quick estimation is 500. Since we’re adding 2 numbers, the front of the number needs to be +/-1 from the front of the answer. The FRONT END ESTIMATION is 5, your calculated answer is 6, that is REASONABLE as a quick check. It isn’t the ANSWER. IT IS CHECKING YOUR ANSWER WITH FRONT END ESTIMATION.

Regards,

Chris

trisha haas says

I disagree that 500 is reasonable to 645.

But we are allowed to have a difference of opinion.

🙂

Chris says

As a method to make sure you’re not off by an order of magnitude? It is a “sanity” check to help a student learn to quickly realize they have a math error when it is so gross of an error to trigger front end estimation failure. It is to CHECK the answer, not to GET the answer.

Kile says

If I estimated my jobs this way, I’d quickly be out of a job. Being off by 30% is not considered even close to adequate.

Chris says

It’s actually being off by 22.5%. But then, you’re approximately 30% off in your estimate on how far off this answer was. That’s not even close to adequate.

Kile says

If your answer is 500 and the correct answer is 645 you have under estimated by 29%. 645/500 = 1.29. That’s called math.

Chris says

The answer is off by 145, not by 500. The answer was 645. The estimate was 500. The error was 145. 145/600 = ~22.5% That’s called math.

Kile says

The difference between the estimate and the correct answer was 145. 145/500=0.29.

If I gave you an estimate to do a job of $500 and the actual job turns out to cost $645 my bill is 29% more than my estimate. That is significantly off.

Chris says

You’re wrong again Kile. You’re again using the incorrect answer to calculate how far off you are. The correct answer is 645. The incorrect answer is 500. The amount the incorrect answer is off from the correct answer is 145. 145/645 == the incorrect amount being ~22.5% of 645.

We don’t care how large the incorrect answer is, we care how far it was off from the correct answer. Again, the correct answer is ~22.5%, of which you estimated it was 30-22.5 = 7.5. 7.5/22.5 = 33% off.

Chris says

This is actually a common mistake. You just reversed the numbers for your fraction.

Kile says

No. You made the mistake. I was right all along.

Chris says

Check again. You’re wrong. You’re doing the division of the amount off by the incorrect answer. To get the percent the incorrect answer was off from the correct answer you divide the CORRECT answer by the amount the incorrect answer was off, in this case 145/645, not the 145/500 you listed above.

Kile says

If you get an estimate to build a house of $100,000 and the contractor’s final bill is $150,000 what is the percentage of the cost overrun? Is the actual bill not 50% more than the estimate?

Chris says

That’s a different question than how much off the final price was he, which is what you said to start. We’re apparently looking at different questions here. The error is only 33% of the final cost. Do you disagree?

Kile says

No, I don’t agree. The final bill was 50% more than the estimate. Just like the correct answer was 29% more than the estimate.

Chris says

Then you’re wrong. The error was 50,000. that’s only 1/3 of 150,000.

Kile says

No, $50,000 is 50% more than the estimate. This isn’t rocket surgery.

Chris says

As I said, we’re answer 2 different questions. If you believe the answer to the question of what percent of the final answer was the error, then you get 33%. If you ask how much MORE was the final answer than the incorrect answer you get 50%. This actually CAN be rocket science, since there is a lot of math there. You’re answer one question, I’m answering another. The fact that you can’t get your head around that leaves me at saying good night to you. I’m done with the yes/no/yes/no/yes/no argument you insist on.

Good night.

Kile says

I make my living by estimating. If I’m ever off by 50% I’ll let you explain to my customer that really I’m only off by 33% as he writes me a check for 50% more than his budget. I’m sure that will make him feel better.

Sharon P says

Since we are now in the era of Common Core, there is no “right” answer, as long as you can argue your point until your opponent gives up.

Chris says

@Kile: If you’re doing estimating I assume you also work with tools. Do you use a shovel to put a nail in? Do you use a nail to dig a hole? No? Then why would you use Front end estimation on something like the estimation you’re doing. It is a tool, nothing more. If you choose to use it incorrectly that’s on you. If you also choose to ignore the truth of what I have said that is also on you.

@Sharon: I presume you were talking about me in your comment. I went to sleep.

B. says

So what if the error is in the awkward “estimation” step, forcing a check calculation in both? Seems to me this “check” will only encourage laziness in students failing to see the need to do the “actual” calculation. My favorite hobby remains giving the cashier $2.11 when the register says my bill is $1.61 just to see the reaction on their face. 95% won’t know what to do. Estimation? Won’t work here…

RaymondofCanada says

B. I like your example. I do that all the time. It seems the money I need to tend to round off my change comes automatically, I suppose because I’ve done it so many times. But last summer I worked in a ticket booth at a fair and people did it to me. I was so damn confused. The person next to me had to help me out. I had a mental block to responding. That is weird. I still tender my money like that but cashiers always seem to handle it with ease.

Chris says

As a cashier my favorite hobby was to give them that 50 cents back as a quarter, two dimes and five pennies.

Or no, I just gave them the change because it’s faster and makes my metrics for the company better and I get raises for speed and accuracy. You on the other hand stand there counting out pennies to get exact change, hold up the line you were just complaining was too long and then very likely get the wrong amount of change to boot.

Michelle says

I have probably made that face myself. Takes me a couple extra seconds because I personally don’t see numbers correctly in my head. I have to change them into a shape I understand first. It is easier with money as it always remains the same. I must admit that I depend on my computer to help me with change. Chris and Kile’s conversation was so far over my head, but hey…. that is why I will never be more than a cashier. 😉 Please be kind to us as our jobs royally suck.

Ellie Javier says

I am a Math Teacher, too, as far as I know when you say Front End Estimation – we only round and add the very last number on the left. This means that all the numbers in other places will be zeros while the number in the leftmost place after the numbers are rounded. So in this estimation there is still the rounding of numbers. Ex. for two-digit numbers — 68 + 44 = 70 + 40 = 110; 21 + 59 = 20 + 60 = 80 or for three-digits—- Ex. 174 + 590 = 200 + 600 = 800, so, if you notice it should be rounded to the nearest hundred place before adding the leftmost digits or numbers. Please take note that with front end estimation, as mentioned or discussed earlier, all other numbers except the leftmost digits — 2 and 6, are equal to 0 and we only added the leftmost digits as shown above. So, in that problem above about using FRONT END ESTIMATION, I would say that 354 + 291 = 300 + 300 = 600 is your estimation which is nearer to the reasonable answer of 645.

RD Bowker says

Chris has hit my objection to Common Core on the head when writing that this is a “parents needs [sic] to learn it” skill. Rather than making sure that the students have mastered the core of learning, the new standards require students to learn a new procedure/skill, and require parents, who may well be masters of the actual common core of knowledge, to learn and accept a new and uncommon skill. Any government standard that is successful only if it can require well-educated adults to learn a new skill is setting an unusual and intrusive burden on the parents of our communities and the teachers whose pay and very jobs depend on how well they train said parents.

Chris says

I understand that some parents don’t want to be a part of their kids education. That’s not my problem. That’s theirs. If a parent is so ingraned into their own way of thinking they can’t sit down and learn what their third grader is learning in school (If only as a check that they don’t object to the material) then I have no sympathy for that parent.

Oh no, a parent has to pay attention to their kid and learn something new. Boo Hoo.

steve says

Don’t teach your kids spelling.

Kile says

This is indoctrination. They are purposely trying to drive a wedge between parents and students. This is all by design.

Chris says

I feel sorry for any parent who is so out of the loop with their child’s school and curriculum that they feel the kid getting a better education than they had is indoctrination. You don’t like it, home school. But then that would require effort on your part.

How about you fight this indoctrination by volunteering at your school. Be in the classes, watch what they are learning. Be a class mom or class dad. In what way are you bring locked out of this?

LisaG says

will say again: if the child is SO bad at math that they cannot add together the original numbers, then what in heaven’s name makes you think they can add together the “rounded” or “estimated” numbers?????? You even say that they could say a wildly wrong answer, so what use is this? Tech the children to add, do it over and over, use flash cards, quizzes, on a board, verbal, whatever, until they learn that they are doing it correctly and can come up with an answer easily and confidently. If they cannot add, they cannot add original nor estimated numbers, this is just dumb.

Virginia says

This technique is not rounding, it’s truncating. Truncating an answer is never reasonable, especially when what is truncated is so close to the next higher place that you would round to (i.e. 291 rounded to the nearest 100 would be 300).

The thing the blogger is saying is that there is little to no explanation, and that in itself makes for a poor lesson. No book to refer to? No instructions to refer to? Reminds me of some of the mimeographs my nephew was given (and even I, some 40 years ago) to complete. There was no rhyme or reason to it, and my dad was a physicist, well-read in mathematics and HE couldn’t make heads or tails of it.

A millionaire would know the difference between 5.00 million and 6.45 million was enough to call his accountants and money handlers to task. Who was scraping off 1.45 million off the top? If it were one of his employees, they would get the boot for embezzlement. If it were an outsider, he would have his lawyers on it in a second. Since 500 is about 22% less than 645, that would be grounds for dismissal for anyone! It might even be a red flag to the IRS.

This practice is setting children up for a fall later on in life.

Chris says

This technique is for doing sanity checking, not for getting the answer. If you’re not teaching kids how to quickly do sanity checks on their answers, you’re setting them up to fall later in life.

Seth says

I was taught sanity checking by third grade, and front end estimation was not the way to do it.

This way is setting them up for a fail.

Stina says

or the basic concept of fact families (learned in kinder or first) could, by third grade, be translated into using subtraction to check the answer to addition (pretty basic and would likely encourage better fluency with numbers anyway as long as we’re fiddling with extra steps we could waste time differently with a better result)…

But let’s just play devil’s advocate with the front end model… Okay so let’s say a kid is less than fluent in “regrouping,” he could easily decide that 354 + 291 = 545 then he does his front end estimating 300 + 200 = 500 not only will he find his own answer reasonable… would he not be quite confused when the teacher claims that the correct answer is 645, and lost at how that is *more* reasonable given it’s further from the front end estimate than his own answer?

Since “regrouping” errors are wildly common in weak math students, this sounds to me like it’d be a teacher’s nightmare to battle, not a brilliant ‘sanity check’ for kids. But I guess that may all be immaterial now, since under the common core model 3 x 4 can equal 11 if the kid can illustrate and make a good case for he arrived at the wrong answer… maybe with the new math ideals, if you can get to 545 and justify it with front end estimation as ‘reasonable’ you’re actually good to go. So maybe my point is moot afterall and the teacher wouldn’t take up arms in the first place. At any rate math fluency is dying and one would think more math teachers would be disturbed as well instead of getting flustered at parents… but sadly that appears all too often not to be the case.

Ellie Javier says

I don’t think it’s truncating or about truncation because the problem is on front end estimation. We are not cutting off or discarding specified digit/digits here. And truncation does not round up or round down the digits, truncating may have the same result as rounding or estimating but the error may be twice or more.

Pam Patterson says

What is concerning me the most about this discussion is that I can hear the parents sitting down with their child and after 3 minutes of barely reading the example or attempting to understand it, are exclaiming, “This is so stupid!” “These dumb teachers are too lazy to teach the right way”, etc. That’s assuming those parents are sitting down with their child, and that they helped their child learn the math basics of adding, subtracting, multiplication and division facts. Front-end estimation is just one of many ways to find a quick estimate (not a house remodeling estimate) that will let you know if you are close in your final answer. Although it is the usually the farthest from the actual answer, it still has its place. “the nearest hundreds, tens, hundredths, etc coming closer and closer. Help your child discover the joy of math, and the wonder of the ability to come close to the answer without adding all of the numbers. Then teach them “rounding up” (so useful in the grocery store to make sure you haven’t overspent!). Keep complaining in front of your child, and you are a detriment and your child will carry resentment of learning to school. One more thing: the magnitude of all that must be taught and mastered in each grade takes away the time to teach a child to read an analog clock. It is taught, but as a parent, you must teach it, as well! Behavior and teaching and a sound belief system is a parent’s job! School helps to direct the learning, as well as reinforce the behavior. School helps the student to reach higher and learn more than their parent did. My children, now adults, certainly know more than I do, and theirs will know more than they! I think most working adults will agree that they continue to learn different ways to accomplish their tasks, and that their tasks themselves have changed throughout their career! End of rant!

Trev says

My father was a math professor, and through the years he taught me all these little tricks (estimations) that I could use to see if my answers were right or wrong based on an estimation. I am not a super smart guy, I only have a BS undergrad education; yet I am faster at ball-parking figures than most people who have grad/phd/engineering/math degrees; I don’t need a pencil and paper, I just simplify and do it in my head.

Maybe if they rounded the numbers instead of truncating (rounding down) this might have been a little easier to see the educational value. At first I looked at it and thought, that’s stupid… but then I thought about it a little and it made sense. I know that I will be teaching my children all the tricks my father taught me when they are old enough.

Cheers.

Judy Allen says

I’ve decided I cannot continue to be silent while my profession is dragged through the mud by people that don’t know the first thing about what goes on in a classroom on a daily basis. I am seeing so much about Common Core that is inaccurate and misleading. It doesn’t dictate whether or not schools use textbooks. SCHOOLS make that decision because textbooks are enormously expensive and are obsolete before they make it to the classroom. School funding is woefully inadequate, so you make cuts where you can to balance the budget, just as you do with your own household budget. In this age of technology, textbooks are like horse drawn carriages. My school has adopted Common Core. It doesn’t mean we’ve thrown common sense out the window. Common Core does not dictate specific problems. It would have a broad statement that students should be taught how to find an exact answer, how to estimate an answer, and how to determine what is a reasonable answer. Those are not new skills! I learned them when I was in school and I’m sure you did too. The problem is not the curriculum, but rather how the curriculum is taught (or not taught as the case may be). The directions to the problem said to use front-end estimation to find a reasonable answer. Front-end estimation is a strategy to find a ballpark idea quickly, not to find an exact answer. There is a difference between front-end estimation where you only look at the number in the largest place value and more traditional estimation like we all learned in school. We still explicitly teach how to round a number to the nearest ten, hundred, thousand, etc. The pundits would have you believe that isn’t being taught anymore. Every politician and news commentator is an expert and has all the answers for how to “fix” our schools even though they never step foot inside them. Some would have you believe that all teachers are liberals bent on destroying our country. I can only speak for myself when I say that that could not be further from the truth. These people are not educators, they do not have degrees in education, nor do they spend any substantive time in a classroom EVER. I’d like to see them do the job of a teacher day in and day out, week after week, month after month, year after year. They wouldn’t last through their first school year! DON’T BELIEVE THE HYPE ABOUT COMMON CORE!

Melissa says

Where is my LOVE button, Judy??? YES!!!

Renee Dailey says

PRAISE THE LORD for the sanity I see in your post. I, too, am sick of all the bad hype common core is receiving. Most of it is because Obama (no, I am not a fan) attached it to the Race to the Top school funding. People don’t realize that textbook companies are now trying to compete with schools using technology instead of textbooks, therefore, they will “advertise” that they are common core presenting themselves as if they ARE the curriculum. But EVERY good teacher knows, textbooks are NOT the curriculum but a tool and those tools should be chosen carefully! Common Core is the best idea I have seen come along in education in all of my years of teaching. My students’ math capabilities are growing through all of the application they are required to do now where before we didn’t have time to teach anything but the algorithm only and no time to teach application. This hysteria has to stop!

LisaG says

what makes you all think that these comments, or at least some, are NOT from other teachers? Seems to me July Allen’s comments are the “I love me” type from teachers who are just so certain that they are the only way, know the only ways to all wisdom – have run into this with too many teachers. All teachers may not be liberals bent on destroying this country, but the curriculum sure does – the overarching program, the desired end results, sure do. Is it a coincidence that teacher’s unions have been unabashedly been aligned with liberal causes, candidates, democratic party for decades now, and the individual result has tanked? It is very funny to watch when Jay Leno or someone else asks random questions of people and they don’t know even the most basic of answers, but it is very very sad and disgusting when it is looked at in reality. So who and what IS responsible? and then we are supposed to embrace teaching fuzziness? I watched a video of a kid doing this “new math” and it was painful to watch, I cast back to my days learning, and yes I do recall them, and cannot imagine having to learn this way.

Chuck XProf says

The real source of frustration here seems to be that parents can’t make sense of the assignments, and assume, erroneously, that the assignments don’t make sense. Part of improving the curriculum involves giving children a better education than their parents had. The main reason I see that people are criticizing this assignment seems to be that they just don’t get it.

I spent over a ten years teaching university-level physics, often to the slower students: pre-meds, pre-nursing students, other healthcare professionals, bio and geo majors, etc. (Many of these students were actually very bright, and could have handled the calculus-based courses that Physics, Engineering, and Chemistry majors took, but algebra-based was all that was required of them.) But my comments apply to life skills, not just advanced science studies. Everyone needs to know how to do a reality check. The first step is for them to know what a reality check is, and that they can do one.

Now first: I do have concerns with Common Core, especially with the way textbook publishers would like corner their markets. They don’t object to publishing decent stuff, but it’s not their goal. Their goal is to publish whatever might sell, then lock it in. This is a threat to flexible teaching, and to quality education.

But now, for this assignment. Over the years, I became fed up, then despondent, then just plain amused at the inability of college students to estimate their answers. Students who thought that a heavy object (heavy enough to ignore air resistance) falling 4.9 meters (about 16 feet) would fall for 10 seconds, or 0.1 second, because they blindly copied the answer from the calculator. (It’s about 1 second.) Students who estimated that their instructor was about 200 meters tall. Students who found converting inches to cm to be an intolerable burden of math (and who would later be employed as x-ray techs, putting radiation through people’s bodies to make pictures–please be able to do at least some math, OK?). People who had absolutely no concept about what a reasonable answer was or how to find it. Strangely, with their own finances, they were usually pretty good at this, and I tried to use that as a starting point–but I just didn’t have time to do much with it. These were actually intelligent students, but they weren’t used to doing this except with money (and then, only for simple cases).

3rd grade is not too early to start learning about estimation. So, what exactly is going on here? Front-end-rounded estimation may seem strange to a lot of parents. Why do it? At a guess, perhaps it’s because it’s easier than rounding up or down, and it’s more likely that the whole class will understand it, quickly, and well. Estimation by rounding can follow later. (From the comments, it looked like rounding was taught earlier, and that really does seem confusing.) Is this a typo? If so, one would hope that the teacher would have flagged it, corrected it, and told the children about it, who would then (mostly) tell the parents. But that’s not certain, so it could possibly be a typo.

So, perhaps the idea is to teach it the easiest way first, so kids get a taste of how to estimate, and why. Then they can add as step and round up/down, rather than learning rounding and estimating at the same time. Is this the idea? Does it help? I don’t know; I’m missing the context.

