Gifted Issues Discussion homepage Forums Learning Environments "Story Problems" -- references on terms

DS9 is running into issues in math (6th grade) -- which has always been his favorite subject (after gym class). We're watching him do what I would call story problems and he doesn't seem to know the terms -- that is, how to tell whether to add, subtract, divide, multiply. Nor does he know how to divide decimals. This is of course showing up in his grade.

DH showed him some Khan videos but that's confusing DS as it isn't a Common Core approach. Suggestions for helping him get through this? Do we approach the teacher for extra help (she offers it)? Is there a good online guide that won't confuse him more?

Feeling awful that we didn't know this was happening. He has been doing his homework at school and turning it in... without us seeing it.

Do you have any examples of problems he's had difficulty with? Maybe that would give people a better idea of what's going on. What about the Khan Academy videos is confusing? I thought Khan Academy was tied to common core.

Our DS has used MathTacular to help with this. He has learned from videos since he was little. He's in third grade, but fifth grade math.

MathTacular

This message has been approved by DS; current word problem master!

The dividing decimals issues should be simple to fix. Regarding knowing to do on word problems, while it may not be the same issue, my DD11 has struggled off and on with word problems for years. When it comes to math, she does beautifully with learning and applying algorithms that involve only numbers (geometry is also fine), but "Bob left Phoenix on a train traveling 60 mph..." can tie her into knots. She has a hard time figuring out how to set up the problem. I suspect this is not uncommon, but it is certainly something I notice. One remedy I suggest when she seems to not know what number goes where and what to do with what is to sub in easy numbers for the numbers in the problem and see if that makes things become more intuitive (that is, it helps you see that what you need to do is divide, or whatever). I don't know how "legit" this method is, but I used it for years to help me get by with problems that stumped me at first.

I would try tackling real life problems, and see if that engages him. The problem may be one of motivation. Giving him far more difficult problems to solve might also help. He may perceive the problems he's given as simple, misgauges how much cognitive effort to spend to solve them, and thus relies too much on heuristics.

One technique I find effective, after making sure all the normal terms are understood is to practice going the other way. Start with an equation or expression, you or your son can choose, and figure out the English description for it. Just in the same way as when learning a language you need to both read and write to gain mastery, sometimes the same is true for these type problems.

Thank you all for the great suggestions! We will try them. Trying to have him set up the problem is an interesting approach -- he does better when he understands things fully, so that might really work.

blackcat, I wasn't the one watching the Khan Academy with him, but DH said there was something about the terms being used that was confusing him as it was different than his text (probably the point, lol). I will ask him.

Some of the examples seem pretty easy, ex. 15 tennis balls weigh 60 ounces, how many ounces do 5 tennis balls weigh? It seems he gave up and guessed at the answer on that one.

However, we had real progress this morning on figuring out how to calculate percentages using decimals (ex. 12% of 25 is?). I explained the process verbally and he caught on after one or two examples, then he was on fire and asking for more to try. He even said "I'm going to look at my homework again, because I think I did some weird stuff on it before I knew this!" I'm wondering if talking it through works better for him than simply reading the text.

I am assuming that your DS has already mastered long division with integers so that it is just a matter of cases where there are decimals in the dividend and divisor. When only the dividend has a decimal, your DS only has to remember that the decimal lines up in the same spot in the quotient so that's also unlikely the problem. He likely only has trouble remembering the algorithm for how many places to shift the decimal to the left for the quotient to correspond to the requisite rightward shift for the divisor. Some kids, like my DD, just memorizes algorithms automatically, so the challenge is to make her go back and assimilate the logical reasoning and develop number sense. Other kids, like my DS, has an incredible number sense, so the challenge is to make him assimilate the algorithms after he can already see where the decimal should go. Perhaps first figure out where your DS' weakness lay. If he has already developed a strong number sense so that he can automatically tell where the decimal should be in the quotient, leverage that to help him remember the algorithm (i.e., by working backwards).

As for the story problem troubles, it is odd that this is only cropping up with 6th grade math unless curriculums really vary that much across the country? Even my oldest, who was in 2nd grade a dozen years ago, started with addition and subtraction word problems by 2nd grade. This approach makes it easier for most kids to master word problems due to repeated exposure over many years and the gradual expansion of the variety (+,-,x,/, algebra, geometry, etc.) and complexity of word problems. Perhaps it would help to focus your DS' attention on just one type of word problems at a time to allow him to assimilate typical language before contrasting the different types. Does your DS have any language processing weaknesses that may impact comprehension of word problems? If he does not, it may simply be an issue of complexity, which requires more cognitive resources including working memory. By 6th grade math, a word problem likely requires multiple operations to reach the final solution. While some kids can manage to execute multiple operations in a single problem when it is laid out for them, having to "set up" the problems simultaneously pushes them beyond their current cognitive resources. I sometimes see this manifest with very young kids who can do calculations in their head but initially struggle when they have to simultaneously write out the solution.

