Gifted Issues Discussion homepage Forums Parenting and Advocacy Math related question

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?

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!

For instance in this kind of problem, 769 divided by 47, I think he uses estimation to come to the answer. He ends up with the correct answer with a remainder more quickly than he could write out the problem and i take nearly the same amount of time to check his answer using traditional long division--but i compute very quickly. I've never computed in my head though.

I guess I'm surprised because this is my verbal kid who finds math concepts exciting but not the computation.

Well, it *is* purely mechanical: you just gave the procedure yourself.

This does relate to various interesting issues (that might make good discussion points with interested children) though. For example, we can get an approximation of the answer by using approximations of the arguments, and we can bound the error, but nevertheless, knowing when we have been precise enough to be sure about the first digit can be tricky. If you don't have access to full information about the arguments, it can be more than tricky, and one can go off into study of the on-line computable functions (which do not include division, IIRR)...

As to the long division, I would encourage him to continue to practice the mental skills. Then use the long division only as explanation or proof. I'm still a little peeved almost forty years later that school broke my ability to do complex division quickly in my head when they forced me to do long division. I think at some point later I would've understood it well enough to bullet proof it against their methods, but without continuing to use it I lost it. It didn't occur to me at the time that I would need to do something to preserve the skill.

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.)