But I didn see that anyone else thought of that. (Apologies if I missed it in some comment.) Mostly, what I see is, “I don’t understand this, it’s stupid! Kids shouldn’t have to do this!” This is business as usual for children, but it’s a problem when parents react this way too.

It’s clear that assignments like this, and the curricula they arise from, need a lot of explaining. Parents who don’t understand a technique may easily assume that it’s senseless. One thing that would help would be to have the textbooks available, to actually get the context. And, of course, it helps when the teacher can explain it well. Some of the teachers may not understand the assignment either. Frankly, it’s difficult to get people who are really good at math to teach elementary school. More importantly, it’s much better to have a teacher who’s OK at math and great with kids, than one who’s great at math and just OK with kids. The teacher might not grasp the ultimate aim or significance of the curriculum, especially at first, but they will be better at getting across what they do know.

Parents–if you see an assignment that doesn’t make sense to you, you might be better off swallowing your annoyance a bit, and helping your kids through it as best you can. Even if you have to say, “I’m not sure why you do this” and maybe even, “I’ll try to find out. But when you decide that the class is pointless, and say so, you give the child permission to give up on it too. And if there is a point to it, the kid misses it. Stay in touch with other parents, in case somebody figures it out. Everyone should question authority, but at the very least, when looking at a puzzling assignment, try to allow that there MIGHT be an actual point to the lesson even if you don’t see it yourself, right away.

Some parents think Common Core is about teaching students to blindly, uncritically, follow directions. For this assignment, I can promise you that this is completely backwards. If you teach kids to do it “the right way,” without knowing how to estimate, or break a multiplication problem down (27 x 354 = 20 x 354 + 7 x 354, etc.)–if they only do it “the right way,” i.e., the (only) way YOU learned, then they will know how to follow traditional instructions and no more. The factory jobs that once awaited such people have left America. They are leaving Korea for China, and leaving China for Indonesia. In the marketing jobs, graphic design jobs, etc. that they can do, those who can do estimates and reality checks will have at least some edge. In healthcare, high-tech, engineering, and science, they will be seriously handicapped unless they can estimate and reality-check. Eventually, they may learn to do this, even if they are unaware of it, but they’re always much better off starting early.

There are many real-world applications; I’ll give one: If a drug is described according to milligrams of the drug per kilogram of patient weight, then it’s really important for a doctor or nurse to get the right answer before injecting a 70-year-old with antibiotics, or an infant with opiates. Punching the wrong calculator key could give a factor of 2 error, which some estimates might not catch. But just about any estimate would catch errors of a factor of 10, or 100. Experience, and careful procedures, minimize the chances of such errors. Estimates are one part of being certain your answer is right. Some nurses out there knew about reality-checking before my class; others learned a bit about it in my class; others, well, I hope, and believe, that they learned it somewhere. But the earlier they start, the better. A tiny taste of it in 3rd grade, then more in other grades, will be a lot better than getting it in 11th or 12th grade first, after which half or more of the students will forget it.

An afterthought, not related to 3rd -grade math: front-end estimation right at the decimal point, or “truncation” of real numbers into integers, shows up in computer science. If you convert a real number (with a decimal point, and digits after that) into an integer, you might round up/down, or you might just chop off whatever’s after the decimal point, always rounding down. If you’re not careful, you could possibly do that without even knowing it, with bad results–so you need to know the difference. 3rd graders won’t worry about that, but the very idea does have real-world applications.

Rogue Warrior 6 says

I hope to God you’re no longer teaching Math. And with all the babbling within your comment above, it’s obvious you’re a lonely and lost person. You should open a store and call it “Idiots-or-us”!

Joe Blow says

Uh… I think you mean “Idiots ‘R’ Us”.

You kind of look like an idiot when you make a mistake while calling someone out for being an idiot.

Just sayin’

Hannah says

I don’t like his post either, but that’s a little harsh, don’t you think?

Melissa says

YES!!! As a National Board Certified Teacher, thank you for your explanation! Brilliantly written!!!

Tazilon says

What complete and utter hogwash Chuck. When you are doing math, there is no “reasonable” answer. There is a correct answer and a bunch of incorrect ones. If give a cashier 100 dollars for a 78 dollar purchase and they decide that 20 dollar is “reasonable’ change, I am going to have issues.

If a parachute design calls a width of 8cm on a D ring and 10cm seems “reasonable” to the person making it, someone may die as a result. I’m not making that one up. When I went through HALO school for the Air Force at Ft Bragg, our entire class got grounded because our new parachutes were manufactured incorrectly and the reserve would not properly deploy if needed – because 1 D-ring was 2cm off. A student in the class ahead ended up in the hospital because when his main failed, he tried to deploy his reserve but the main never broke away as it was supposed to. The end result was him slamming into the ground about 10 times faster than he was supposed to; it could have ended MUCH worse.

Imagine your cars brake pads manufactured to a “reasonable” amount. Or parts on the next plane you fly being engineered to a “reasonable” answer.

I have no issues if estimation is taught as producing APPROXIMATE answer – “approximate” implies the answer is close but not quite. “reasonable”? BW – it ISN”T reasonable – it is UNREASONABLE because it it INCORRECT.

Common Core is a bane to education. Its problems are legion and well documented. EVERYONE in the country needs to research Common Core and fight like hell to keep it out of their schools.

Chris says

Why would you use the wrong tool for the job. If you’re making an exact item, you don’t estimate, you measure. If you’re checking a math problem for order of magnitude issues, you can estimate quickly. You don’t dig a hole in your garden with a spoon just like you don’t serve your ice cream with a shovel.

Hannah says

I love this answer. totally sums up my feelings. thanks!

Renee says

Thank you for this response. It is exactly what parents need to read to truly understand what is going on here. I teach 6th grade math and I 100% agree with what you posted here. I often have to tell parents that I am teaching their child methods that they did not learn before. And I know they are frustrating to them because they don’t understand what their child has to do on their homework. Usually I end up having kids come in and say, well, my mom helped me but she said to forget what you taught me and to do it this way. Usually parents revert back to what they know, which is totally understandable… but they don’t know why it is important that the student masters the way they were taught in class. It is usually leading to something the parent is unaware of or mastering a skill that they may not know themselves. We are preparing these students for a different world with technology changing at a rapid pace every day. Parents need to think about the jobs they were prepared for and understand the job opportunities their child will have are far different, so why would the methods they were taught look exactly the same?

Kile says

Really? Math has changed in the last 30 years? Are you serious?

Alex F says

math has not changed. Our needs have. We now have smart phones and calculators where for the past couple of decades we had Excel and Lotus before that. Our needs now are for thinkers, not simply data entry folks. These lesson start teaching that there is more to the math than the final answer. there is application of the information, the approach to the data, and more.

Kristi says

Third graders do not begin to be at a developmental level for that sort of thinking. Third graders shouldn’t even be learning “mathematics,” as a general, higher level term. They should be learning “arithmetic.” You don’t teach children to read Shakespeare before you teach them how to read basic CVC words. We’re trying to teach our kids how to do completely developmentally inappropriate math, before we teach them arithmetic. Which is why they’re failing. To a third grader, application of the information is too much. They need to understand how to plug the data in first, before they can apply it.

Good grief, this should be child development 101. The fact that it’s not says a lot about CCS.

Chris says

You haven’t had a third grader in a long time have you? Third graders are past basic arithmetic.

Kristi says

Actually, I have a 7th grader, 5th grader, and 1st grader now. So, yes, I do know of what I speak. And, no, third graders are not past basic arithmetic. It’s not a matter of what the book teaches them, it’s a matter of what they’re developmentally ready to learn. Young children are NOT ready to learn mathematics. They’re just not. You can shove it down their throats all day long, it’s only going to hurt them in the long run.

Chris says

Maybe your young children aren’t ready. Young children in general soak up information and concepts. Third graders are past basic arithmetic (In third grade I was on multiplication and division tables and that wasn’t common core). What are are you in that your kids are still learning basic arithmetic in third grade? This is why we need common core, to make sure kids in some area’s aren’t being left behind kids elsewhere.

Kristi says

No, young children in general soak up INFORMATION. Not concepts. They can’t think that abstractly yet. I could teach my kids algebra. They might even memorize the formulas, but they wouldn’t get much else out of it, they’d probably learn to hate math, because they can’t grasp the concepts, and it would be detrimental to them in the long run.

This isn’t Star Trek. We don’t need young kids doing Calculus. These are real, live kids who are really failing math after formally loving it. This writer’s story isn’t unique, in the LEAST. It’s EVERYWHERE. It’s happening a lot. I homeschool my kids, so it’s not happening to them, but I see my friends and the tears and fights and HOURS worth of homework they have every. single. night. It’s not right.

I said below that they’re trying to build the pyramid from the top down, and that’s not right. What this math does is absolutely refuse to build the base at all. Then they wonder why the pyramid won’t magically “float”. You can’t do that. You have to take things one step at a time, in PARTICULAR with regards to math.

Good grief, there’s no reason to rush it.

Renee says

I hope you are challenging your “homeschooled” kids to new levels. From the way you are talking, your kids breeze through the math at a basic level. If they don’t struggle a little to try to make sense of a problem a little beyond their current understanding, they will struggle when they go to college some day or when they try to problem solve on their own. I hope you are preparing them to work through something difficult on their own. (And by the way, even a 5 year old can understand very basic levels of calculus, you probably just don’t realize what you are actually teaching is the very foundation of calculus at that point. )

Kristi says

Actually, I do. We use incredibly rigorous curricula, from a variety of sources, along with teaching informal and formal logic. So, yes. They’ll finish calculus (without a calculator is my 12 year old’s goal, since the Babylonians didn’t use calculators to develop calculus) before college. The difference is, they will have a FIRM foundation in arithmetic before I move them on to higher level math, which will make the higher level math easier, make mental math possible, and, in the end, give them a more complete understanding of mathematics in general. I’m doubting the same will remotely happen in public schools.

Seth says

So was i Chris, thank you!

I was learning my multiplication tables and division.

Alex F says

I am in a position to argue if this is too advanced for many 3rd graders. I would argue that this is too advanced for many of the parents.

But, you just changed this discussion from whether this lesson is dumbing down education as the detractors of CC are arguing to the point that those of us who teach math are making. This is actually pushing the lesson to a more advanced and more interesting level.

Thanks for supporting the notion that CC challenges kids more than old ways of teaching.

Kristi says

The point is, young elementary school student’s don’t NEED, and aren’t READY for a “new, more advanced, more interesting” level. They NEED to establish their foundations. You’re not challenging them, you’re setting them up for failure. There’s a difference. You’re trying to build the pyramid from the top down.

Chris says

Again, if your kids are still on basic arithmetic in grade three not only has the school already failed, you as a parent have failed. Third grade has ALWAYS been beyond basic arithmetic. Multiplication and division is started in third even 27 years ago when I was there.

Kristi says

Multiplication and division ARE basic arithmetic. Mathematics is the higher level concepts. You might want to research the terms.

Chris says

I feel for your kids. I do hope you’re following state law and making sure you’re not holding your children back in learning. I wish them all the best with you as a teacher.

Kristi says

I really do hope you’re not a teacher. Really truly, if you can’t handle learning the difference between “arithmetic” and “mathematics.” There’s just no call for that. My children are advancing nicely, scoring extremely well (better than the average student in the US) on their standardized tests, and we are just fine, thank you very much.

Chris says

My kids, who I spend time with each night on homework are in advanced math classes and not only scoring better than average, they are top 94th percentile on the common core tests. Because I take the time to explain the different concepts and when they are to be used and when they are not useful. I don’t tell them they don’t need to learn something because they find it hard. I figure out what the course is trying to teach and help them.

I will admit my need to do so isn’t often, the hardest part for my kids was realizing that the rote memorization of the tables was important even though they could do the math in their head very quickly.

EVERY parent should be a teacher to their child. So yes, I am a teacher, even if I don’t have a class.

Kristi says

So… you have your children in school, every day, with an hour (minimum I would guess) of math in school, bring them home, do more homework with them… and they’re scoring approximately what my kids are on standardized tests. My kids do 1 hour a day, and then they quit so as not to overload them. Except my first grader. He does about 20 minutes. He’s working on memorization, rather than concepts at the moment.

I’m struggling to see how the CCS way is better…

Chris says

I have my kids in school, Monday through Friday. 40 minutes of math. The homework is quick (less than an hour) and they’re WAY above average. Your kids are average per your own words. Were you lying? If lying, why? What did you gain by lying?

You do a total of 1 hour of school per day? In what weird world is that overloading your child?

Kristi says

What?? I said they only do 1 hour of math a day, so they DON’T get overloaded. 1 hour of math a day is plenty. They don’t need any more than that.

I also said they are above average on their testing. What I said exactly is, “My children are advancing nicely, scoring extremely well (better than the average student in the US) on their standardized tests, ” I didn’t lie. They scored better than the national average, closer to what your children scored. I’d have to go through my records to see their exact scores, but I never said they scored average, because they didn’t.

Good for you that your kids have less than an hour of homework a night. Most parents that I’ve talked to have kids with 2-4 hours of homework on average a night. Mostly because they aren’t grasping the math, because the concepts are above them, or they’re silly tricks like this that confuse them.

Renee says

Yes, the way we teach math has changed in the last 30 years. We have started taking methods they use in other cultures and implemented them into our curriculum in the United States. Your comment doesn’t make sense in the fact that no one ever said the actual math has changed. Just because you don’t understand the method used doesn’t mean the child will not have the same end result of learning.

Kristi says

Arithmetic has not changed. 2+2 will always equal 4. 5 isn’t “good enough.” Nope, that’s not how it works.

Chris says

Actually Kristi, 2+2=5 for sufficiently large values of 2. Lets say we take what everyone here has been confusing and round to the nearest whole number. 2.48+2.47=4.97. If you round before the math you get 2+2=4, which is right, but you round after and you get 2+2=5. This is a mathematical concept beyond third grade, but one that is there to remind you that compounding estimations can bring serious issues into your math. To have it seen by the students prior to getting to that concept isn’t a bad thing.

It’s a joke … but a joke with a somewhat serious point. All measurements in the real world (as opposed to the esoteric whirled of mathematics) are estimates; they’re always rounded to something. There’s no such thing as absolute precision. So rounding must come into play sometime or other, and the joke about 2 + 2 = 5 if 2 is large enough, is a reminder about the way that estimation errors compound.

Kile says

Actually there is such a thing as absolute precision. It’s called the RIGHT answer and 2+2 is ALWAYS 4. I bet you voted for Obama. You’d have to with your convoluted illogic.

Kristi says

Exactly. Thank you Kile. Chris’ answer proves my point exactly… 3rd graders don’t need the higher level of understanding. It will only confuse them. They need to master their arithmetic skills (which, again, if someone doesn’t understand that term, you should look it up), so that the higher level math is easier and better understood when they are developmentally ready.

Chris says

Third graders need to start somewhere. You teach addition and subtraction and how to check your answer by changing operands. 391+244=645. 645-244=391. 645-391=244. You check your work with work.

Then when the child has understanding of that, you move to higher math. Estimating to quickly check your work (You’re done it so much you should have mistakes, if you do you want to catch the really obvious ones). So you teach front end estimation. This gives you 300+200=500. 500 in this instance is close to 645 (As in you’ll realize if you messed up and your answer was 6450 because you put an extra 0 in there.)

After they get down Front End Estimation, which gives them the concept of rounding by dropping off numbers, you show them that there is a large difference between Front End Estimation and the final answer. Then, based on that skill you teach actual rounding. 391+244 = ~400+~200=600. You’re close to 645. You can also go further. Round only the last number. ~390+250=660, even closer.

You’re looking at this from a “I already know how to do this” standpoint, not from a “I’ve never heard of rounding, just adding, I got marked wrong when the answer was wrong, my rounding answer isn’t correct, why do they want me to do this” standpoint.

It is a staircase. Teach each step and teach multiple ways and your children will thrive.

Kristi says

Or, you could just teach them how to round, which is much simpler and more accurate…

Chris says

And which is what has been done with my children. Do all children fit the same mold when it comes to teaching? The answer is no. So there are different methods for different things.

Kristi says

And, yet, you’re advocating for CCS? Hmm…

Chris says

Did you read my post? You’re completely incapable of higher thought. I explained the point of 2+2=5. If you again choose to argue a different point, you’re just being thick-headed and ignorant.

Kristi says

No, you’re missing the point. I’m an ADULT. Of course I get it. A third grader doesn’t. Please, obviously you haven’t studied child development. You might want to do that.

Chris says

Of course you’re an ADULT. Which completely misses the POINT of the fact that your CHILD IS NOT. You’re missing that this is a step towards teaching rounding. If your child gets it and doesn’t need this step, GREAT! WONDERFUL! Don’t teach them this. How about for the children who need it (My child didn’t, but then, she’s in advanced math for her grades where they don’t teach this simple concept — perhaps the blog writer should consider increasing the challenge for her child)

Kristi says

Except… this isn’t rounding, as has been pointed out repeatedly. If it WAS rounding, the problem would’ve been wrong. You don’t round 291 to 200. This is… front end estimation? I don’t know, we skipped over that because it was stupid and confused my kids, and rightly so. We stuck with true estimation and rounding.

And there, again, is the problem. Teach kids the basics. Don’t overload them with tips and tricks they’re not ready for. Give them a firm foundation first, and the other stuff will come. Tips and tricks should NEVER be the foundation.

Chris says

Except this IS A STEP TOWARDS ROUNDING. Of course it’s not rounding. Learning to type isn’t writing a novel, but it’s a skill that helps you get there (You could of course use a pen and paper, which is a different skill).

Some kids don’t get rounding. This helps those children see what is going on as a foundation. The fact that you believe it’s not a foundation portion is certainly a valid point. I don’t see the value as a parent to Front End Estimation because my kids could skip that and understand rounding. Apparently your kids could as well. Congratulations. Now, because we’re on common core, the kids who don’t get that can be in a class that teaches Front End Estimation, and the kids who can get the advanced math where things are taught at a faster pace to keep challenging the kids.

I’m sorry you felt clearing up the confusion of front end estimation was stupid and confusing. I am also sorry that you gave your kids a lesson that if they don’t understand it they can skip it. I’m sure that lesson will help them in the future.

trisha haas says

Chris, I wanted to clarify that this was taught AFTER rounding in my daughters class. At 8 years old you can imagine that after learning how to properly round this became a very confusing issue and also a “what is the point” issue. As an update to this blog post, I wanted to say that they sent home another work sheet of “front end estimation.”

It is sitting on my desk.

It says 260 + 350 =

_______ + ________ =

The estimated sum is ___________.

Is the answer reasonable? ___________

My daughter has answered:

260 + 350 = 610

___200____ + _300_______ = 500

The estimated sum is _____500______.

Is the answer reasonable? ____ no_______

I can see where she wrote yes first and then erased it and wrote no. She did this exercise in class.