If he has a decent teacher, I would approach her for help since this has the added benefit of a custom fit with his curriculum.

FWIW, we've had this exact issue with word problems crop up just this year with one of my dds taking *algebra*. (The issue with not understanding how to interpret words meaning +, -, x, /). She's never really loved word problems, but she's a good math student and she's understood word problems up until this year when she was tasked in word problems this year to explain when you add, subtract, etc. The issue cropped up here is related to curriculum, which is wrapped up in common core. It also came up for the first time this year, in Algebra, in a set of curriculum that my kids have used now for 3 courses leading up to Algebra.... soooo... one would think it had come up before but it hadn't lol!

My suggestion is to meet with the teacher to go over what specifically seems to be a challenge for your ds, and to have the teacher explain *how* she expects him to do each type of problem. If it's anything like the math curriculum our kids have had for the past few years, there are very specific "tricks" allegedly designed to make math "easier" to conceptualize which can in fact trip up very bright kids. It's possible your ds absolutely understands how to do something per a parental explanation or a Khan Academy video, but he might not be doing it the same way the teacher expects him to do it.

Best wishes,

polarbear

The example you gave sounds like a ratio or proportion problem and most kids would need instruction on how to set that up and then solve it like an equivalent fraction or cross multiply. I think Khan actually did a decent job explaining that if you go to the sections on ratios.

With the 12% of 20 or whatever problems, remember to keep telling him that OF means "MULTIPLY" in story problems involving decimals or fractions. But you can't multiply a percent you have to convert to a decimal first (my kids struggled with this as well).

He has very strong number sense, which is what helped things click today, I believe. He just was not grasping what a decimal point related to (i.e., where to place it). It's sort of like he was absent during that lesson (which he wasn't, or maybe he mentally was...).

I'm going to go back through his work (now that we finally have it, sigh) and see what else I can spot. No issues with word problems and no language processing concerns (he was tested at a center that has expertise in 2e, so I'm comfortable ruling that out). Maybe it's the convergence of these new math concepts with the word problems that's the issue? We're planning to talk with the teacher as well.

One more thought: a lot of these issues (word problems, decimals) are covered in early chapters of AoPS pre-Algebra too. Although AoPS almost certainly won't use the same language, it is really good at showing *why* things work, not just what, and how to come at them from multiple approaches. Possibly if your DS got that deeper understanding of the underlying math, it would be easier to translate/ apply/ recognize how to deal with the problems, regardless of the specific language and processes used in his class?

The AoPS pre-algebra book is worth having just as a deep intro to almost everything; however, there are also lots of free videos that cover all the concepts, if not the depth: http://artofproblemsolving.com/videos/prealgebra

ETA: Really, AoPS doesn't pay me for all these endorsements. But they ought to.

You are right -- multiplying by converting to a decimal is what he figured out today. Will go look at ratios on Khan. Thanks!

Interesting. We have seen this as well He has been tripped up before by the way the new curriculum explains things but gets it when shown another way. I need to double check on this, but I think they switched texts this year... which might explain some things. Fortunately, if he's correct about this, the teacher isn't too hung up on how to do things, as long as the method makes sense and the answer is right.

Thank you! I've been wondering about AoPS and if it's possible to "jump in" to their books or videos without having done their earlier classes. Sounds as though that book should be on our shopping list.

Um... That's not correct. “%” is shorthand for “/100”.

12% = 12/100 = 0.12

These are just different ways to express the same number, so you can indeed multiply by a percent.

I'm saying you need to rewrite the percent as a decimal you can't take 12X20 and get the answer. So yes, you are correct about the terminology (if we want to nitpick). REWRITE rather than convert.

Oh... but you could take “12% * 20”, or “12/100 * 20”. I think it's important to teach understanding that “percent” means “per hundred” or “division by hundred” instead of just teaching to rewrite. Rewriting can be useful, but it isn't necessary.

It's also useful to know that you can shorten “/100” to “%” in any longer equations.

Obviously a parent or teacher would explain why/how it works, and what a percentage is, rather than just the mechanics. That really wasn't my point. The point is learning the terminology. OF means multiply when you are dealing with a fraction (and yes, I realize that you don't necessarily need to rewrite as a decimal, you can rewrite as a fraction. My point is that it needs to be rewritten. You can't multiply it when it's written as a percent).

You can multiply it when it's written as a percent—that is, as 12%.

You cannot write 12% as 12.

I don't nitpick. I point out a mistake that if taught to ConnectingDots's son (or anyone, for that matter) would teach something wrong.

