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

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.

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).

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

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.

But you can't multiply a percent you have to convert to a decimal first (my kids struggled with this as well).

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).