However the answer based on the assignment lesson would technically be yes. The front end estimation is supposed to show her that her answer of 610 is reasonable based on this method of “checking”. All it really did was make her second guess if she got it right.

*head bang*

Kristi says

Rounding is not a difficult concept. Why in the world would you have a “step towards rounding”?? It adds an unnecessary step to a rather simple process.

My kids are not exceptionally gifted. They’re regular kids. And we’ve absolutely had math problems. Most people have. But rounding? That’s never been a problem. It’s a very simple concept.

Chris says

I agree it is an unnecessary process for my kids. I’m not so sure about some others I have seen doing work. It amazes me sometimes how little parents choose to have to do with their kids schooling that the child is unable to take even little steps like rounding. If this gets them there what is the harm to learn this step? If you can understand it and move on, you’ve helped a child who was having issues. If you can skip the step and move on to “proper” rounding, then do that. If this stuff is so easy for the child of the blog poster, why doesn’t she talk to the teacher about moving her child to a higher level math class?

trisha haas says

I also want to respond and say personally we ARE involved in her schooling. That is why, after worksheets and worksheets of fuzzy math, I mentioned something on my blog. We sit with her while she does her homework. She is also required to nightly read and study her spelling words. We are finding that she is spending 2-3 hours of time after school doing additional work, often work they have yet to even go over in the school. This snippet of blog post is only part of the issue that lead up to my complaint. We did have a conference with the instructor about it (which was set up prior to this latest sheet) but came after the blog post.

I am far from an uninvolved parent. That is why I am concerned.

Substitute says

On the whole, I agree with you. This does seem like a good way of introducing students to estimation if you teach rounding after, and give them more accurate ways of estimating an answer. Unfortunately, that doesn’t seem to be the case. The textbook I worked from today talked about rounding first, then front-end estimation.

trisha haas says

I would agree that not having a text book is an issue. In all her years of school we have yet to have text books. We did ask the teacher about that at a conference yesterday and she said that while there ARE text books, they do not let the kids bring them home as they are often lost/ruined. We expressed that we would like a text book so we can see the entire context. Even the homework sheets are torn out of the workbooks and sent home leaving no explanation of prior lessons or what is to come. Our daughters teacher said if we would take responsibility for the book then she can bring them home. We did agree to do that.

Although I have to admit I am afraid of what I may learn.

Chris says

My school has all of their textbooks the students use available online for both student and parent use. Have you asked if the same is available in your school? It also allows us to track our kids homework and to even print out a lesson if our child is sick for a day. I would push for this if it isn’t available in your district. Just vote YES on the budget instead of making them make cuts every year!

Scotia Phillips says

As one of those “x-ray techs who put radiation into people to make pictures”, I can assure you that the “reasonable” answer in this case would cause an error (in my old fashioned method of rounding off) of 20 to 25%. That is unacceptable and is precisely the reason that math is important in all areas of medicine. You are not teaching life skills when you teach this method of estimation, you are teaching that larger errors are reasonable. There are no real world applications of large mathematical errors and this front-end method would not reduce medication or radiation exposure errors.

If the student cannot perform math correctly, he or she should not be allowed to proceed in a specialized field. If that student has not learned basic math, we have a problem with the primary education system in this country.

Mike says

There’s an even larger problem at play going on, and it is a false understanding of the teaching (and possibly a false teaching by teachers of the time) about how English itself works, as descriptive rather than prescriptive. For some reason there is a very widespread belief that a dictionary lists what words unequivocally “mean” as if a dictionary limited the ways in which a word could be used, spelled or pronounced — but it’s just the reverse.

The dictionary is an observation of how ordinary people use words, and compiled as a description (rather than a prescription) of how the largest numbers of people have used a particular word previously, as an instrument to figure out what the speaker/writer might be intending to say. A newspaper describing a murder does not list the limited ways in which a murder may occur, but describes observed details about a murder. Similarly, a dictionary lists the most common contexts in which people have used words, rather than the limited ways in which a word may be used.

When the dictionary is properly used as an assistant to aid in figuring out what someone MIGHT have meant by seeing how others have used a word as a possibility, instead of being used as a legal document explaining the rules of how words are permitted to be used, confusion tend properly tends to result in questioning one’s own first impressions of the statement instead of immediately leaping to fault in the delivery. In my experience, the people who immediately leap to fault in the delivery of information seem to have this “prescriptivist” philosophy about words that completely defies evidence about the nature of English at its deeper elements, and they are completely unconcerned with investigating it.

That said, there appears to be a confusion about the word “reasonable” in this particular article, and “reasonable” is getting thrown around in two completely different contexts — something that is “reasonable” mathematically (which can be argued objectively) is rather different than something one personally finds emotionally/subjectively reasonable.

From what I gathered strictly from the instructions itself, was that problem example is showing something mathematically reasonable (in a logic or true/false sense), whereas 291 becoming 200 is reasonable by comparison to 2000, and in context with doing math quickly, rather than by meticulously calculating. If someone is very quickly adding 291 and 354 and come up an answer more in the ballpark of 2000-3000, rather than the neighborhood of 500-600 because they improperly carried a number to hundreds when it should have been in the tens, then when they can more quickly realize their error by doing the front-end assessment and see that the answer should actually only probably be something more in the 500-600 range.

I think the wording of “reasonable” is instead being treated by the original poster and naysayers as the subjective/emotional “reasonable” in that it is simply an unfamiliar technique from what OP/naysayers were taught to do, and therefore is not “reasonable” for emotional reasons like confusion or uncertainty in why it is necessary.

ducks says

What kind of person would approximate 291as 200? They that in a store and see how far it gets you. This must be Washington D.C. math. No wonder we’re in trouble. I would make the 345 estimate at 350 and the 291 as 300.

Melissa says

^^^^ Not if you’re doing front-end estimation.

Simon says

It is truly upsetting that you are condemning this style of teaching AND spreading your fear and dislike so publicly while you lack understanding of the concept this lesson is teaching.

First, let me clarify a few things:

1. Common Core DOES teach the rounding you are more familiar with. This is a separate skill with its own merit.

2. This is a HIGHLY PRACTICAL skill. It provides a concrete system which provides a “ballpark figure”. It is not intended to provide an accurate solution, simply to be a quick indication of whereabouts the accurate solution can be expected.

3. This skill becomes more relevant LATER in the students’ education. In this scenario, it seems silly to ask the child to do some front end estimation, as the sum is so easily verified. However, in a multi-step word problem many children (and adults) have a tendency to incorrectly use the information provided AND can become lost in algorithms, solving problems without any understanding. This front-end estimation provides a quick “answer check” so the student can verify whether they are on their way towards an accurate solution.

To further address your concerns: Indeed “5 million is not the same as 6.5 millions”, as you so claim. But 5 million is not a terrible estimate for 6.5 million, especially if the estimate can be achieved significantly more quickly than the final sum.

Also, how can you think having MORE tools with which to analyze a mathematical situation is detrimental? Our education system has been following the “teach for the test” algorithm/formula approach for years, and we see where that has gotten us.

This blog has a wide enough reach to impact many concerned parents. Please be more careful in the future before presenting material without some understanding of its value.

My credentials: I am a PhD. in Mathematics, with extensive experience teaching 3rd and 7th grade in public school, as well as teaching Mathematics Education courses at the university level.

tl;dr Don’t be so quick to dismiss something you don’t understand without careful investigation.

trisha haas says

The only reason this blog has a “wide outreach” is because other parents saw this post and agreed with it enough to share it with someone. This is an experience that we all have in common. If I was unique in this opinion the only person that would have read it would have been my parents and friends. Normally this is my small little corner of the web to talk about parenting….which I did here.

Additionally sharing the material we have been sent home time and time again with others is not irresponsible – the MATERIAL is irresponsible. I presented it the exact way it was presented to me.

You may have your opinion on if this is valid and I can have mine. That is the beauty of this country. And I should never ever have to “investigate” 3rd grade math.

Melissa says

Hi! When you communicated with your child’s teacher, what has been her response?

trisha haas says

Actually she was really great about it. She agreed that the methodologies and much of what they are forced to teach now is not what she would prefer to teach. She passed on our name to the woman that is a part of the governing body that decides curriculum for the school so we can get involved. My daughter came home that afternoon with a post it note with the woman’s info and it said she will be reaching out. The teacher also told us the entire class is struggling. I would say for the most part she was really easy to talk to and work with about this. I know she is a product of what the school says she has to teach, so this is not her fault.

Don says

if you were my child’s teacher I would remove them from your classroom. Rounding 291 to 300 is reasonable. rounding it to 200 is anything but. that would make sense. No wonder our school kids are falling so far behind other countries in academics.

Chris says

Did you miss the part where this isn’t ROUNDING? When ROUNDING is taught they will learn ROUNDING. This is a different concept completely called “Front End Estimation”. The merits of which are debatable, but don’t go assuming it’s rounding. Rounding is mentioned 0 times in the example problem.

Roy says

Can we tell those that understand math, the reason for using this type of estimation and those that cannot? It’s pretty clear to me what is going on with this lesson and should not confuse the child…particularly if you explain it to them. The problem here is that many people are making the problem harder than it is, just like the child is. .

Frustrated Teacher says

I am a teacher and I also H.A.T.E. the common core. I feel so bad teaching my students this mess that we are required to teach. The government has no business in our schools. I think the plan is to make sure that our citizens are dumb enough to have to depend of the government….sad state of affairs!

trisha haas says

Thank you for your comment!

Angie Vogt says

I’m getting tired of parents and activists blaming every bas education experience on Common Core. There is nothing in this assignment to suggest it has anything to do with Common Core. I have homeschooled my children and they all attended good Catholic schools as well. I now work for a public school system in a very high performing High School. I see first hand the effects of these new CCS standards and they are wonderful.

The most important thing to know is thatCommon Core is NOT a curriculum. It is a set of standards. This example is from a curriculum book that momdot.com’s local school district or teacher chose. The mom needs to look at what the CCS say about her daughter’s grade level standards for math and then ask the teacher how the hell is this kind of problem is achieving that end. This is a curriculum problem…not a standards problem.

If you want to see grade by grade what the standards are for math, go to the actual source. Here are the standards:

http://ccsstoolbox.agilemind.com/pdf/CCSSI_Math%20Standards.pdf

Rogue Warrior 6 says

High Performance High School… Either it’s a Charter School, or an Oxymoron!

Heather says

I’m going to strongly disagree with you regarding the Common Core Standards not being a curriculum. Whenever you have assessments based on these standards, especially assessments that have high-stakes attached to them, the assessments will drive the curriculum,

This process couldn’t be clearer in NY. Their common core website (engageNY.org) has the curriculum listed by grade, broken into modules and units. It is essentially a script that tells teachers what to teach, how to teach it, when to teach it, and how much time should be spent on each unit. Teacher manuals are printed directly from the site and parents are directed to the website for assistance with homework. This goes well beyond the idea of “standards.”

Sten says

I think the blogger missed the point based on a quick read.

The work being done here wasn’t to get a super accurate answer. The task was to get a very quick estimate on whether a given number was reasonable. I can’t tell you how many times a day I do this kind of super quick estimation in my job. It is necessary, it’s valuable, and sometimes it’s all you need for certain kinds of tasks. The original text writer wasn’t trying to encourage future young adults to “Just pay your bills by estimation method.”

hillplus says

I am OK with estimates, but the estimate should be more like 350 + 300. Much closer and more reasonable estimate. Or if one is rounding, it should be 400 + 300. 300+ 200 is just too far away to be usable.

Simon says

Rounding is taught in addition to this skill. It’s simply an additional technique, adding flexibility to a student’s methods of approach.

Master of Science says

Why teach children an additional approach with “complicated rules” when rounding is faster, simpler, and quicker? Seems like a waste of class time. “Let me try to illustrate some of the problems with this approach by a mundane personal example. Whenever I hear discussions of fairness in education, my automatic response is: “Thank God my teachers were unfair to me when I was a kid growing up in Harlem.” One of these teachers was a lady named Miss Simon, who was from what might be called the General Patton school of education. Every word that we misspelled in class had to be written 50 times– not in class, but in our homework that was due the next morning, on top of all the other homework that she and other teachers loaded onto us. Misspell four or five words and you had quite an evening ahead of you.

Was this fair? Of course not. Like many of the children in Harlem at that time, I came from a family where no one had been educated beyond elementary school. We could not afford to buy books and magazines, like children in more affluent neighborhood schools, so we were far less likely to be familiar with these words that we were required to write 50 times.

But fairness in this cosmic sense was never an option. As noted at the outset, the impossible is not going to be achieved. Nothing that the schools could do would make things fair in this sense. It would have been an irresponsible self-indulgence for them to have pretended to make things fair. Far worse than unfairness is make-believe fairness. Instead, they forced us to meet standards that were harder for us to meet– but far more necessary for us to meet, as these were the main avenues for our escape from poverty.

Many years later, I happened to run into one of my Harlem schoolmates on the streets of San Francisco. He was now a psychiatrist and owned a home and property out in the Napa valley. As we reminisced about the past and caught up on things that had happened to us in between, he mentioned that his various secretaries over the years had commented on the fact that he seldom misspelled a word. My secretaries have made the same comment– but, if they knew Miss Simon, it would be no mystery why we seldom misspelled words.

It so happens that I was a high school dropout. But what I was taught before I dropped out was enough for me to score higher on the verbal SAT than the average Harvard student. That may well have had something to do with my being admitted to Harvard in an era before the concept of “affirmative action” was conceived.

What if our teachers had been imbued with the present-day conception of “fairness”? Clearly we would not have been tested with the same tests and held to standards as other kids in higher-income neighborhoods, whose parents had at least twice as many years of schooling as ours and probably much more than twice as much money. And where would my schoolmate and I have ended up? Perhaps in some half-way house, if we were lucky.

And would that not have been an injustice– to take individuals capable of being independent, self-supporting, and self-directed men and women, with pride in their own achievements, and turn them into dependents, clients, supplicants, mascots? Currently, the Educational Testing Service is adopting minority students as mascots by turning the SAT exams into race-normed instruments to circumvent the growing number of prohibitions against group preferences. The primary purpose of mascots is to symbolize something that makes others feel good. The well-being of the mascot himself is seldom a major consideration.

The argument here is not against real justice or real equality. Both of these things are desirable in themselves, just as immortality may be considered desirable in itself. The only arguments against any of these things is that they are impossible– and the cost of pursuing impossible dreams are not negligible.”

ducks says

AMEN!

Shane says

I think you missed the point regarding “reasonability”. 500 is not a “reasonable” estimate when compared to the correct answer of 645.

354 ~ 350

291 ~ 300

300 + 350 = 650

645 ~ 650

650 would be a much more “reasonable” estimate.

Homer says

You are a moron Sten.

Cindy W says

No the blogger had it spot on – where in the realm of the normal world does 291 “estimate” out to 200? 350 and 300 are better estimates if you are going to estimate.

Patty says

The blogger is COMPLETELY CORRECT!!!! “estimating”.., “rounding off”.., if a number is a 5 or over, you round UP.., if it is 4 or lower, you round DOWN!!! Which simply means the correct ESTIMATED answer would be 400 + 300.., NOT 300 + 200…, Maybe you need a diagram in blue crayon to simplify this concept! If we taught our children REAL math REAL respect, and REAL fear of the natural consequences of their actions.., we wouldn’t have so many “grown” children still living at home with Mommy and Daddy.., and so many “LOST” children, with no concept of self respect in a job well done, or fear of any form of authority, out shooting up our communities!!!!! Too much????

PChem Doc says

As a Research I University Chemistry Lecturer, I teach nearly every single chemistry and chemical engineering major on our campus before they graduate. Front-end rounding may be ‘acceptable’ in many areas, but it is NOT in any way acceptable as presented in this example. I expect my students, at worst, to estimate the answer at 700, at best, 650. I realize this is a 3rd grade problem, but teaching them the worst way to estimate first skews their expectations of what is reasonable. Better than front-end estimations is to take away the calculators and teach them how to round properly and do the sums CORRECTLY and quickly in their heads. My colleagues and I will have a devil of a time undoing these bad habits in 10-12 years. I’m already having to take a quarter of a semester in my LAB courses to teach college seniors how to WRITE. God help us when we have to re-teach them how to add, too. FWIW, I don’t buy the argument that few of these kids will be taking my courses. My point is that even those taking my courses are undereducated late in their college career. We need to encourage them to reach higher not lower. We’ve catered to the lowest common denominator for far too long, and it makes my job harder every year. If the BEST students are underprepared, what can we say about the average and below average students?

Sohailah says

Whether you like front end estimating or not, this is not a problem of COMMON CORE. COMMON CORE is simply a standards tool. Says a 23 year veteran of education – public and private. And as I link my CC standards to my lesson plans, I find them almost identical to the PASS standards that have been in place since 2002. They are a much less bigger deal than people want them to be. And I am a hard-core conservative. Stop blaming what isn’t blameworthy.

Melissa says

Thank you!!!

Jeff Elliott says

I was captain of the math team- you’re way off base. IF you want an estimate, it would have been 350 + 300 for an estimate of 650. THAT is the CORRECT Estimation. I’ll debate anybody for 24 hours a day, seven days a week on this subject matter. 4.0 doesn’t LIE!

Charles says

Sten, doing a quick rough estimate to make sure that your answer is in the ballpark is a great idea. I do it routinely, just about every day. But “rounding 291 down to 200 instead of up to 300 is stupid.

Charity Zierten says

You are witnessing the beginning of the end for America. The fastest track to poverty is the inability to manage money. Only those students educated in private schools would be able to balance a budget, run a company (or our country) – thereby creating a TRUE second-class. Shame, shame, shame on the people who came up with this.

trisha haas says

Interesting theory!

Kev says

This might be the case if those privately educated kids have teachers that can get the concept of estimation over to the kids and the parents trust those teachers enough to let them do it. Where the schooling isn’t so good and the task is left to parents, as you can see from the majority of the comments on here, then the concept will be lost in many cases. The ability to produce hundreds of quick estimates quickly, and understand the consequences, is massively important in business. This method is the simplest and the quickest but not the most accurate – there’s so much a kid can learn by being taught this exercise well.

Sten says

I think the problem was that the point of the exercise was missed by a lot of people. This has nothing to do with “Common Core” being inherently bad or good. This is just simple estimation found inside or outside “Common Core”.

ducks says

and in Washington D.C. and by the mathematically challenged.

Charity Zierten says

I don’t know where you went to school but when I grew up “estimation” was about appropriately rounding up and down. No where in the world does 291 = 200. I could see estimation (correctly taught) as being useful. However, educating a child that 291 is close to 200 sets them up to fail.

Simon says

The style of estimation you are describing IS taught by common core. Front-end estimation is an ADDITIONAL technique, thus providing students with a versatile mathematical arsenal with which to analyze problems.

Master of Science says

Why? You don’t need to estimate anything just add the numbers up and get the right number.