Hmmmm-- I think that reducing any of this to an algorithmic kind of place to start with may be a disservice to a child with sound number sense.

In that sense, I think that Nyaanyaa's point is a good one-- understanding that those things are completely equivalent (and I wouldn't assume that a teacher HAS done that with the class) means that it may fit more neatly into his own framework of "what does this sentence translate into in symbolic, mathematical terms?"

In other words, don't go with the flow when that flow fights against the way that your child actually understands concepts. Work WITH it, and then figure out how to get to the place that the teacher is wanting to see.

~Mom to math major and tutor extraordinaire, who LOVES word problems and applications problems of all kinds.

Isn't that what I just said? You can't write 12 percent as 12? You have to rewrite it as a decimal or fraction before you can do the computation. If you were going to solve this using a calculator, you would have to type in .12 X 20. So then how you would YOU explain to the kid how you find 12 percent of 20? Since you are apparently a math master and expert teacher, why don't you write it out step by step for the OP's son, so that he can understand how to solve that or similar problems. (and now I'm refraining from discussing anything having to do with mathematics as long as people like this are on the forum--Geez).

This is a perfect example of a case when plugging in easy numbers would illuminate what needs to be done. The first thing your child needs to see is that we need to know how much one tennis ball weighs (well, okay, you could do it another way, but for sake of simplicity). He probably sees this, or my DD would have). But how do we get that number? It's interesting that you say he has good number sense because to me, a child with great number sense would know (mine might not have). Regardless, you could approach this problem by saying okay, let's try it like this--2 tennis balls weigh 10 ounces. Oh, your brain says intuitively, so obviously one tennis ball weighs 5 ounces. Wait, but how did I actually get that number? Looks like I divided the second number by the first. So I will need to divide 60 by 15 to know how much each tennis ball weighs, and then I can proceed to find out how much 4 weigh.

I agree with blackcat; you can't multiply "12% * 20" directly because the two terms have different units. The % sign indicates that the 12 is on a scale that the 20 isn't on.

You need to include a conversion factor first, which you're doing with the fraction, but maybe not realizing that this is what you're doing. (?) The conversion to 12/100 puts the percent on the same scale as the 20.

This is a concept that a learner needs to understand completely in order to internalize these ideas. A teacher needs to be able to explain what's going on and how things work; you're not (but blackcat has been saying this consistently).

I taught this stuff to my DD about a year ago. We went one skill at a time, and she was able to to perform each operation easily. The problems started when a bit of time passed and she was confronted with a variety of problems. Some were straightforward operations, and some were word problems. She had trouble seeing the forest for the trees. I taught her some second-level ideas (e.g. conversion factor) that helped her see how everything related to each other.

The same thing happened a month ago with mixture problems. After she struggled through some of them, she had a vague idea of what was going on. I then showed her that they're all based on C1V1 = C2V2 and that if you add something to the first side, you have to add it to the second one. This ties nicely with that basic stuff she learned when she was learning to solve equations: if you add something to one side, add it to the other.

Thank you for clarifying this, because I feel like I must have fallen into a different dimension!

FWIW, I agree with blackcat and Val too

Ah... something like that, yes. I stand corrected.

Okay... so, back on now and yes, we talked about percentages (which he understands as x of 100). The conversion to do the calculation was the issue.

Going back the original question vs. direction this post has taken. My older DD has language processing LD and while learning math operations with numbers wasn't a problem for her word problems were a HUGE issues. I'm not suggesting your son has an LD but I figured I could share what i did with her. These are a basic idea's but sometimes basic suggestions gets overlooked. Read the problem out loud if you can (hard during a test), underline the important numbers & their units, cross off the unnecessary verbiage, circle the words that describe the operation. If it's homework trying to explain the problem and/or what you don't understand to someone else even if it's the cat or dog often works wonders. Basically slow down and treat it like a puzzle to be decoded and practice, practice, practice.

I love the idea of having him try to write his own word problems.

Yes, I'm confused by his missing this one, too. He grasped it pretty quickly once we talked briefly about it (and was able to do variants on it easily), but there was something about it on paper that made him react like this: "WHAT?! I will just guess." This is the same kid who used to happily do problems like this for fun and who can figure out money math in a snap (i.e. with the same root concept, like at the grocery store). When I say he has good number sense, I'm thinking of his ability, going back to his early learning using Montessori methods, to turn numbers every which way and understand the relationships quite quickly. Sometimes I think that something about this curriculum is messing with that sense.

Wow. I think I used to use this technique of crossing out and underlining myself! Thanks for the reminder.

FWIW, I think my DD, who is actually very gifted verbally, has some pragmatic language difficulties. This helps to explain her word problem issues, IMO. She sometimes is completely stymied by phrasing in a problem that seems like it should be obvious. It may have nothing to do with math. She just needs me to say, "What they mean is..." a few different ways. I suspect this is related to some of her ASD traits--rigidity about interpreting words and phrases or something.

