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

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.