Patty says

HERE – HERE!!!!

Kev says

This is estimation, using a specific type of rounding called front-end rounding. It is the least accurate but the fastest way to quickly generate an estimate. The idea is to get a rough idea of the answer to then compare with the fully calculated result so that you can quickly spot common errors (e.g. a misplaced decimal point). Different types of rounding would give more accurate estimates but they would also take longer and require more effort. This exercise is designed to expose kids to the pros and cons of this type of rounding. If you find yourself with 5 minutes left at the end of an exam, this is the quickest method available for gaining confidence in your answers and spotting which answers you need to revisit. It isn’t the answer you provide to the question, it’s just the quick checker. At 3rd grade level it actually IS the answer to the question, and it’s one of the important concepts they need to grasp. As you must now be aware, it is not an easy concept. Trying to grasp it while their parents are telling them that this is all wrong, because they’ve either forgotten or they learned a different way or their degrees aren’t scientific, means that they might miss the concept.

D

Could do better. Try again.

Sheri says

I am so sorry you actually feel this is acceptable. Yes this is an important concept, but this way of teaching it is not clear. Any child will tell you they are having issues with it. I don’t know one child who is doing well in their grade level with it. And I don’t know one teacher who also doesn’t feel undermined by this “not a part of real life” way of teaching.

Simon says

I’m sorry you don’t understand the value of this lesson.

You shouldn’t speak for “any child”. And here is one teacher who fully supports this technique in addition to the other material taught in common core. This is one of the more “part of real life” skills you will find in a mathematics class (we estimate all the time), and I might further add that teachers who care strictly for the “practical” value of the material they teach might not be the best judges of what students ought to be learning in the first place. Education is about more than “what might I need to get through Tuesday?”

Patty says

Slow and steady wins the race! The guy figuring the estimate the “quick” way for example on a contractors bid.., just lost out on a couple hundred dollars (but that’s just an estimate!!!)

Jennie says

Perhaps a better explaination of “front end” rounding and what it would be used for might have prevented this frustration. I too looked at this the same as the author, rounding 291 to 200 didn’t look right. After reading the explaination by Kev I believe I understand the concept and why it was rounded to 200. I can also see how this could lead to problems down the road for children if they don’t understand when to use it, and that it is not the answer just a quick way to check their answer. Myself I will continue to round the way I was taught as I believe I can do just as quick a check of my answers and obtain a closer estimation for real world applications, such as keeping track of a bank balance while paying my bills.

The teacher needs to explain to the parents who will be helping with homework what is being taught and why. If, as someone else suggested, the teachers don’t understand it that is a whole other problem, can’t teach what you don’t understand.

Barry1156 says

This is just stupid. The answer of 645 is not reasonable, it’s correct. Any other answer is simply wrong. I use estimation when I estimate fees and costs in casual conversation with a potential client (I’m a lawyer). “To file that suit will cost you around $350.00” as I add up the numbers in my head, but I assure you that I will way off if the client sends me a check for that amount. It doesn’t sound like estimation is being taught here, I don’t know what’s being taught but it makes no sense. I’ll admit that I have no elementary school age children anymore, but it seems to me the best thing that you parents can do for your kids, short of homeschooling them, is to help them get through this charade by teaching them how to do real arithmetic. I feel sorry for all of you and your children to be subjected to this nightmare (which, regrettably, will scar your child for life unless you can inoculate your child against this stupidity now).

Lydia says

Typos in math book are common. We were doing the regular state math for most of the nearly 3 years we’ve been homeschooling and there were calculation errors frequently. We are now in a common core book, and the methods (we are in the estimation chapter right now in fact) are proving to be easier to understand. I don’t think errors in textbook proofreading have anything to do specifically with common core, and they were rampant in the “old” textbooks I’ve worked with too. We always took the opportunity to discuss why it was wrong, and what you would do to fix it.

Larry G Smith P.E. says

I graduated from high school with 5 hours of Math, am an Electrical Engineer and have over 40 hours of college math plus the Engineering math. Math is an Exact Subject, it is not an estimated subject. Yes there are problems in the math books, that is WHY the GOOD Math teachers have the book, go through the problems and make the corrections and show the students WHY.

Patty says

I completely agree! This coming from the mother of twin 22 year old stepsons, and a 20 year old stepson! Thank GOD, when they learned NOTHING this way, because their mother was perfectly content with this “bass-ackward” way of teaching, they all get to live with their MOMMY at this age, and not me! I was the “abusive” stepmother who tried to teach them the “old-fashioned ” method! When I had my restaurant, none of them could even count back change if they punched the wrong button on the register (which showed how much change to hand out)!!!

Kris Barrett says

Yes the estimating is wrong in this problem. HOW can the teachers buy into this? They know its wrong. I’m a former teacher.

Watch the movie Idiocracy, it is a foreshadowing of things to come. Warning, it has a lot of offensive language because it has been accepted in the year 2500.

Nat says

It is not wrong. It is a way to check whether or not the calculated result is REASONABLE. Unlike many countries, American students rely heavily on calculators and have machines are always right mentality. It’s important to learn how to use quantitative reasoning. Arithmetic is simple but logic and reasoning are more complicated and need an early start.

paul says

I am a microbiology lab supervisor with a masters in biotechnology and work with people with very varied educational backgrounds. Often, misuse of language leads to confusion, and it is often too apparent that they picked up bad lingual habits from the educational system itself rather than mere colloquial exposure. You response shows the effect of how wrong this is. The calculated result is not reasonable, it is correct. It is the estimation that should be considered reasonable or not, not the answer. The calculated result is the standard, not something to be judged. Additionally, to consider 645 reasonably close to 500 is ridiculous. This kind of backward sum prioritization has dangerous ramifications in lab work, and sadly, even when dealing with pharmaceutical math, departments are beginning to back engineer their results instead of adjusting things on the front end for accuracy.

Kevin Kavanaugh says

This method works well in the kitchen. Not so much for bridge building or moon missions.

trisha haas says

You may not cook much if you think that… 😛

heidi says

This method makes sense to me if I were doing the math problem in my head. I don’t start from the ones place and carry the numbers over in my head. I’d add the hundreds (500), then the tens (640), then the ones (645). Maybe front end estimation is a jump off point for doing addition logically and faster in your head.

Tiffany says

That would make way more sense. I can see where the frustration is coming from but unless you know where it is that these lessons are going, maybe you should ask before getting upset. I asmit when I looked at this blog I was bothered that this is how math was being taught. But after reading your reply the term front end estimation made sense (call it a brain fart) and I could see that if they were going to continue builiding on this then this tactic would make sense. It was untill I was in Trigonometry that I realized that as math got more and more complex it was just anther form of 2+2 really.

I beat the next assignment will be

354+ 291

350 + 290

=640

or something like that. Give them a chance and if you’re concerned about it ask the teacher, that’s what I did.

Brian says

Front-end estimation is a valid and valuable math tool. However, the example cited above uses faulty rounding techniques. The rounded numbers should be 400 and 300 (should have rounded up, rather than down) for a rounded total of 700, which is significantly closer to the true answer of 645 that the example rounded answer of 500.

Kev says

“Front-end” rounding takes the most significant digit, as is, and fills the rest with zeros. Other methods exist and may produce more accurate estimates; however, they are not using front-end rounding.

Trish says

Brian is correct. The example is completely incorrect, and given by someone who doesn’t understand front end rounding/front end estimation. Front-end rounding means rounding the entire number to the highest place in the number, NOT “taking the most significant digit as is and filling the rest with zeros.” Therefore, you find the highest place {hundreds, thousands, ten-thousandths,), then determine whether that number stays the same or goes up one number based on the number immediately to its right. So in the above example, correct front end rounding would have yielded 400 and 300. Whoever taught this example needs to relearn his or her math.

Missie says

Okay, after reading this thread for hours, it seems to me that there’s a lot of misunderstanding. You have the FEE concept where only the ACTUAL front (hence the term front end) numbers are used in the estimation; the rest of the numbers become 0’s. So, it becomes 300 + 200 which is 500. Then you have the rounding concept where you can either take the 354 and round it to 350 or 400 and take the 291 and round it to 300, getting 650 or 700. The misunderstanding is the FEE method isn’t using the rounding concept, only the front end numbers. That being said, it appears, to me at least, that the FEE method is too generalized to really get an accurate estimate. The rounding method seems clearer and gets one closer to the actual answer. I realize it’s important to be able to quickly mentally recognize if you have an egregious mistake, say if you’re using a machine; calculator, cash register, etc… Or providing an estimate; real life applications. And, yes, we do need to challenge our youth to THINK but, my feeling is that the FEE method muddies the waters while the rounding method is rather simple and, again, gets one much closer to the real number. How is FEE superior or even truly useful? How does FEE really support critical thinking? To me, it just confuses things by introducing another, less accurate method of quick calculation/checking. I’ve always had to think a little harder than most people as math doesn’t come easy to me but, I can give correct change from a cash register without using the register but by counting it back, even when someone gives $2.11 for a $1.61 bill. I can calculate a tip in my head and take 25% off that shirt on sale and stay within my budget in the grocery store. Granted, I’m not an engineer and I probably won’t ever build a bridge or design an airplane but how exactly will FEE help one do that? What is the point? I believe it’s just a convoluted method of teaching a simple concept of checking oneself in a simple math problem. Maybe the people who design new curriculum or new teaching methods are overthinking it. I’ve always been a believer in K.I.S.S.- keep it simple , stupid. The fastest way from point a to point b is – and always will be – a straight line.

Laurie says

I would also like to know where you are located. We live in Maryland and the Common Core is just being implemented this year at my daughter’s school but not statewide quite yet.

trisha haas says

I live in Mobile, Alabama

Kimberly Black says

Oh my I am in Foley Al. I am 49 yrs. old, I CRINGE when our little ones come in with math homework, and I will tell you, this “NEW” way is absolute torture to my soul!!!……more frustration than I can describe, I hate not being able to help these children, but I am challenged at regular old fashioned math, how am I ever going to be able to help!!!?????????????? Poor kids get so frustrated with me, and I them, I hate afternoons, a time I used to look forward to. My husband an I are raising my grands, and help with two other grands and my stepson for a grand total of six children, and I can assure you this is not REASONABLE in our house…LOL…..HOWEVER….. I sure am glad to know it’s not just me!!!

Laurie says

Trisha, I feel your frustration. In 3rd grade my daughter was an “A” student and the first one to pass the division exam (one of only 5 in her class that passed the exam all year). In 4th grade she is suddenly a “C” student in simple addition and subtraction because she can calculate the correct sum but not explain how she got the answer using the “Common Core” definition. I received completed homework yesterday where the answer was marked wrong (even though she actually wrote down the CORRECT sum) because she had to “carry the 1” from the tens column to the 100s column. The teacher didn’t accept her explanation of what the carried-over 1 represented and told her what the correct explanation should have been. This is a direct quote from the teacher, “Because 50 + 80 = 100….” WHAT?!?!? I have two college degrees and I still don’t understand how 50 + 80 = 100. If *I* can’t understand it, how am I supposed to help my daughter with her homework?

Kathryn Crisci says

We are in the same boat ! I received an instructional video from the teacher via email, so that we could “teach” the method at home. I was equally as confused as you during a section in which the teacher said ( and wrote ) that 8 X 14 = 352…..and continued to repeat it throughout her instruction. Both my husband and I kept asking ourselves ( and each other! ) WHERE she got 14 from….8 X 44 = 352 ….certainly NOT 8 X 14….but to not even notice yourself writing and saying it…OVER AND OVER ?

LW says

It isn’t “carrying over” any longer (as I am constantly reminded by the kids) its “regrouping.”

Elmer Arbogast says

I hope that our kids are not being taught like this. However with the state of our public education is they properly are. I will expand to expose the problem with this method. What if you were remodeling your house and you need 291 plus 354 of a item that cost $18.00. You have to make a decision quickly so you estimate. Uses the method they are teaching in common core you would estimate (200+300) * 10 = $5000.00. If you estimate it properly you would estimate (300 + 400) * 20 = $14,000.00. The actual answer is $11,610.00. Clearly you can see the issues that teaching our kids this way will create later in life. If this is truly a common core teaching it needs to be fixed or this program needs to be eliminated.

Sandi Whisnant says

I was shocked the first time I saw this type of example of “math education” …….OK I was shocked the first few times. We still joke about estimation, guesstimation, and consensus when we run low on an ingredient in the kitchen, for example, and I proclaim that indeed there are 3 1/2 tablespoons in 1/2 cup, “right?”…

My point is: it’s in the ball park; it’s close. You have a starting point. The teaching of the concepts doesn’t stop here. My 15 year old has always been in public schools. She was made for it. She has thrived there. She is in THE best Charter public school in North Carolina or anywhere! My 12 year old is home schooled and this is where she thrives. She may spend her high school years at Gray Stone Day School with her sister. They teach Common Core Math there. I had many migraines last year until “I” finally got it. We still joke about it at home, but the homeschooling mama with the Physics degree has learned to let 3 1/2 tablespoons be 1/2 cup of butter if that is all you have because it is close enough. Who says you’ll never use this stuff in real life……………..?

Joanne Yurchak says

Whoever thinks there are 3 1/2 T in one cup has NEVER cooked. Better be careful. There are 3 1/2 T in 1/4 c — 16 T in ONE cup. This isn’t an estimation; this is an ERROR! Better warn people going to dinner at your house!

Sandi Whisnant says

You adjust the recipe you moron

Sandra says

I use front-end estimation ALL THE TIME, I just didn’t realize what it was called. I do not remember when I learned it either. I use it at the supermarket for a fast calculation of what I am purchasing, I use it when I am comparing prices between items, I use it when I compare what amounts of something I have on hand compared to what I really need to get an idea if I have enough or need more. When it comes time to do an exact calculation…I do that then.

Now that I have a clearer understanding of what the intention of front-end estimation IS, I cannot imagine NOT teaching it to kids. HOWEVER, the context is everything. I was not in the class, I don’t know what the context was.

DougV says

Sandra:

The point (in my opinion) isn’t that front-end estimation is bad, it’s the way this example shows it. When you do your estimation, and you have an item that is $4.95, do you do your estimation using 4 or 5? Using the technique shown here, if you had $9, and you had two items, one that is $4.95 and one that is $5.75, you would think you had enough money, only to find out (embarrassingly so, perhaps) at the register that you were almost $2 short. Teach estimation, but teach rounding, too.

Daniel says

The definition of”reasonable” in math and engineering is within an order of magnitude.

These are good skills to be teaching and I have a feeling that this worksheet isn’t handed out without explanation.

Nicole says

My mom teaches middle school math, and says one of her biggest issues is kids not knowing if the answer they have reached is reasonable. The kids just do not have the math sense to understand when they are *really wrong*. Which becomes important when you bring in the calculators, which of course need to be brought in once you start dealing with irrational numbers and algebraic equations, which are now introduced in middle school (when I was in school, where we did it the ‘traditional way’, we didn’t get algebra until high school)

I’ve helped my third grade brother with his math homework. It was a lot like this. At the top it would say

show 645+418

And then below it it said

Start with 600+400

So basically, it wanted the kids to do something like 600+400=1000, 40+10=50, 5+8=13 (which is about how I’d do it mentally), so 645+418=1063. After that it had problems like “start with 45+18” and “start with 600+418”. That ‘fuzzy’ math involved a great deal more reasoning understanding of math than just doing 645+418 via the traditional algorithm. The ‘fuzzy’ math both of my brothers bring home generally challenges them more than the traditional math (which they also bring home- it’s about half and half).

Eric Ashley says

Front end calculation is useful but would you estimate a gallon of milk that cost 2.91 as two dollars? Hardly, you’d estimate it as three dollars.

Besides, estimation is better taught, IMO, after learning basic addition.

Kimberly Black says

YES!!!!!…they have got to be able to do basics addition, that is exactly my point!!! These little third grade children do not understand the concept if they don’t already know what simple addition of numbers is, PLEASE DO NOT pass them on up, have them feeling humiliated because they feel stupid, in front of the child in second grade that is already almost ahead of the child in third grade, due to early teaching in another school!!!!….I’m sure I cannot be the only one that is seeing this, and that humiliation will definitely scarrrrrrr, and hinder the learning process, I am a prime example, schooled in Southern Ms. Al., moved to Texas in the seventh grade, SCARRED by feeling DUMB!!

Keith says

We used to call it “rounding” back when real math was taught in school. Front end estimation sounds like a lot of the dumbed down math techniques my kids were getting from their public school, and is one (of many) reasons they are out of that teaching environment. Front end estimation is not a suitable substitution for rounding, and I had to re-train my kids constantly so they actually knew how to perform addition (beyond single digits) and division without resorting to this type of “trick.”

Albert says

Your brain is broken.

Elane says

I am not a common core fan but like to check my resources. Do you have the name and publisher of the book you got this out of?

trisha haas says

They dont send home books. This is a worksheet that was sent home as school work. I just scanned in the sample problem. They dont send home books or workbooks in Elementary school anymore (which is part of the problem). They tear out sheets and assign them. She has turned it in already but often brings completed work home. Ill see if its here and has a number on the bottom.

trisha haas says

Nope, I do not have it here, but when Charlotte gets home from school, I’ll check her bag for a current worksheet. Chances are it all comes from the same book. I’ll get back to you this afternoon.

Mary says

Textbooks are available online and often publishers will send you an exam copy if you request it. Ask the teacher for the title and publisher and save your readers the negative tone of your blog-chances are they might not be fans of CC because they keep hearing the “I hate” buzz. Have you communicated your feelings about common core to your daughter’s teacher or become involved if your school has PTA or Site Group? A negative attitude will not help your daughter learn. Common Core is also aligned with Next Generation Science Standards so if you are convinced that you don’t like the math, you may also be poisoning the well for additional changes headed your way. Other children and work in and out of the home may preclude a level of involvement that would help you find answers-good luck in your quest.

trisha haas says

Yes, we had a conference with her. This is a personal blog and my daughter doesn’t read it (or surf the internet) and is a parenting and adult outlet. This was the “last straw” of a stream of bad math coming through our hands. I have reached out to many people prior and this scan was just another example that evening when I was fed up teaching (what I feel) should not be taught. My blog is not a political outcry, it is a parenting outcry.

We already had a meeting set up with our school prior to this paper (which was yesterday morning) and our teacher was very receptive during that meeting. She agreed that the math and much of the way the materials are being taught is unacceptable. She is a product of the state and is as frustrated as we are. She sent home the information for us to be involved in curriculum choosing and we have a follow up with that adviser. I am not a “complainer”, I am a “doer” as well. We are not negative in our household, but its fair to show this material to other parents for feed back.

I am clearly not the only parent that realizes this is the wrong direction.

JDNappers says

“Estimation is Guesstimation”. That’s what my math teachers taught me. They taught me to find the correct answer, not to piddle around with guessing games till I happened across the correct one. We did math drill worksheets constantly to hone our basic ASMD skills.