My son does this as well. He takes the wording so literally that he gets frustrated and ends up over-analyzing questions. Often the problems are terrible written and he's correct that they can't be done the way they are written. On the other hand most of the other kids seem to be able to interpret the question it was intended or make the inference that was left out.

Drawing sketches helps, too-- though this gets to be a better strategy in algebra and beyond. Most scientists I know always work problems this way. It helps, sometimes, to draw a picture and label it with the values from the "word" problem, and then convert directly into symbolic mathematical representations from there.

Not always time in a pinch on an exam, of course-- but I suspect that this is behind the notions implemented in Common Core regarding "visual representations" of math. It does help when it comes to applied problem-solving.

This is, of course, the procedure taught in the Singapore Method. Only more effectively than in most CC textbooks.

I had similar difficulties when these types of problems were introduced in school. I could solve everything up to that point practically instantly; suddenly being unable to do so, I felt it was impossible, and that I had to quickly guess the correct answer. I think it took me some time of solving these questions very slowly and precisely to raise my confidence (ignoring my teacher's complaints that I wasn't keeping up with class, or even listening, because I was still working on problems from 5-10 minutes ago at my own pace). Once I could answer consistently correctly, my pace picked up, and I was eventually ahead of everyone again. It is probably important for your son to build that confidence, too.

I think I panicked because I felt I had to answer instantly. My existence was basically defined as the math genius who solves everything instantly, at that point. Your son's difficulties sound similar in a way. His expectations of himself are possibly unrealistic; thus, he panics.

I wondered if there was a psychological element, too. DD is never intimidated by pure numbers, or indeed by shapes and angles, but there's something about the unpredictability of words ("What do I do with it?") that freaks her out. It's less scripted. I'm not sure if this reflects more on her personality or how she has been taught.

The way I understand it is that, at its core, math is a language we use to describe relationships. Your DD speaks English, and she speaks math, but she's still developing her skills in translating one to the other.

Math is purely abstract, after all, and a "story problem" is more concrete.

What Dude said.

I think for the OP switching textbook/curriculum may have something to do with it. My DS uses Go Math and for all its faults, it started with word problem in K and does ask the kid to come up with word problems for a equation too.

I never had a problem with word problem in Math. But I had a hard time in Newtonian physics. I often had trouble knowing how to translate the stated problem into equations. I never had problems with the other parts of physics either. In my case, I didn't really understand the physics.

It's weird about the pictures. DD was taught to do all those stupid arrays and to draw blocks and circles and whatever for certain scripted operations early on (and God forbid you NOT do that, even if you already knew the answer without it). But these days, I am not aware of anyone encouraging her to draw pictures or use tables or other graphic representations to solve word problems, another strategy I used with success to help me get around my own poor intrinsic number sense. I'm always suggesting this, and she looks at me like I'm nuts because it's not something they seem to do. Of course, this is not always helpful, but it's just a thing to try when you don't know how to approach something. Meanwhile, DD does not like "trying things"-- when it comes to math, she wants to know "how to do it." Here, in fact, I see some emotional roadblocks to good problem-solving that may be a result of underchallenge OR of unimaginative teaching.

For those wanting to get in more practice with story problems, or applied math, Edward Zaccaro has some good books. We have "Challenge Math"

Agree...love all of his books

Many thanks for all the suggestions! I do think there are a few things going on here, and the suggested resources/techniques are worth trying. I talked with him about the underlining/crossing out technique and he nodded like that made sense to him.

It could be the transition to constant story problems has thrown him, especially because, as someone pointed out, he's used to easily being quite good at math (although this is certainly not the first time he's had to wrestle with it, it is the most notable). I'm seeing some evidence of sloppiness (ex. it's pretty clear that he wrote something down wrong or didn't take enough time to set up the problem). So we can work on that...

Wondering about the teacher's role in all of this, though. Certainly, he's got some things to work on and we will support that happening, but wouldn't you think that she would have reached out to us or suggested something for him? Because he's been accelerated, she knows about his math grades for prior years and that he has always been at the top of the class. I'm thinking as a teacher, I would have said something when a student like that was pulling Cs. Or, perhaps all the students are getting Cs and he doesn't stand out? (As DH said, it's hard to believe that he's the only one struggling this term, given how he's done in respect to classmates previously.) He also just did a ton of extra credit pages (all on his own, this is something he wanted to do to try to raise his grade) and she just said "you should have been doing these all along." Yes, but not exactly encouraging. Unfortunately, he also missed several problems on those (not all, some pages were 100%s). And she doesn't say anything like "it looks like you are having trouble with x, go look at these pages again."