Gifted Issues Discussion homepage Forums Parenting and Advocacy Math related question

When doing long divsion with DS11, so far the only math practice he abhors, we had an important realization. He can divide, with accuracy, faster in his head than he can writing out all the steps. So...how to convince him to do division the way the schools want him to do it?

Get him to do things like 7834095.56 / 143.8 ? Or can he really do that in his head? I'm serious; make the sums hard enough that he sees the benefit of writing it out. It's great that he has strong mental arithmetic too. Sometimes he'll have to grin and bear the requirement to write out working for something he can do confidently in his head, but if for now he needs practice, it's probably better to practise on things he can't do in his head, because that's less frustrating! (At the same time, encourage estimation and other sanity checks.)

Can you be more specific about the kind of numbers involved?

How many digits is the divisor (the b in a/b)?

Yup.

DD balked this way at writing out dimensional analysis when she was about 8-- but her dad and I both know that there is wayyyyyy more at stake there than being able to convert units properly-- basically about 90% of quantitative determination is being able to recognize when you have the right quantities in the right locations in calculations, and following the units and making sure that they "come out" right is the KEY to doing them.

So we wanted her to very definitely view equivalent values as fractional conversion factors which equal one, and to WRITE.THEM.OUT.

She was very resistant because she could do the (simple) assigned conversions in her head just fine. Except, of course, when she got something turned upside down, which was about 20% of the tine.

Eventually, I came up with a story about Henrietta* the chicken, who was having a dinner party, but wanted things "just so" for her many guests... and needed the proportions of guests to cockroach appetizers, musical numbers, etc. to be perfect.

It was quite a complex problem-- far more complex than I've ever given to a freshman college student struggling with dimensional analysis, but it worked with DD.

Yes to making the problems HARD ENOUGH TO REQUIRE what you're seeking from them.

* Henrietta was a sort of barnyard Martha Stewart on a budget, as it happened... so she needed to make sure that she had planned out her shopping with her purchasing power in mind. (My own DD responds best to problems which are quirky or surreal. IMMV.)

In DD's case, she needs to have problems which are difficult enough that she makes a LOT of mistakes trying to do it without writing things out.

Ah, yes. I get it now. And admittedly, these were at most three to four digits divided by two to three digits. So tomorrow's "lesson" will be on showing ds the value of steps with more difficult problems.

Thank you, all.

KADmom: sometimes math proofs are really fun to read. Mabye it can help inspire your DS?

HowlerKarma: It sounds like your DD is the same. Perhaps she also needs more challenging problems that can encourage her to write steps out.

Mabye your children can eventually progress to unsolved math equations, or work on Fermat's theorem?

I'm curious of some specific examples of divsion problems that "he can divide, with accuracy, faster in his head than he can writing out all the steps". I'm wondering what exactly is it that makes them "easy" enough to do mentally (where "easy" is understood as a relative term).

In your example 7834095.56/143.8 it doesn't divide evenly (as a terminating decimal). When do you stop calculating, and in what form is the anser to be given?

When I use a calculator I get 54479.10682 (a 10 digit approximation, not exact). But when you use long division, do you know a way of getting that the first digit of the quotient is 5 straight away without some trial and error (and subsequently the other digits the same way). Suppose, when you ask how many 10000's of 143.8 go into 7834095.56, if you carelessly guess 4 of them instead of 5, and subtract those off, you'll realise you haven't subtracted off enough 10000's of 143.8 and you have to subtract off one more before proceeding to the next digit of the quotient. The only way of avoiding this that I can see is to know the multiples of 143.8 up to 9*143.8, but I'd be curious to here other ideas. Can it be made purely mechanical. Of course it would be easier if we all used base 2.

DS 5.5 is reluctant to writing out anything as well. Same thing, 2-4 digit division. Sometimes I will MAKE him do it to show me how he came to this answer and to make sure he knows how to "show his work". If I am not mistaken schools are big into this..... I like the idea of giving them really difficult problems so they see the benefit of writing it out. Great idea!