Andrew says

I disagree. Estimation/guesstimation is a skill unto itself, and has its own adult real-world applications. I think it’s important for children to learn both how to solve math problems AND how to estimate (properly, of course!) the answers.

Theron says

reason# 513 Why we home school.

Anastasia @ eco-babyz says

Wow, ridiculous doesn’t begin to describe it. I’m glad we’re going out of our way to homeschool and teach our kids normal math skills they’ll actually use in life. I guess it’s a bonus they will not be stuck in a classroom with their nose in a textbook for 12 years, the world is our classroom and there is so much more to learn and see than any school could ever hope to teach. We like the student/teacher ratio! 🙂

cori says

Omg. Mom of special needs child

Omg this is our second time in second grade

I cannot understand how to do this. The teacher said it is wring. I asked to meet het to discuss in a meeting

She has no time

This is not a concept he understands and telling the answer means nothing

Why do they want to make the kids feel even more insecure

Just asking

Dawn Blaus says

I know this is confusing – but just to clarify; this is not a “new” common core concept. We have been teaching different strategies for estimating for as long as I can remember. Front-end estimation and rounding are both estimation techniques to check for reasonableness of an answer. Estimation is essential in developing number sense, which is the foundation for mathematical thinking.

L. Carlon says

Thank you, Dawn! I was wanting to clarify the same thing as I was reading through this post. As you stated, this has nothing to do with Common Core. In fact, as an educator for many years, I am impressed with the ways that our math instruction has developed and advanced. Many of the new techniques, while challenging at first for those of us who learned so differently, are excellent in developing proper number sense and better (much-needed) mathematical thinking skills in students.

ann says

So what your saying is “those of us who learned so differently” are mathematically stupid? You know all those people who are adults right now and are doctors, lawyers, scientists, teachers, engineers, oh hell…how about Bill gates and Arne Duncan since they love Common Core so much? And I guess that would include yourself?

Michael Paul Goldenberg says

@Ann: I don’t hear people saying that. There’s a huge difference between “stupid” and “closed-minded.” Intelligent people can readily be the latter.

I know this will shock many people here, but I am a consistent, vehement critic of the CCSS INITIATIVE. I emphasize that last word to stress that my focus is on the overall game plan of the Common Core, and its intimate connections to high-stakes tests, Race to the Top (which should be declared unconstitutional), and the big disaster capitalist agenda.

But that does not mean that everything in the math and literacy standards is wrong. Trying to get people to step back and separate the wheat from the chaff, however, is well-nigh impossible when people go into a “feeding frenzy” as is happening now, and rejecting anything and everything they associate with Common Core. First, there IS NO COMMON CORE MATH. Only a set of overall practice standards for teachers (most of which I happen to agree with, and have agreed with since 1989, when they were laid out in the first of several volumes from the National Council of Teachers of Mathematics, an independent association of mathematics teachers, teacher educators, researchers, etc., that has been around since the 1920s and has no political affiliation), and content standards, which I and many others probably take issue with parts of, but no knowledgeable person can argue that anything in them is new to mathematics or not in fact mathematics. We might argue that some of these specific standards have been placed too far down the grade band. Some might argue that there are things missing from them we’d like to see (e.g., anything from discrete mathematics). Some, like Stanford mathematician, educational conservative, and harsh critic of anything innovative in K-12 math teaching – R. James Milgram – might argue that these content standards aren’t “rigorous” enough (which might drive parents whose 6 y.o.s are lost in the dust a little crazy given that it seems like there are topics in K-5 math now that many of us didn’t learn until 1-5 years later, and yet we managed to not only take high school mathematics for 4 years, but have done quite a bit more mathematics thereafter). I think Milgram is an elitist who couldn’t care less about anyone not on the fast track for a Ph.D in mathematics, physics, engineering, etc., but the point worth noting is that the criticism of the content standards is in itself contradictory when looked at from a neutral perspective: it’s too hard, it’s too easy – gee, folks, make up your minds!

But none of what is in the CCSS-Math is in itself curriculum. We see some questionable stuff coming out from PUBLISHERS (and in the case of Engage-NY, from a partnership between a state and publishers). But that’s a different kettle of fish entirely, and I see virtually nothing that isn’t mathematically sound.

Reading the reactions to this issue of front-end estimation both here and in many other places, just as an example, what I’m hearing is a combination of some ignorance (not everyone has done well even with “traditional” mathematics instruction and materials), but a lot more pointed, willful rejection of anything that is unfamiliar or that asks that kids look at things flexibly and from different perspectives. I guess that sounds too seditious to some people. Math is supposed to be all about one right answer, one right method, one outcome, right?

In fact, that’s untrue. Sure, if the question is What is the sum of 2 + 3? (assuming we are in base 10, dealing with real numbers, etc.) there’s only one correct final answer. The sum is 5, not any other number (except that 4.999. . . . , which is the same as 5, as is 5/1, 10/2, etc., -5/-1, . . . and many other ways to represent the correct sum. Uh, oh.

But while most adults know on sight that 2 + 3 = 5, a very young child might not know that. But she might reason that 2 + 2 = 4 and that “one more than 4” is 5. It takes longer to write that to think that through if you know those two closely related facts, and teachers are being asked to help students see arithmetic more fluidly and flexibly to help increase facility and understanding. Such an approach links very naturally to ideas in algebra, and it is NOT beyond the capacity of most young children to think this way. But if their parents throw hissy fits because it’s not something they were ever taught or asked to think about, that is going to cause a lot of conflict for those children. If the parents rail against the teacher, the math, and everything else that isn’t just the way they were taught, that is going to severely undermine the student’s willingness to learn anything from the teacher. (“My dad says you don’t know math and I don’t have to learn this stuff”).

This fight isn’t new. It’s not peculiar to the Common Core. But it has gained new impetus from a lot of politicized issues connected in no small part to hatred of that melanin-ridden (that’s a joke, son) fellow in the Oval Office, and the latest wave of cultural conservatism. A year or so ago, you heard very little from the political Right about the Common Core or anything connected with it. But having failed to bring down a hated president with: Benghazi, Affordable Health Care, birth certificates, Bill Ayers, Rev. Jeremiah Wright, fist-bumps, Fast and Furious, ad nauseam, education has suddenly emerged as another chance to attack him. And for progressives like me, education has been a key, if not THE key issue since 2009 we’ve been critical of Obama over. Nice of the Tea Party to wake up in 2013, but I’m afraid that most of their criticism is ill-motivated and poorly grounded. It’s another scatter-gun attack in which truth is irrelevant.

I can’t sit here and be quiet while people attack sensible ideas merely because we may all agree that there are very serious problems with Obama’s entire educational agenda, particularly given that some of us have been critical of this agenda for 30 years, as it is a bipartisan, corporate/billionaire-funded effort to privatize public education for profit, NOT to improve a damned thing about teaching or learning. Obama and Arne “Dimwit” Duncan will be gone in Jan. 2017, but these ridiculous efforts to use high-stakes testing to kill public education will continue as long as Congress remains a wholly-owned subsidiary of the Koch Brothers, the Coors Family, the Gates Foundation, the Walton Foundation, the Broad Foundation, and so on. They are the really enemy, and their main motive is profit. Wake up before it’s too late.

Or don’t. If and when the Common Core is defeated, what will you replace it with? “Back to Basics” is the most frequent chant. But we’ve done that, repeatedly so, and it has failed every time. The “better ideas” I keep hearing are not backed by real evidence, but rather fond nostalgia for a Golden Age of education that never existed in the real United States, at least not in the past 125 years or so.

So by all means: homeschool your children. Of course, you’d best be careful that you or your partner or someone your family can rely upon is sufficiently competent in the wide range of subjects most people want their kids to learn that the children aren’t left with unreasonable blanks due to parents who “aren’t good at,” say, math. Or who use the A Beka home-schooling materials which proclaim in part:

” Unlike the “modern math” theorists, who believe that mathematics is a creation of man and thus arbitrary and relative, A Beka Book teaches that the laws of mathematics are a creation of God and thus absolute. Man’s task is to search out and make use of the laws of the universe, both scientific and mathematical.

“A Beka Book provides attractive, legible, and workable traditional mathematics texts that are not burdened with modern theories such as set theory.”

Good luck with that if you ever hope to learn any higher mathematics. That darned set theory stuff, unholy as it may be, seems to crop up in the introductory sections of pretty much 90% of the undergraduate math books past basic calculus. I hadn’t realized until bumping in A Beka last year that mathematicians, too, are part of the vast anti-Christian conspiracy!

Dave Paisley says

So why has actual math achievement been plummeting?

Sara says

Thank you for being the voice of reason and facts here. Front-End Estimation has been around FAR longer than common core, and is in fact a basic math principle. We just don’t see it often, and so it is easy for her to use this to stir up angry parents. I am not saying common core is great, but facts should be checked by the author before using them to argue a position. Perhaps she should spend some time doing the worksheet.

Dave Paisley says

Typical bullshit educator arrogance. What’s your evidence that any of your new math education principles actually work in real life – i.e. outcomes 20+ years downstream? They’ll be just like the old new math – all theory and no substance.

And did you ever think that parents (you know, those engineers, doctors and lawyers) would actually be educational allies, rather than continually churning to new and unproven methods that confuse everybody outside the pedagogical echo chamber?

Oh wait, those people probably send their kids to private schools that use methods that actually work. Pity the poor public school students (and parents) who have to live with his crap.

Jill says

Gee Dave, could be that the parents of kids that send their kids to private schools also have more time to spend with their children. Could be that the poor public school kids live in poverty, go to school hungry, come home to empty homes because their parents work to support them. Could be the kid failing math has a dad in jail and a drug addicted mom and is so full of anger he can’t get anything done. Could be kids don’t understand their math homework because mommy and daddy grab the paper from their hands and tell them what to do so why bother paying attention. Could be your “typical bullshit educator arrogance” is some serious pot meeting the kettle (minus the educator part). And could be that none of this has anything to do with front end estimation, which has been around for a very long time, or whether or not kids are smart enough to learn if we let them.

Master of Science says

“There’s nothing that does so much harm as good intentions.” — Dr. Milton Friedman

“Of all ignorance, the ignorance of the educated is the most dangerous. Not only are educated people likely to have more influence, they are the last people to suspect that they don’t know what they are talking about when they go outside their narrow fields.” — Thomas Sowell

“The study of history is a powerful antidote to contemporary arrogance. It is humbling to discover how many of our glib assumptions, which seem to us noble and plausible, have been tested before, not once but many times and in innumerable guises; and discovered to be, at great human cost, wholly false.” — Paul Johnson

“One of the surprising privileges of intellectuals is that they are free to be scandalously asinine without harming their reputations.” — Eric Hoffer

“The Left is very good at articulation. They do a better job of explaining away failure than the people on the other side do of explaining success.” Tomas Sowell

Jessica says

I left a comment, but don’t see it. Sorry if it reposts, but I think it’s important.

Being a middle school math teacher and trying to teach long division with multiple numbers, this method is great. The reason why is because instead of guessing and multiplying every single number to figure out how many times 84 goes into 759, you can use front end estimation. Example, 80 goes into 800 how many times? 10, we know we can’t use 10, so try 9. Then they multiply 84 times 9 and see if it works. It gives them a starting point. It really makes division sooooo much easier. Without explaining why the need for this is important, parents don’t understand the use of it. I hope this helps. I don’t agree with a few things for common core, but this method was out way before common core.

Also, when I do teach my kids this method, they have to know when to use this estimation as a reasonable estimate. Ex. The problem you pose, is this reasonable for knowing how much money you need to take with you when you go grocery shopping? The students then have to explain to me that it is not a reasonable estimate because they would not have enough money. If they were to use it to help the solve a multi digit division problem, then it is a reasonable estimate because its a starting point an not an exact answer they need. I really hope this helps!!!

trisha haas says

Jessica, new commenters go into a holding system for admin approval in case its spam (happens a lot) so both comments have now been approved. Sorry about that!

Kelli says

I get WHY estimation is important, but I think we are all asking why they round everything down? I homeschool my 7 year old in 2nd grade math and she gets the concept of when to go up and when to go down. It took her all of 2-3 days to master this. You actually get closer to the number, when applying this method to division, if you round correctly. Just my 2 cents.

Samantha says

The problem is not that they’re teaching estimating, it is that they are teaching it wrong. 291 rounds to 300. It isn’t closer to 200. It is closer to 300. If you are going to the grocery store and need to know how close you are to your budgeted amount, then rounding to a further away number, especially a lower number, will not help you at all. I’m a math teacher and yes, we’ve taught estimating as a means of roughly predicting the answer to your problem for a long time. But we didn’t teach it this way.

My next point is: WHY is a parent at home being asked to teach her child math??? Math should be taught by the TEACHER and the child should be sent home to practice the skills being taught. If you are going to expect the parent to teach the concept, then you need to send home resources for the parent to learn the concept and method so they can be helpful to the child. I have always preferred that my students’ parents NOT help with math homework because when I check it the next day I want to be able to see if the child has understood the concept. If they bring in a perfect paper I don’t know if the child gets it or if they just had a lot of good “help” if the parent was doing it with them. Most parents aren’t good at helping without over-helping.

Sue Hanson says

Of course you have to estimate, but proper estimation is required and I don’t think it should be made into such a big part of the process. I’m 67 years old and back when I went to school, we learned our sums and basic multiplication, so had a good basis for making estimations. I think there is way too much complexity put into math these days. Math is not uncertain. It’s right or it’s wrong and, in elementary school math, it’s simple and straightforward.

David Helm says

Jessica, when I was a kid, we were taught the multiplication tables. When you know these, division is very easy because you automatically know that 7 goes into 84 twelve times. The problem as I see it is that the basics are not taught so there is no foundation to do the work.

Lee says

Back in the late 80’s, I was banned from my little brothers school because I went and questioned them about their math curriculum. It was simple division, but you weren’t supposed to do the problem. The instructions literally were “Guesstimate to the nearest 10.”

Neal Clayton says

Stupider isn’t a word.

Are you sure you have degrees?

trisha haas says

Um, Neal, that is the point. It isn’t a word.

Kenda says

It was a joke. Are you sure you have a sense of humor?

Laura (Got Chocolate) says

DON’T FIX IT IF IT AIN’T BROKE!!!

Dan says

It is broke.

Master of Science says

http://www.amazon.com/Inside-American-Education-Thomas-Sowell/dp/0743254082

Josh Ripper says

The reason they do this to get kids to start thinking about, “is what I’m seeing a reasonable answer for this problem”.

I have a BS in mathematics and I know many people when doing applied math questions simply compute and hope their computations are correct. But you really need to see if that answer makes any sense at all. This is just starting that mentality at an earlier age. Sure the poor rounding gives a large error margin, but that’s not the point.

Wesley Takahashi says

I got to agree with Josh on this one. I do this when I do quick mental math. Say 400 and 300 = 700 and you know it’s a bit less as you rounded up to 400. Then 650 or so is a quick answer to come up with.

Wendy says

Bullshit, excuse my language, but it is what it is…. Reasonable answer for this problem, what about the correct answer for the problem… You teach these kids this way of thinking how will, that improve there way of thinking for the real world… I know if in the position I work when it comes time to do monthly balancing if I do my books according to this math… My boss wouldn’t be too happy, and I would be fired.

Daniel says

Wendy, this isn’t about a final answer. The point is you have to do both. It’s a way of double checking your answers.

I’m an engineer, and most math mistakes will put you off by several orders of magnitude. “Reasonable” is used to refer to answers within one order of magnitude. So using this method, you can see if you’re within that one order of magnitude range.

And, if you bothered to look, you’d see that you still have to compute the correct answer as well. It’s teaching two different skills.

Ask any engineer in the country how important estimation is and you’ll see that this is a good skill to be teaching, especially if it means that kids will constantly be mentally checking the order of magnitude of problems.

Angela says

Yes, the example you gave makes sense and is reasonable. I would do that kind of thing mentally as well. Their example is ridiculous and unreasonable and going to confuse children.

Kristie says

I understand that, but why round down. I have noticed I round up in life way more than down. 700 is a more reasonable answer than 500 in my mind.

chris says

This common core strategy is absolutely bogus. My thid grade daughter is having a very hard time with this form of critical thinking. Its a complete waste of time. I disregard any common core lessons and teach my kidsthe proper methods which have been the norm for ages… I then write on homework worksheet in capital letters… STUPID,STUPID,STUPID! I suggest every parent do the same while at same time expressing to children the ignorance of school boards nation wide and the clear neglect that has been formed due to greed and capitalism trying to negate the and control the future with failed knowledge which will dumb down our nations society.

Jeff says

I’m with you Chris, and all the others that think ‘Common Core’ is STUPID STUPID STUPID! The way I was taught math, back in the 70’s, worked for hundreds of year. This crap doesn’t work AT ALL!

Jessica says

Being a middle school math teacher and trying to teach long division with multiple numbers, this method is great. The reason why is because instead of guessing and multiplying every single number to figure out how many times 84 goes into 759, you can use front end estimation. Example, 80 goes into 800 how many times? 10, we know we can’t use 10, so try 9. Then they multiply 84 times 9 and see if it works. It gives them a starting point. It really makes division sooooo much easier. Without explaining why the need for this is important, parents don’t understand the use of it. I hope this helps. I don’t agree with a few things for common core, but this method was out way before common core.

Samantha says

Yes, but using the method here, you would ask how many times does 80 go into 700 and your guess would be 8 and you would have to try again. 80 into 800 makes more sense, hence proving the point of the author.

Sandra says

Children have been taught estimating for decades. What adult does not use it as well. This is NOT a common core strategy, but an important math skill. To me, it is a poorly written example for practicing. That is a problem that rests with the publishing company.

Erin says

I have a 4th grader who also struggles with some of these math tactics. I can agree with the teachers who say that estimation is a good skill to have. I think where we are getting off track is with the age these skills are taught. We need to look at the developmental stages and ages of children more closely and match that up with the critical thinking skills being taught! Things that were difficult for my child last year in third grade may be fine to teach this year or next year.

Samantha says

Yes! Exactly! If you look at the stages of development for critical thinking skills, there is a threshold when things should be expected and that is IF a child is on the expected development track. I think that they are introducing things earlier and earlier and discounting the point at which the logical thinking stage begins and other important markers. Sure, some kids will get it early, but most will be confused and frustrated and I think that just sets them back further.

DrBilbo says

I have to wonder about your grasp of some simple facts. “Common Core” and other failed pedagogical innovations are the direct result of socialism, not capitalism. Our GOVERNMENT schools are models of top-heavy bureacratic inefficiency and social engineering and control. Economic freedom (capitalism) is the solution to our educational and ideological woes.

Camela Giraud says

If anything is going to undermine our system of education, Chris, it will be parents like you who undermine learning and belittle educators. You are setting your child up to be a miserable student, unhappy and distrustful of the system she must navigate. I can think of no bigger impediment to learning. Not to mention the fine job you are doing of teaching her how to disregard authority. Great preparation for the world of work. Ultimately, your child’s failures in school and work will have much to do with YOU!

Catherine says

ummm…. did you read other peoples posts that are saying their kids are saying a book that cost $9.95 would mean they only have to pay $9 for the book??? do you get that we adults have not learned this in school and can not understand it ourselves. do you know how many people their are in this country that now have to re learn some kind of math just so they can try and help their child. i am so sick of people trying to change everything.. i feel for these families and their kids. i dont know anyone who learned it this way at all. no offense to you, but this is bull.

Ryan L. Natschke says

This is third grade homework, they have to understand how to add, subtract, multiply, and then divide before they can be taught more steps to screw up what they were already taught. I have to spend literally HOURS every night helping my daughter do her homework. She has been a straight A student, tests well above her grade level, yet this crap has her completely confused, and she is now getting a C in math because of it. She is marked wrong for having the RIGHT answer simply because she did not get it how the Common Core teaches it. That is absolutely WRONG! Common Core testing has been developed by Linda Darling Hammond. If you don’t know who she is, look her up. She is a radical progressive, and partner of Domestic Terrorist, and Obama mentor Bill Ayers. It needs to be stopped.

Bill Pinson says

Maybe they should use this type of math when paying the morons who come up with this crap, 55,000 per year should be rounded to 30,000, that would be reasonable.

escowler says

A couple of things: first, this is not a specific common core standard but a means to an end of teaching children what estimation means. Front end estimation has been around forever just like most other estimation methods. Second, it comes in a series of lessons that help kids learn the value and purpose of an estimate. When a particular lesson like this one is taken out of context, it appears to be stupid but if you saw the series you’d think, “Wow, I wish they taught it to me that way.” The front end method is used to help with place value, to teach the “ballpark” idea, then the idea of a “good estimate” vs “just an estimate” then to work with the remaining digits to adjust an estimate (which, incidentally, builds number sense and more place value) and finally helps the kids move on to rounding, compatible numbers, and adjusting/compensating. Common Core is simply a list of standards–it’s not much different that any other list we’ve had except that it is more grounded in conceptual development. It takes time to build concepts and for teachers to adjust to the new (actually old school) way of doing things.

Samantha says

So you teach a wrong method of estimating. Then next year you teach a somewhat less wrong method of estimating. Then somewhere down the line you change the rules again and maybe get around to the correct method of estimating? When I was in school, we were taught the correct method of estimating when we were developmentally ready to estimate. But when we were young and not at the developmental stage that we were ready for it, we weren’t confused by a bunch of equivocation. They just taught us good, basic, concrete operations and saved the estimating for the day when we were mature enough to do it right the first time.

escowler says

This is not a “wrong” method but simply another method that leads to greater learning through conceptual development. It’s based heavily in number sense and place value and is the first step in helping children to developmentally understand a difficult concept. The structure has been used for 50 years–it’s not new or radical. The series of lessons that includes this one is done in one unit, not over several years BUT estimate skills are honed year after year so that the children become stronger over time with greater numbers and more complicated situations.

Dawn W. says

Thank you for this explanation. Nicely put and explains it well!

And, for those complaining about “new” math, at 46 years old, I have heard the term “new math” more than once in my lifetime. So, I hope you realize that the methodology used to teach math concepts to you, were most likely different than those used to teach your parents, and certainly different than those used to teach their parents. Actually, all three of my children (ages 21, 14 and 10) have each been taught different methodologies (from each other) at some point during their school years, and all three adjusted – as have I.

I do agree with others that the example given on the worksheet is poorly written, though.

ann says

They are a list of standards yes but they are not developmentally age appropriate in many cases. Look up what child psychologists during are saying about it. Did you know there was a joint statement from 500 early childhood experts who warned about the developmentally inappropriateness of them during the validation process? Standards are a fine idea but they have to be age appropriate. period. They have to follow the right order. period. You cannot teach children to think critically about something before they understand the basics of it. Have you read the standards? You can find those online too. When you have read them then you can make a better estimation on whether or not they are a reasonable.

escowler says

This is not a “wrong” method but simply another method that leads to greater learning through conceptual development. It’s based heavily in number sense and place value and is the first step in helping children to developmentally understand a difficult concept. The structure has been used for 50 years–it’s not new or radical. The series of lessons that includes this one is done in one unit, not over several years BUT estimate skills are honed year after year so that the children become stronger over time with greater numbers and more complicated situations.

Joe Drager says

What BS; the only “reasonable” answer to a math problem is the correct answer.

Jason S says

The concept of approximating the answer, to know if one is reasonably close is actually a good one. Many of us do that anyway without even thinking about it. We do it at grocery stores to keep some idea of how much we are spending, etc. The only real “issue” here would seem to be the rounding down from 291 to 200, where common sense would suggest that rounding up by 9 makes infinite more sense than down by 91…

When “rounding numbers”, going to the “nearest hundred” is much more logical for such a purpose, teaching third graders otherwise, will require UN-teaching that at a later date…

Susan Gill says

But then what is the point? Why would anyone want students to consider a math answer reasonable ? The answer is either right or wrong. When you start thinking that all these estimates are correct or reasonable , then you drift far away from the objectivity of absolutes. Maybe that is exactly the point.

David Modeste says

Just one other quick comment to add to what I said earlier. I noticed that many commenters either ignored or didn’t noti ce that the way the problem is stated its really 2 problems. The first part is actually doing the addition to get the answer 645. The second part is demontrating that you know how to check that your answer is right by another method “rounding” to be specific. Some people did mention that it may have been better to round to 400 + 300 to get 700 which is also close to 645 and would show that you were in the right ball-park… Question is which rounding approach is better for third graders…

Thearica Burroughs says

What is wrong with the way “rounding” has been taught for many years… less than 50 round to the hundred before… higher than 50, round to the next 100.

Susan Gill says

Yes, we all learned how to estimate. But you simply cannot take these numbers and round them off to the nearest hundred and say the answers actual and estimate are reasonable conclusions. They are very far apart and would not be practical. Yes, the first answer is the real one, but it does not say that. It says it is REASONABLE. The word reasonable means you have given it some thought and it makes sense. In reality, the answer is RIGHT. It seems to me that beneath all of these machinations, there is an effort to eliminate the word “right” and the word, “wrong.”

Mark Halpert says

I teach kids math, and the new stuff is enough to drive a student, a parent and a teacher crazy. There may be an explanation for how this builds critical thinking skills. but first one should examine the question “Does this stuff really make sense”

Tough to teach someone to round 291 to 200 under any circumstances — take the number halfway between 200 and 300 – if it is 250 or above round to 300 and 249 or less round to 200. A 3rd grader can understand that — and you will not have to reteach them how to estimate properly later — if that is not true, wait till the students are old enough to be taught how to estimate correctly

Alex F says

except that you are not teaching rounding, you are teaching estimating. Estimating by definition is only a starting point and not the final destination. I use this approach with my beginning students and my calculus students.

Sandra says

It is not a reasonable estimate for a final sum. It is confusing to estimate 500 and the sum equal 645. What shouldn’t basic “rounding” be a step in estimating? When did that change?

Catherine says

It is called Front End Estimation. I don’t prefer it, but it appears in Math textbooks as a strategy to be taught. It’s in my 4th grade Harcourt book. It’s a strategy. Don’t miss the importance of teaching the students to ask if their math answer is reasonable. The problem you posted is not easy for all students, and using the front end estimation to compare with the sum they got helps them to evaluate the reasonableness of their answer. There’s more to it than a parent might realize on the surface.

Danielle says

It is ridiculous; if they can’t teach it in class so the majority of students “get it”, there is a problem with this program. It makes parents look like morons, the kids feel helpless, and it isn’t doing anything helpful for anyone.

Andrea says

While I disagree with this whole thing, I don’t understand how it makes parents look like morons. I have never heard of front end estimation until I read this. I figured out what they were doing within seconds, without reading any comments or explanations. I understand *some* things may be difficult to understand for parents, but surely, this isn’t one them, as far as what it’s asking the children to do. It’s easy to see what they were doing (whether you agree it’s a good teaching strategy or not).

Danielle says

You’re telling me that when our 3rd graders come to us for help, and we cheerfully tell them, “sure, come on over here, I’d be happy to help you with your homework”, and THEN, we can’t really help them, because it is ILLOGICAL, that THAT experience doesn’t change how our kids look at us? It does.

While it may be something we can “figure out”, I vehemently disagree that it is “easy to see” what they were doing. It seriously looks like a typo to me.

Andrea says

It’s really not that complicated. It says “find the sum” and then to use front end estimation to check the answer. So, first, you do the “correct” math, add the numbers and get the sum. The next step is to use “Front end estimation”. Again, I had never heard of this before, but seeing the worksheet, it was easy to see they used the first numbers “3” (hundred) and “2” (hundred) to get an ESTIMATE of 500. This is not rounding or anything I have ever done in school or heard of, but its easy to see the concept. This is not a typo, and as many others have stated is apparently a math strategy that has been taught for YEARS, not just something new or only related to CC. A typo would be a misspelled word, or a missing word. What do you think they were trying to say instead of what they did say? Apparently you are unfamiliar with the concept and automatically think it’s illogical simply because you do not know it. That is not a valid argument against it. There are several valid arguments against it, but it being difficult to understand doesn’t seem to be one to me. Maybe you don’t pick up on things quite as quickly. Maybe the public school system failed you or something. lol

Brad says

Maybe it is harder for people to pick up. and I have never heard of front end estimation. the fact is, how is THIS going to help them with math in the future. This is basic math that 3rd and 4th graders learn. Rounding 291 to 200 (front end estimation or not) is not a helpful tool for children or anyone. You will never use it in your life! If they said round to the nearest 50 or nearest 10 ok that might help, those can be useful in real life situations. but this is useless and it will ultimately hurt our already terrible country wide math abilities. There is no plausible reason to teach this other than because “I said so”.

Andrea says

I can’t say for sure what their ultimate goal is with teaching kids this. However, I do use front end estimation in real life, only I take it a step further. Maybe this is the introduction to kids before teaching them full rounding?

An example would be: I’m at the store (with two young children so I can’t carry around a calculator or stand around and figure it up in my head).

I only have so much money with me, so I do quick math in my head. I put two items in the cart. The first costs $11.91 and the second item costs $9.14. I quickly add 11 and 9 to get $20. This is front end estimation. But I take it the step further and add an extra dollar to account for the change.

You could do it another way, by rounding up $11.91 to $12, and rounding down $9.14 to $9 to get the same result. But honestly, I use the first method all the time and rarely round up. Not sure why- it’s just the way I do it. I could do it the other way, I just don’t. It’s a personal preference.

So, I do see how this could be helpful, in a sense. Although I wish they kept going to get a closer estimate. Maybe they have a “back end estimation” they add on to it for all I know.

Sandra says

Sorry Andrea – if the sum is 645, then why would after the fact front-end estimation of 500 be reasonable? or more reasonable that an estimate of 600, using rounding. So I do not understand the validity of the approach no matter how many years it has been used.

Andrea says

Read my response to brad above your comment. I address this.

Sandra says

Thank you Andrea…out of context, it is hard to understand this especially if unfamiliar with the jargon. I never heard of front-end estimation before and after reading a little more, I can see how I use it without even knowing it is called front-end estimation. Sharing the homework assignment puts the practice and usefulness out of context, doesn’t it. The intentions are not clear from one example. And I learn that teaching front-end estimation is not a new thing at all.

Andrea says

Glad my comment was helpful to you. There are lots of good comments on here that have taught me a lot!

Catherine says

I think many people here are misunderstanding the purpose of judging whether an answer is “reasonable”. The” reasonableness” of the answer is relative. The “reasonable” estimate is never viewed as the sum of the two numbers. It works to help the student who has made a big error due to inexperience. It happens when you are just 8 or 9 or 10 years old. The correct answer isn’t as obvious to a child as it may be to you. A child might make an error and instead get 3831 as a sum because the numbers were not aligned correctly, especially because it looks like it was meant to be done in their head. If a child lines the five up in the hundreds place in their head, they get 3831. They then check to see if this sum seem reasonable. They realize quickly that it is too far off from the front end estimation and look for their mistake. Of course there is room in the real world for “reasonableness” in math. No one is saying to use front end estimation to arrive at an exact sum when one is needed.

Danielle says

You’re funny, Andrea. I’m sorry you never got over your bully phase.

Andrea says

Wow, now you sound like one of the liberals. Calling people bullies whenever they don’t agree with them. Sure you’re on the right website?

Danielle says

Until you mocked me, this discussion was about Common Core. So yes, you are a bully, when you mock and make fun of another person.

Cornelius Greenwood says

I don’t see what’s illogical here. They’re showing a method that guarantees your answer will be correct to the right order of magnitude. If you try doing the addition steps all the way out and get 5 or 5,000 you’ll know you did something wrong – or as they’re probably trying to teach, if you type it in to a calculator and it gives you 5 or 5000 you’ll know you made a typo. This seems perfectly logical.

Susan Gill says

Why, would teachers simply not teach how to do the arithmetic? Teaching kids to be alert to what amounts to a “typo” is presuming they are unintelligent in the first place. In the days when education really educated, arithmetic was a matter of memorization and application. It was often tedious but you never forgot the basics. I doubt a child in the 19th century would have to” guesstimate” an answer to an arithmetic problem.

Cornelius Greenwood says

The student in the above assignment is required to do both the arithmetic and a check. Being able to quickly get an answer within an order of magnitude is an invaluable real world skill that will save lots of time. Also, students will be using calculators and computers earlier than ever, so it is critical that they get a feel for what a “correct” answer is.

Math and science are about more than arithmetic. Arithmetic is one tool, which is why it is still taught in the above lesson. But students also need to know how to check their results – which is also taught. Is your object that they are learning too much, as opposed to just adding sums?

Susan Gill says

In the referenced problem, it basically asserts that the sum has two “reasonable” answers. The right one and a wildly estimated one. Each is said to be correct. My objection is that this is a right and wrong problem. Adding three digit numbers together and estimating the answer to the nearest hundred is giving a poor message to students. The bottom line is this. All this manipulation of arithmetic, and yes, adding three digit numbers together is arithmetic, has done nothing in improving the math scores of Americans. Interesting that few people recognize this.

Catherine says

I wish I had said it as well as Cornelius Greenwood has!

Kerri says

There is no use for “reasonable” math in the real world.

Alex says

ofc there is.

This is all about double checking and fast and efficient estimates IF a certain absolute answer CAN be correct.

People do it all the time (“well… that looks off to me… let me redo that sum” or better “my feeling says that is not correct, let me double check that”) and it is a very healthy way of ensuring something is correct.

Some people learn this automatically, others don’t.

It simply gives an (unconscious?) insight into the possible presented solution or outcome of a problem, and this should be wired into a person’s head.

This totally ties into science, teamwork and quality control of completing a task.

Keep in mind that this is aimed at more complex things but needs to be learned with simple sums (we all learned 1×2=2, 2×2=4, 3×2=6 etc for the same reason and we now instantly “feel” the error when we see a 3×2=7 without actually doing the math 🙂

Rachel says

I am a special education teacher by profession, and I have been away from academics for a number of years due to teaching those with severe disabilities in a life skills approach. However, I am not teaching this year and have offered to help out in the Christian school where my son attends. Yesterday, I had the opportunity to learn front-end estimation, which is not something new. From what I’ve researched so far, it’s been around for quite sometime. In the example given above, when using front-end estimation, you only add the two digits on the left, which in this case is 3 and 2, the remaining digits become zeroes, making the answer 500. Yes, it seems to go against what we were taught about rounding, which would make the numbers 400 and 300 if we round to the nearest hundred and the answer would be 700. by using front end estimation, the answer will be “off” more often than not to those of us who round to the nearest hundred. I hope my explanation of this problem helps. I know when I was trying to help the students yesterday I was a bit confused, even with the answer key in front of me.

Andrea says

I don’t support common core for so many reasons. But, as others have said, the “500” is what the worksheet is asking the child to do per the instructions. However, again as others have said, what is the point?? The only reason I can think of is these are young children- 3rd grade. Maybe they aren’t at the level to do that large addition work yet, but it’s a way to introduce them to bigger numbers, so they can be taught the full way to add the next school year/grade level up? Just a thought. Surely they don’t continue to teach this year after year, and the kids eventually learn to add. Hopefully anyway.

Amy says

Just so you know, my 1st graders – at the end of first grade, learns to round to tens and hundreds. But middle of 2nd grade, they perfect it.

This math, presented here in the lesson above – is horrible.

Andrea says

Thanks Amy! Yes, if that’s the case my *guess* for the reason they may be doing it is of course invalid. My children aren’t in school yet (and we will be homeschooling) so I have no idea what they are teaching nowdays!

Andrea says

I can see the problem it creates though. If this is the reason, it’s a poor reason. If the kid isn’t mature enough to handle how to do it correctly, just wait to teach it until they are. There’s no way they are going to understand the difference between “front sum estimation” and regular math if they aren’t mature enough to add in the first place. Yikes. This is insane.

Stephanie says

If 3rd graders can’t properly round to 10’s and 100’s, they are already two years behind and a new school needs to be found.

Honour says

This post has shed light on a recent disagreement my 8 year old nephew and I had in a book store. I told him we would buy him a book and he had $10 to spend. He argued with me that because the book was $9.95 he still had a dollar to spend. I kept telling him that spending 9 dollars and 95 cents only left him 5 cents and that with tax he could actually owe me money if he wanted to get picky. He must be learning this special math because all he could say was, “This is only $9, I have $1 left.” Stop teaching close enough, it’s all good, if it makes sense to you, well you and your friends should just vote me off the island math! @_@ Blah!!!! Facts are facts. Truth is truth. Knowledge is Power! Kids are not stupid. If you teach them (right) they will learn.

trisha haas says

Now you know it wasn’t his fault. He was told that was correct. It’s interesting if you think about it. My daughter is also 8, so same age.

Honour says

I was shaking my head and smirking as I typed my comment. It is very funny but in a sad kind of way. He used to believe me and have faith in my wisdom. But now, because of how he is being taught and what the teacher said is right because she is the teacher, I have become the crazy lady trying to cheat him out of $1. Happy Ending: He ended up with a $13 Lego book because he’s so cute and adorable and I love him all to pieces! ^_^

Andrea says

My thoughts exactly when I read that. They are putting teachers as the sense of final authority, over parents. And then we wonder why children aren’t listening to their parents anymore. I think this may be intentional; they are trying to place controversy in the home and have children respect their teachers more (who are going to pass or fail them) so the system can indoctrinate them further. So sad!

Nico says

:/ but just on side note. Having read some of the comments here. Some parents just want things ‘their way’ and couldn’t care less about what is being taught since they were taught differently.

Then go and do things like write: “STUPID STUPID STUPID” on the paper and tell their kids how dumb the system is.

Honestly. I’m just out of words at that. I mean you just taught your kid that school is stupid. This one thing you have just taught him will make things more complicated than all the small quirks about this math system combined. And while their are many responsible and truly great parents, there are even more ignorant, heartless & thoughtless parents.

As a teacher, I ask you, what are we supposed to do? We know that the system we use works (even if in a roundabout way) and know it will benefit them greatly at 6th grade though it will annoy them in 3rd grade. Even if we meet with parents, sometimes they don’t even want to hear an explanation and they just mention how stupid everything is then leave.

So yeah. Please before bashing something, consider the other sides affected by it – your kid included.

Stephanie says

Most teachers merely show up to collect a check and really don’t care if the kids learn or not. As a parent, we pretty much all know this. I spend 25% of my salary just so I can put my child in private school where she can have decent teachers who actually care about her education and are in it for more than just a paycheck and retirement plan Sorry, but the public school system in most areas is nothing more than a daycare. Again, most parents know this as well, but most don’t have the option to do anything different but continue to send them there. Now I know why kids in my college classes couldn’t do simple math when I went back to college a few years ago. I’d say that only about 25% of the 20-somethings we have on payroll can even completely fill out their time card and properly calculate the hours owed to them. And, don’t get me started on how many can’t balance a check book. This right here is proof the system you use, especially to teach math, does NOT work. LISTEN to the parents. They see how it relates to the real world, not just the classroom. And, LISTEN to employers as well. Go talk to any company out there. They will tell you that these kids are NOT being properly prepared for work. Stop blaming the economy on why so many young adults are unemployed. They are unemployed because they have no skills. Even the ones being graduated from college have no skills beyond what most high school graduates possessed a generation ago when they walked across the high school stage. The economy isn’t as much a problem as is the education level of those being graduated. I have job openings that have been open for over a year that we can’t fill because we can’t find people who can do the work. High paying jobs with excellent benefits and retirement plans that would be coveted by anybody. Stop living with your head in the sand in the fantasy land of a classroom and go out and ask people just how prepared these kids are that you guys are cranking out.

Danielle says

Which was the intent of the comment above, about children looking at their parents like morons. I’m surprised you agree they are undermining parental authority, but don’t see that it will affect the child’s image of their parent.

Catherine says

I agree!! this is scary. This country has enough stupid people in it already… are they doing this on purpose???

Barry Parker says

I can understand the frustration with unexplained homework assignments and the lack of textbooks or other materials provided by the school to give a context to a problem’s meaning or purpose, especially in elementary grades.

The first question is what does the word “reasonable” mean in the context of this question. It appears that “reasonable” means that the answer arrived at is not obviously in the wrong ballpark in terms of powers of 10. If a student got the answer 6.45 or 6,450 instead of 645, the estimated sum of 500 would indicate that his or her answer was not correct in terms of the general number range in which the answer should lie. Here the estimate indicates that the answer should number somewhere in the hundreds, not in the thousands, tens, or ones. An answer outside the hundreds range should lead the student to double check his or her answer and the steps by which he or she arrived at it. Techniques of estimation in of this kind are common in all forms of arithmetical thinking and teaching with which I am familiar. I was taught to estimate in a way similar to this to do a quick check of my answers when I was in grade school, junior high, and high school in the 1950’s and 60’s. The technique is not something invented by supporters of the common core standards curriculum. It is important to note that an estimate is not a final answer. The exact answer will always be more specific and accurate than an estimate. The purpose of an estimate is to determine if a mistake may have been made in the calculation, not to replicate the exact answer.

The second issue is the accuracy of the example of estimation given in the original assignment. Since the example’s estimates are 200 (for 291) and 300 (for 354), it appears that the teacher is asking children to estimate the value of each number only to the level of hundreds. Accordingly, I would have given 291 an estimated value of 300 and would have given 354 an estimated value of 400 (rounding off each to the nearest value in hundreds). And by adding 300 to 400, I would have gotten an estimated total of 700, which is a much closer to estimate to the correct total of 645 than the suggested estimate of 500.

But the teacher is dealing with third graders, and may be using a simplified version in which the rule for estimation is to get rid of the ones and tens in each number and to keep the only the hundreds, reducing 354 to 300 and 291 to 200, with a resulting estimated total of 500 for adding 354 to 291. Is 500 a close enough estimate for the third grade teacher’s purposes? Probably. Is it close enough for estimating weight limits on bridges, payments on bills, or company budgets? Probably not.

Amy says

3rd graders are perfectly capable of rounding properly to 100s tens and even thousands. Taught many to do it. I have even taught 1st graders to do it in a simple way

Withheld says

I can help the parents help teach your child this math. I went through the same type of math with my kids. One of my kids kept putting down the actual correct sum of the 2 numbers, because he just seemed to be pretty good at math. However, he never read the directions, so he didn’t understand why his answers were wrong. So, I explained to him that first of all, he had to read, understand and then follow the directions. The more IMPORTANT thing I said to him next, got him through the homework. I told him that they weren’t looking for the RIGHT answer, just an answer that was close. He said, “So, they want me to put down a number that is close, but wrong”. I said yes. We never had an issue with this math again, and eventually he understood the estimating process.

That said, the US is the LAST country in the 1st world to adopt this method. As much as I hate hearing about China, the Chinese kids are good at math, and this is how they do it. I first came across this method in college, and when the numbers are a bit tougher, like in the millions, and there are a half of a dozen of them, this eventually leads to a way to very quickly sum up seemingly hard numbers. That said, I think in 3rd grade, it is more important to teach the kids how to get to the correct answer, before explaining a good way to guess…of course, the philosophy is to teach the guessing…er, estimating, first, so that it becomes ingrained, instead of ingraining the “carry the 1” method.

Jen says

http://mylearningspringboard.com/why-teaching-both-estimation-and-accuracy-is-important-in-math-instruction/

Benjamin West says

The only reason that I knew how they were doing this was because for the past three years I have been teaching fourth through sixth grades in a private school. Front end and rounding are both forms of rounding. Most people do not remember this step because once a student reached high school, estimation is not used anymore. The bigger problem I have is with children being able to do work that is not being taught and with there being no textbook. Our country is content to let our kids just get by in school with a passing grade instead of teaching them the importance of doing their best. A lot of fault also falls to the teachers and many times parents that do not always care what their children learn or that their children learn.

Tricia Gronlund says

I don’t think you can lay much fault at the teachers’ feet. I have had parents tell me that they don’t make their children do homework or study at home because that is what school is for. I have had students (high school) tell me that they don’t do work outside of school. They also tell me that as long as they pass, their parents are okay with it. I have often felt that I care more about the students’ grades/learning that he/she or the parents do.

Megan says

Yes, this is wrong – very wrong. Please, please, please speak up about this, for the sake of all of our children. Most people cannot afford to home school. Please talk to your legislators. Tell them you do not support common core and will not vote for them if they continue to support it. Make it clear to your legislators that you stand with the teachers and support them.

JaxFL says

Most teachers DO NOT like common core! It has been forced on us by for-profit ed lobbyists $$ who’ve convinced the Obama administration to bribe states into adopting it. Teachers have been speaking against it for some time, but the reality is, teachers have NO voice whatsoever in public education anymore. The only people who do are the PARENTS and the VOTERS! I urge those of you reading this who are “horrified” to please contact your legislators and encourage them to drop out of common core and return to more traditional curriculums. This will truly hurt generations of kids and waste millions in tax money until the pendulum swings back- and it certainly will NOT help kids be more prepared for college. Please understand that this is the choice of politicians all over the country, not the choice of teachers or local school boards, and the only way it will change is if parents and constituents speak up and threaten legislators’ re-elections if it continues.

CarolynG. says

How is this new math going to prepare our children for the real world? Are these kids going to able to estimate and round when they are older working keeping track of finances for their employer, or their personal finances? It really scares me. No wonder our country is in such financial turmoil.

LauraB says

I completely understand how this estimation is done (add the hundreds together and voila, you have an answer that is the minimum answer of a range of anything reasonable) but what I don’t get is how that is going to help a child learn the right math that will allow them to grow up and get a job that requires them to measure accurately, count money, manage time (clock math would be more useful!), calculate productivity, or simply balance their own bank account? I’m sure this is meant to be a building block, but it seems to be going backward instead of progressing.

Sandra says

Not new math…

Stephanie says

No, it doesn’t. And, as an employer of over 250 people, I can tell you that most of what the schools are sending out today into the work force – both high school graduates and even college graduates – are not prepared with basic job skills. Most can not even calculate their own time on a time card. And, don’t get me started on the people that can’t make change.

Quinn says

First of all, that math problem makes ZERO sense. Second of all, I thought you might like to read this article. In fact, EVERYONE should read it:

http://www.rethinkingschools.org/archive/27_04/edit274.shtml

mary bern says

It’s “nice” that the teacher says it will be all right with her if YOU do HER job.

Mind you, I am NOT blaming the teacher. She has no power to change this.

My point is that having the government-run school teach this nonsense, and then the parents teaching correct math, assumes that the child and the parents have enough time after school and work to have home-school after school-school, It also assumes that the parents are capable of TEACHING. Not everyone is. Never mind the question: “why are we paying the teacher/school to not really teach our children?” If what they teach must be un-taught so we can teach the correct methods and information, then they are not really teaching, in my book.

Michelle says

The teachers are forced to teach it that way, and believe me, the teachers are just as frustrated. We should be suing whoever wrote the material, not blaming the teachers.

Michael Paul Goldenberg says

I know that few people on this site are capable of or interested in rational thought about mathematics education, but I will make a futile attempt at clarifying things and reducing the hysteria. First, though, I should state that I am unequivocally opposed to federal standards for education and have been fighting the CCSSI since I first learned of it in 2009 (well, really a lot longer than that, going back to the ’90s). But most anti-Common Core folks with right-wing politics who are just waking up to reasons to dislike it seem to get hung up on fantasy, trivia, exaggeration, lies, distortion, and pure nonsense, none of which makes fighting the Common Core easier and gives ample ammunition to its well-heeled defenders and promoters, because they can (and do) dismiss you (with the cooperation of the cowardly and ignorant media) as crazy Tea Party members. And in many cases, sad to say, they’re not too far wrong.

Now, as for this math: it’s not “Common Core.” It’s not new. It’s not fuzzy. It’s perfectly sensible, if you take it in context. The US has always been weak at teaching three crucial areas of skill that kids need to be good in K-12 math and beyond: estimation, number sense, and mental math. This particular approach to estimation is only one of several that has been offered in many K-5 textbook series for a long time. My son, just graduated h.s. in June, had books that taught this. We looked at it, I read the material, he got it, we moved on. It’s not hard, and it’s not useless. That kid got a 33 on the ACT and was getting letters from most of the top Ivy League and equivalent schools last fall. I guess the irreparable damage done by fuzzy math wasn’t quite so deep.

When I go to the grocery store with no more than, say, $50 to spend, front-end estimation is exactly what I use. I want to underestimate so as to be sure to not go over. It works. If I want to be sure to spend as much as I can without going over a fixed amount, I use a combination of over- and under-estimating, and can generally get within $1 of my limit. Without a calculator or pencil and paper, thank you.

All these approaches to estimation are useful. The combination of them is powerful. But ANY system is better for students than none at all, which is where we’ve been for a long time. Most kids by the time they are told by upper-grade teachers to estimate will insist that an exact calculation is what they must do. They’re brainwashed to think that only exact answers matter in math class. And, frankly, some of the folks on this list and those like you contribute to that bad idea because you’re SO upset when kids are asked to explain their thinking (OMG!!!! Thinking in math class!!! Somebody call a cop!!!) because you (falsely) conclude or swallow the propaganda that Common Core (or earlier math approaches) “don’t think the right answer matters.” Not only is that nonsense, of course, but here, with estimation, we see that there is a RANGE of acceptable answers that make sense, and it suffices to find a number in that range, or to find the boundaries of that range. Ever heard of inequalities? There is no single number that is right when you look at most inequalities. And yet they are widely used in both practical and theoretical mathematics, and the world hasn’t crumbled as a result.

If I seem to be annoyed, it’s because I’ve been fighting the sort of ridiculous things most people are saying here for over 25 years, and it’s sad that the same nonsense is still being repeated by folks who either should know better or just haven’t given it sufficient thought to realize that not everything they learned about math in school was well-taught, and that not everything worth knowing about K-12 math was taught at all 20, 30, 40, or more years ago.

I started this knowing that it will fall almost entirely upon deaf ears and closed minds. But if one person reads it and starts to think a little bit about K-12 math teaching and learning, it will have been worth the effort. For the rest of you folks, I pity your kids, as they will be undermined by your biases and fears.

Michelle says

I think you missed the point. The material was written incorrectly. 291 is much, much closer to 300 than 200. I wonder if it was a typo, but even so, it is a bad one, because the estimation was WRONG. Estimation is too important of a skill to be taught wrong!

Mtam tam says

Man I feel sorry for you if you actually think this is a valid lesson. This is moronic and ridiculous. So when this child is taught real estimation and rounding and 291 goes to 300 (a MUCH more logical estimate) he or she will be confused and get it wrong. Then we will realize how stupid this system is and change it only after these poor children suffer… Maybe we need teachers and administration that actually understand basic math. Any rational person can see how blatantly ridiculous this is..

Angela says

My problem with these lessons on front end estimation is not that there could never be a situation where it might be applicable, thus a worthy lesson, but that they are teaching it fairly young and without the kind of understanding that should be given with the principle. Someone else above gave an explanation of why to learn this and along with yours they make sense, but it isn’t explained like this to these young students who are learning it. So they make mistakes like the child in the example above. Either wait until they are a little bit older, maybe not high school, but older, or make sure you are explaining why they are doing it and how it might help them do math, so they don’t get confused or feel the information useless. I might do the same thing with shopping, but don’t remember lessons on this in school. Either I forgot and really learning this was great, or what I did learn in math I was able to apply to real life circumstances on my own. I don’t like the way these kind of principles are explained or not explained and that is my main problem with them.

David Modeste says

So, I can see why some people may be frustrated with the way this problem and the solutions are presented. Actually, they way I look at it, there is no problem with this. two key things should be kept in mind as you look at the whole thing.

1. They called it a “front-end estimation”

2. It is a way to check if your answer is “reasonable” not correct

so ,

354 + 291 = 645 is the CORRECT answer,

but what if you were a someone learning to add, and you werent quite sure your answer made sense..

Then a quick way would be just to look at the big picture and say… I am adding a number that is around 300

to a number that is around 200… so my answer should be around 500. Now I got 645, which is a little more than 500

BUT, there is the amount above the 300, and the amount above the 200 that will probably make up the difference, so I must be pretty close to the right answer. I think thats the kind of reasoning they are trying to teach the student.

That would work really well for a multiple choice quizz for the same problem where the answers were

(a) 154, (b) 645 (c) 1200 (d) 92

The smart student would just add 300 + 200 and get the answer by process of elimination.

Jason says

Aha! Your explanation is the first one that gets to the root of how this would be a “reasonable’ answer. We are teaching the kids to be better test takers. It’s always all about the tests.

smack26 says

I get that there is a misprint, but this is not common core. I taught this exact method 20 years ago, and my own kids did this exact method too. What is bad is that they didn’t proof what they sent out, but that isn’t new either!

I would rather focus on why my 6th grader has to analyze an Emily Dickson (grade 12) reading segment!

lily says

My daughter is doing 12th grade literature work in 7th grade. The content is SO OVER THE TOP for a 12 yr old to understand!

Chris says

Oddly this is exactly the problem my daughter had on a “pre-test” for her math before we decided to homeschool her again. They were marking her problems wrong because she did the old time honored thing and found the proper answer, rather than follow the way the school wanted her to do it. Since she did this they marked the problems wrong, which showed her as getting a 10% on a math test, but every single answer was right.

She did not miss a single problem because we requested to see the test, but the teacher said she was not doing the work properly because she did not follow the stated guidelines even with the answers she gave being the exact answer. Kind of really pissed me off. However, since we started to homeschool her again she has not missed a single problem. Able to do all of her work and complete it in a timely manner, where before the teacher said she was the dumbest kid in class.

Rebecca Brown says

Can you show me where the CC requires this? All I can find is that they be able to “Assess the reasonableness of answers using mental computation and estimation strategies including rounding.” It does not say that front end estimation is required, and it also explicitly states that “The standards themselves do not dictate curriculum, pedagogy, or delivery of content.” It seems your school chose a curriculum that chose this method to teach it.

Dana Kullmann says

At least offer this to local TV news stations. I would blow this up to poster size and take it to the next PTA and school board meetings and ask them to justify this disaster.

Homeschool Daddy says

Absolute IDIOCY! Crazy that this would pass any kind of board or panel for approval of what’s helpful and educational to our children.

Nadia says

well dear here you go more about the … …. “Common Core” check it out now ,,,,

Nadia says

http://www.foxnews.com/opinion/2013/09/19/fourth-graders-taught-about-pimps-and-mobstaz-in-louisiana/

Judi PD says

this totally makes sense to me — the front end means that you want the highest value. in this case the hundreds position. What I think is missing is the lesson that says look at the number immediately to the right the estimating (or rounding) should have been to 400 354 goes to 400 the 291 to 300 If you estimated your bills using this method, you’d have money left over to treat the teacher to a lesson on rounding 😉 I teach 7th grade math and we will be going common core next year. Still digging into what they really want us to cover. We have textbooks but I usually create my own power points and other presentations. We use hands on often. I have everything including my presentations online. I find that very few parents access my webpage. It becomes frustrating to put in all of that work and then have less than 5% use it. However, most teachers will continue to do the best job that they can. Please ask your school (and get pushy) to have math labs / tutoring at school for students who are struggling.

Kay Weaver says

I work in a public high school in NC – and Common Core is the bane of our math department’s existence. Our kids can’t learn it, our teachers don’t want to teach it, and the parents don’t understand it. It is a royal pain for everyone concerned, and I’m just happy that my kids are old enough to NOT have to go through it. I have even considered early retirement so that I can homeschool my grandchildren – which is NOT the best answer for our family, but then neither is CC.

John says

One thing that might save America from Common Core would be teachers unwilling to go along with it.

The math department is the only place likely to harbor many such teachers, and from what I read in NCTM publications, we are being cajoled into going along and threatened if we don’t.

Lori says

I understand the frustration with this assignment… and the entire situation actually irritates me. The rounding of the numbers is actually correct if you use “front-end estimation” as the worksheet states. So that makes sense. What doesn’t make sense is why Common Core thinks that front-end estimation is an acceptable way to determine if the actual answer to that math problem is “reasonable” or not. I am a financial analyst and I can attest to the importance of being able to estimate and round and the different methods you’d use in different situations, but using that particular estimation method to determine if the answer was reasonable is ridiculous.

Another thing that I find absurd about this situation is that the teacher clearly didn’t understand the worksheet she was supposed to be teaching.

Secondly, the fact that there is no textbook (which is actually common these days) to reinforce the skills being learned and to provide detailed explanations is AWFUL. It has been statistically proven that homework helps kids retain skills learned in class and that parental involvement in that homework makes retention even higher. How can parents who were either 1) never taught these skills or 2) too far out of school to remember these skills be able to teach their children when they don’t have any materials to go by other than the worksheet itself which did not provide any background information at all.

Steve Kittel says

If the numbers were properly rounded, the resulting answer would be much closer to the actual answer…Perhaps they could actually teach kids the correct way to do math, because if they don’t learn how to add or subtract correctly, how can they ever count correct change, let alone do algebra, trig, or calculus…

why not teach them how to break down the numbers and add them that way…or maybe the old way to “carry the 1”.

354 + 291

—————-

300 + 200 = 500

+ 50 + 90 = 140

+ 4 + 1 = 5

————————–

645

Carrie says

Steve, your example is exactly the way Common Core is supposed to be taught. You can check it here with North Carolina’s 2nd grade unpacking of the standards. http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/2nd.pdf

What’s being taught at the school momdot’s daughter goes to is not correct. My guess is there’s an implementation issue within the district and teachers aren’t getting proper training.

Laura Parker says

CC is coming on hard for everyone, the teachers included. No matter how many in-service workshops they attend, they are only going to become good at this stuff after they have used it for a while. The kids are going to the next grade unprepared to do the new curriculum because the Fed. Gov. has thrown a whole new program to them, AGAIN! It’s not the fault of the school district or the teachers. Eventually it will all smooth out…………….but those kids caught in the transitional years will have it the hardest. The excellent district I retired from has been planning and helping teachers prepare for CC for quite some time. Still, I know it is hard for all involved. If you want to point a finger……………….point to the federal govt. Instead of streamlining education across regions and eventually the country, CC has hit schools hard and threatens to wash over some students altogether.

lily says

That’s what I had thought. It could have been implemented at the kindergarten level and worked it’s way up as these young ones rose through the grades. My son is a sophomore in a high school that was always ranked very high nationally. It no longer will have that status. His high school career is over already. The teachers aren’t even teaching. One teacher has the students teach the class! You cannot take a 15 yr old and teach him a new way to learn on a dime.

AtlantisMom says

Thank you! You nailed it. “Reasonable” requires a definition.

Regina says

How does this help them run a check book? No wonder our Government is broke!

trisha haas says

You solved it!!! This is why our country is in debt! They are “front end” estimating!

Baxter says

Hahaha, there it is!

Kerri says

Hi Trisha, great post!

I’m involved with a FB page against common Core in NY, can you tell me the name of this workbook?

beth says

Absolutely what I was thinking!!!

Joy frazier says

This is so crazy. You are correct. What was wrong with plain math. It worked, we all learned it and I can balance a checkbook too. We have got to fix the schools in this nation. Maybe the government now wants our children to fail so they can be taken over by some third world country. I am so disgusted. Sickening….So wonder our kids struggle in school.

Dan says

I think I am going to do that on my tax return… I made 75k…. my wife made 57k…. so we pay taxes on…

75 57

70 50

ok, good only have to pay taxes on 120k… IRS will love us!!!

Alex F says

actually, when you start the year you might want to create a budge and estimate the amount your both will make and the amount of taxes you will pay. Business make these projections all the time. I like the fact that this lesson is teaching thinking in addition to addition.

Kelly says

Some of you especially parents might find this interesting as well. I really suggest watching this lady, because she opens an entire new door what is being taught in our schools and many reasons as to why. Many teachers do not even realize they are and have been indoctrinated.

http://www.deliberatedumbingdown.com/MomsPDFs/DDDoA.sml.pdf

also her videos can be found on youtube. Charlotte Isberyt.

Brande B. says

My son is in 4th grade and working on 2 digit multiplication. It’s ridiculous the methods they are teaching!! What happened to having one number on top of the other and just working it out?? Then…when I show him the “old math” he wants me to teach him that “trick” because it is so easy! Math is math, can’t we just leave it that way??

Tam says

I am no advocate for Common Core. I agree it is detrimental to the education of our children. I also haven’t read through every single comment here, so please forgive if this is a repeat of information. In fact, we homeschool. I haven’t encountered this nor have I taught my children this way. But I think I’ve figured it out.

From the looks of this, they are not “rounding” up or down. They are looking for a FAST estimate that doesn’t include the rounding (If a contractor I hired estimated like this I would be very angry.) They want the children to just look at the first number, in this case the hundreds–300 and 200. So a quick estimate would be 500.

Like you, believe the rounding up or down is much better way to do it. This is just setting them up for more trouble later on.

Carrie S says

Another reason honeschool is becoming so popular.

Carrie S says

I think iPhones autocorrect was taught through common core too

Eddina Symns says

For several years, estimating has seemed to be very important, from the texts standpoint.

When I taught, I told students I thought that estimating had a “place”, so we did it some.

BUT I told them I did not like estimating. I wanted them to learn how to find the exact,

correct number.

I’m not a parent now, but if I were, I’d get a copy of the texts for each subject.

That way, you can supplement, at home, to fill out and/or correct things they

are learning in school.

Every example I have seen from Common Core appalls me. It’s idiocy to let kids

be taught such nonsense. Someday, we’ll be saying, “Why can’t they read? or spell?

or get the correct sum in math? And why don’t they know our history?……..

The answer will be: Because of Common Core.

JMD says

I agree that this “math” estimation is ridiculous…but, I think you mean that you hate it with a “capital” HATE not “capitol” 😉

trisha haas says

See what the anger does to me??

trisha haas says

ALTHOUGH…considering it came from the government, either way it works. 😛

JMD says

Too funny! Thanks for the laugh; and, thanks for the enlightening post. Makes me VERY glad that I homeschool.

dr4u2434 says

If you read the statement you will find that it was written capital H-A-T-E

Alison Moore Smith says

I admit it, it floors me that people put up with this and will leave their kids in school. Yes, they complain a lot, but there the kid sits, for 16,380 hours of his/her life while we futz and putter about it. How sad. What a waste.

trisha haas says

Unfortunately not every family is set up to be able to home school.

Fortunately we had a meeting with our daughters teacher this morning. She was receptive and AGREED with us. She said that the entire class is confused, not just Charlotte, and let us know about the local organization that helps do the curriculum for the school. She is getting us info on how to join.

She also told us that the school my daughter attends have a lot of active parents. We are not the only ones that are concerned and she said moreso than any other school she has taught at, this one has had a parental response. She told us we CAN teach her a different way and as long as she arrives to the end conclusion and can explain how she got there, the teacher is fine with that. We are not complainers, we are doers as well. This meeting was set up prior to this new sheet. We want our daughter, and all the kids in her class, to succeed.

amanda says

The whole theme behind common core is exactly what her teacher told you, “Solve it anyway you want, as long as you can explain it correctly.” Which is fine. I am all up for solving a problem multiple ways or the way that makes sense to you. Front end estimation, like the problem listed above, is not like the regular estimation we learned. Therefore, she will not be able to arrive at the same estimated answer. 🙁

trisha haas says

I think what her teacher was trying to tell us is she disagrees w/ the worksheets entirely and that as her parents if we can teach her a better way, she was giving us carte blanche to do that. I do think the teacher was on our side. I cannot expect her to solve all the schools issues up to the state in one 20 minute parental conference. But I do appreciate her taking the time to say that she agrees its a bit of a mess and the whole class is suffering. At the end of the day we still have to teach our 8 year old how to solve the ORIGINAL problem. (And I would personally like to do that the way I was taught)

Alison Moore Smith says

Although, sincerely, the idea that homeschooling is some other-worldlhy thing that only those somehow “set up” for it can manage, is really just a damning idea that keeps parents at the mercy of school boards and the department of ed, I’m not really talking about homeschooling, per se.

I’m talking about any alternative education that moves people outside the “if only I can reasonably fix the government school” model. And I say that because I’ve been there. (I one kid in graduate school, two undergrads, one high schooler, on junior high, on elementary school.)

You met with the teacher. That’s great and even better that she agreed. That’s a hurdle some never get passed. 🙂

But understand, you have a teacher who

already knewthat “the entire class is confused,” yet she is still teaching the same garbage! She does that BECAUSE she has no control. So she referred you to the “local organization that helps do the curriculum for the school.” But why do you think this local organization has more control than the teacher herself?I should have said that better because it’s not clear, but that is just what I mean about parents “complaining” a lot. You will join a group as I did. (I was on the PTA, elected to the school advisory council and on the technology committee back when were were a by-the-book public school family.) We worked hard at our “complaining,” but in truth we had no authority and no power. It is rare indeed to see a parent organization of a public school that REALLY has input into curriculum and implementation in public schools — unless it’s collecting money and turning it over to the schools.

Even with masses of attentive parents, there isn’t much you can actually do, there isn’t much change you can actually bring about.

The teacher has told you that “…we CAN teach her a different way…” What does that mean? “We” as in the parents? Or “we” as in the teacher?

Either way, think about what you said after that, because is was spot on. “As long as she arrives at the end conclusion.” The end conclusion in CC is a TEST, that is predefined. So, yes, you can teach whatever you want, however you want (this is the cry from my state as well, “We don’t dictate curriculum!”), AS LONG AS you end up being able to pass the test. The test that is created from and mapped to the kind of curriculum you outlined in the OP.

In Utah, where I live, the “end conclusion” is that we can teach whatever we want — as long as it maps to Core Plus, which is a pile of mathematical garbage.

Honestly, I’m not a homeschooling purist or anything. But this whole federal takeover is stultifying. You’ve just scratched the surface here. I hope you and other responsible parents keep digging because it just gets worse.

And whatever you do, remember, that every day, every week, every year, that you spend with your child sitting in a seat dealing with this crap — while you try to fight the bureaucracy, is another year of real learning lost.

I hope you can actually make a difference, but it rarely happens. And parents all over the country spend countless hours trying to reform an institution that has no intention of allowing reform.

Keep us informed at if and how your school changes the way they teach math. If you succeed you could be a model for others.

Diane says

Well said, Alison.

I would also like to point out, Trisha and Chris, that you are already homeschooling Charlotte.

She is having to do school twice. She sits through “school” without learning, then comes HOME where she is actually taught.

Look closely, you may be able to find a way to get her out of the broken system. Many parents, who both work, have found ways to homeschool their children. Many others have decided to live on lower incomes.

I trust you will find the best way to help your daughter.

Joy frazier says

If the answer is correct but they do not show how they concluded the answer if it in correct is what all here are being told.

Scott says

“I admit it, it floors me that people put up with this and will leave their kids in school. Yes, they complain a lot, but there the kid sits, for 16,380 hours of his/her life while we futz and putter about it. How sad. What a waste.”

Well, actually, by their calculation methods it’s really only about 10,000 hours …. 🙂

trisha haas says

Snort.

Alison Moore Smith says

Scott FTW

Tim says

Wow, that is idiotic. By that standard, 200 is a “reasonable” estimate of 199 + 199.

Lincoln says

A few years ago when my kid was taking 7th grade math, I attended the open house because I didn’t understand what they were teaching the kids. The math teacher told me very patiently that the kids get together and do the work in groups and then vote on the right answer. Which ever answer got the most votes was considered correct and others were marked as unacceptable and that they needed to change their answers to the one the class voted for in order to get the points.

Then they wonder why the kids can’t pass a standardized test.

My son got a bad grade in the class because I told him math didn’t work that way and if the answer was right leave it alone regardless what the vote was. He passed the end of the year test while several in the class failed.

It reminded me of the Simpson episode where they are teaching math by asking the girls what does a 4 feel like.

trisha haas says

HOLY CRAP.

Are you serious? They VOTED on the right answer?

Math is a democracy now?

I just died.

Stephanie says

Me too Trisha.

Audrey at Barking Mad! says

I have no words . . .

Actually, teaching kids to obtain the correct answer via democratic vote and then shaming those who didn’t tow the line and vote the same way as the rest, is SHAMEFUL!

Graham Smith says

No, but it does promote conformity, which may be the real “end game” here.

Steve Kittel says

so it’s a like voting for a president…the majority wins, and the minorities need to change to get credit…

Marcel says

Bravo, Steve. Bravo.

Andrea says

They are teaching our children to give in to peer pressure, turning them into “Sheeple”. Sad.

Stephanie says

That is the whole purpose of compulsory public school attendance.

Becky says

Was this Math Investigations by any chance? Math by democracy, sounds legit.

Brandi says

Well that’s just insane.

Tonya Wright says

My husband has a doctorate & he said it is okay because the children are being taught to “follow directions.” #MindBlown

AuthorMom says

Blindly.

Can we say Baaa?

John says

Yet more proof that doctorates don’t make people smart. Or wise.

Tonya Wright says

I agree it is wrong. What is the definition of “front-end estimation”? Why teach children WRONG? I was taught to round UP after the 50 mark. I have NO IDEA why anyone would look at the # 291 & think it is MORE LIKE 200 than 300. It makes no sense to me. WHY!?

My daughter is in 6th grade & is starting this either Common Core year or next year. I will keep an eye on her assignments.

AmyE says

Take them out of public schools and home school. Unless you get a school and a textbook publisher to agree to not use this Common Core crap, kids are going to be even dumber than they are now, and from a hiring perspective, there isn’t much more room to fall.

Alex F says

rounding and estimating are two different techniques. For instance, you can use these lower estimates to check that your final value is greater than your estimate. If you round up, then you would need to change the thinking to check that you answer was lower than your estimate. As a math teacher, it would be helpful to do both. From a problem solving point of view, their approach has many benefits including working on an appreciation of the magnitude of numbers. I like the idea that the teach is not only the mechanics behind adding and subtracting but includes higher thinking.

kevin heller says

I gotta jump in here — the common core state standards for math specify that third grade students should, among other things, understand how to round to the nearest 10 or 100, as well as how to estimate. When a state voluntarily agrees to implement the CCSS, it is up to that state and/or the local educational agency to decide HOW to implement them. I have no idea where that example came from, but it could have come from a state, and it could have come from a textbook publisher. In either case, it’s probably a mistake, and in either case, the people who wrote the CCSS would almost certainly disapprove of rounding 291 to 200. Basically, it’s a typo — and it’s a typo NOT created by the CCSS people.

trisha haas says

My husband met with the teacher today. She said the curriculum comes from the state and its not a typo. She did, however, encourage us to teach our daughter a better method of checking work and that if we wanted to not teach her that, it was ok with the instructor. She said she doesn’t agree w/ the new material either.

kevin says

Interesting. Well, I’m relieved that this is a state issue, and not a problem with the CCSS! Which state is it, btw? I’ll bet when all is said and done, if that teacher gets in touch with the proper state department of education that produced that problem, they’ll agree that it needs to be changed. I’ll be interested to know of any updates that come from this. Thanks!

trisha haas says

It’s Alabama. So I wont hold my breath. 😛

Cathy Hewlett says

I wanted to step in here and let you know that Alabama is not the only state teaching front end estimation. They are teaching it in Illinois, also (which may explain a lot about our state government). My daughter really struggled with it because we were teaching her the correct way of estimating. I finally had to read about it in her text book and start letting her do it their way just so she could keep her grade up.

I, by the way, also HATE this new Common Core way of teaching! We were told by our school principal that the only reason that our school is teaching it is so that we can get more money from the federal government. How sad is that?!!!!!

Michelle Eidschun says

@Kevin no mistake, My family is military and in the last year and 3 mo have lived in NC, TX and Hawaii. This is universal between the three.

Diane says

My kids are grown now but this stuff fries my brain cells! I’m rebellious enough to send a note back with every homework page stating that I’m teaching my child how to get the REAL answer and skip the estimated part. Like you said, no one rounds up or down by 100 -200. That’s ridiculous and feeds into this mamby-pamby, wimpy mindset of our modern culture that there are no absolutes and everything is subjective to whatever a person feels.

Tamara says

I’m curious to know how the meeting with her teacher went this morning. We’re homeschooling this year, and even though I really wasn’t excited to be doing it, this makes me glad that we are. Hanna is a year behind Charlotte, so I only wonder if this was in our future for next year… I’d be angry too. There’s nothing logical about it, and many other much more accurate ways to estimate an answer.

Cassie says

Oh, and it gets even worse…

http://www.monicaboyer.com/common-core-or-pornography-reader-warning-explicit/

JM says

I followed the link, above. That is the most horrific piece of trash I have ever read!

I can not fathom sending my children to a school for one, single day where a book like that is on the 11th grade reading list…or, ANY grade, for that matter. I have friends that were molested by family members when they were young. I can not fathom what would have happened to their minds and souls if a teacher had sent them home with that book to read…the author portrays pedophiles as ‘tender” and “good”! If my children went to outside schools and brought that home, I would have shredded it, burned it, and destroyed it. Then, I would file my affidavit to let the school board know that my children would no longer be attending their school.

I thank you for posting this, though. It has helped to further inform me and make me aware of the dangers that are present; hidden under the guise of “Common Core Standards” and in the schools, today.

Those poor children. Their innocence and purity are being robbed. They are being molested, in a sense, by having this garbage crammed down their throats.

Marlena says

I completely agree with your post. I go back and forth about homeschooling my kids but right now that is not an option. We try to stay on top of what they are teaching and how they are teaching it but like you said when you work and your kids have extra curricular activities it gets harder and harder. I really would love for my kids to have a textbook like I did when I went to school. As parents we have to try and stay on top of what our kids are learning at school and speak up when we do not agree. My biggest problem right now is I feel as though I am teaching them just as much as the teachers are so I wonder what in the heck are they doing for 8 hours at school! I don’t mind teaching but the reason they are going to school is because I am unable to homeschool and I did not go to school to become a teacher. One last problem I have is I feel schools are doing way to much group work. These kids do not know how to do individual work without someone guiding them through it.

vanessa says

I was having to teach my daughter aside from school too. She was learning subtraction in the 1000’s at school, but was instructed to learn her multiplication at home! She was struggling with the subtraction as it was, and now has to figure out x”s on the side? Then 2 weeks later they moved on to telling time, even tho she was still figuring out the subtraction! ugh. And school is only less than 2 months in. My kids will be homeschooled starting Monday actually. I’m so done.

D. Young says

The more that parents take (back) control, opt for homeschooling, and therefore reduce filled seats in schools, the more these bureaucrats will get the message as tax dollars dwindle and make their positions irrelevant.

Dana says

@ D. Young… Nope that isn’t possible now either. Homeschooling are not exempt.. Get a load of this!!!

http://www.examiner.com/article/report-obamacare-provision-will-allow-forced-home-inspections-by-gov-t-agents

Christie says