DS7 has been up since 6AM trying to find all of the factors to 1 trillion. This kind of "bite off way more than you can chew" project is typical of DS. It starts off awesome (that is, we optimistically think it will keep him occupied and math is a good thing right?), then when he figures out that it may take him the next five years, his mood and behavior deteriorate quickly. No advice needed, except it's already been kind of a rough morning and I'm not even through my first cup of coffee. Happy first day of winter break! :)
That sounds like an awesome kid you have there--"no flies on that one," as my Grandma says.
I'll share a few math games our boy has liked, in case one of them might sometime buy you a few more minutes of peaceful coffee--but feel free to ignore :)
Teach the child to play craps (we called it toad), and then invite him to create a set of fake dice that rarely/never loses. The rule is that no two adjacent sides can have the same number (so from all possible single view perspectives, they look like real dice).
Or look at a billiard ball bouncing in a grid of varying sizes (we use inch-size graph paper for this kind of problem) and try to determine the rule for which corner the ball will end up in, if always started from the bottom left. Also the rule for how many bounces it takes to land in a corner.
War using modular arithmetic--go through the whole deck once with mod 11, then mod 7, then mod 5. Each player puts down two cards at once and the higher sum wins. You can play that red is negative.
(The top two are from Math the Human Endeavor, and the bottom one is from the living math website.)
Cheers! Off for more caffeine myself :)
Thanks for the cool ideas!
The main thing is that he loves the "fun" parts of math, but is dismayed by the amount of work in the basics. We just finished excruciating long multiplication and we're just starting excruciating long division. Can't get around the fact that math takes a lot of effort and patience and practice- especially the "bread and butter" like addition, subtraction, multiplication, division.
I bought a few books in the math series, "The Life of Fred." I'm excited to get a bit more into it with him--I've heard good things.
It doesn't have to be that way, you know! There's no reason you have to master long division to explore algebra, calculus, tesselations, trig, ratios, scientific notation, compound interest, radicals, fractals, cartesian graphing and the like. I mean really, if you're doing a trig problem and you are 8 and you can't reliably do long division, why not use a calculator? It's what the high schoolers all do anyway. You can learn long division later. Heck, my ds didn't learn long division until he needed to know how to use it in Algebra 2 to factor complex polynomials. (He had previously used the partial quotient algorithm for multi-digit division problems because it was much more intuitive to him.) Schools do long division to "full mastery" in 4th grade or whenever because they're teaching slightly older kids who can (theoretically) handle the slog better, because they need to ensure every kid gets mastery of every concept in order to simplify teaching them in large groups in the future, and because they lack imagination and the ability to go with the flow.
My dd10 took almost two years to get around to completely mastering operations with fractions, decimals and ratios. It wasn't that it was too difficult; it was just that in order to get really slick at putting it all together and retaining it within easy grasp she needed to do enough practice, and she found it too much of a slog to do so at age 7 or 8. We just let it go and moved on to different things. She'd already completed a children's program in linear algebra, so we picked that thread up, and we did lots of challenging problem-solving, she worked through a lot of the "enrichment topics" I mentioned above, and she did some pretty sophisticated geometric proofs. At age 9 she went back and filled any gaps with the fractions and decimals stuff and it was no big deal.
I would strongly encourage you to think outside the box if it looks like the traditional approach to math scope and sequence is whittling away at your child's love of mathematics.
I would very strongly second this ^^^
IME with a child who is very asynchronous when it comes to math, patience often developmentally does lag behind analytical ability for some time. I do think it's useful to work on how to work carefully even at a young age. Also, though, there is an equal if not greater value in developing an ability to do *hard* work. Whenever I have emphasized drill to the point where my child gets overwhelmed, his interest and ability in what I think of as real math plummets.
Assuming it's not possible to remove *all* tedious work in a school setting, I'd recommend very strongly setting a limit that is consistent with his stamina. Ten minutes, or even five minutes a day. Three correct long division problems in a row, or even one very long and tricky one. Use graph paper (inch is ideal--can be printed free online), with one number in each box, so wandering columns doesn't get in the way. IMO, a few problems worked cheerfully and carefully are more effective in teaching good habits than an overload (remembering that what feels like an overload to a 7yo is different from what it feels like to us!).
We've been talking about some interesting math ideas like prime numbers, perfect numbers, and will need to look at smaller concepts like averaging numbers, representing information in tables and graphs, etc. DS loves interesting things about numbers - calculating negative numbers, multiplying exponents, number facts that we know but don't really think about (an odd number plus an even number will yield an "odd," or if a denominator is a prime the fraction can't be reduced)
I don't know why I'm teaching him this stuff at home (he's not homeschooled). We just started learning math before he entered school because he was interested and capable. I have kept up a bit of after schooling so he didn't "lose" the skills he had accumulated. His first grade class is working on basic addition- perfectly appropriate for first grade but just not where he is academically- we're switching schools after the holidays for a few reasons.
Oh, I didn't realize that. In that case I'd be especially leery of spending time mastering basic arithmetic and instead focus almost entirely on concepts and skills outside the regular K-6 curriculum. If long division is boring now, imagine how boring it'll be in three years when he has to do it all over again!
Apologies Miranda- I realized after I replied that I misunderstood your suggestion. I see that you are suggesting that he learn some cool stuff that may not be in lockstep with K6.
His new school is going to do some assessments when he starts in January- I'm hoping that they won't spend too much time on math mechanics and will move him toward using the skills he has (word problems, analysis, etc.). I'm going to be a better advocate this time around.
In keeping with the ideas here, we're working more out of the "The Life of Fred." DS enjoys it, and we've learned some interesting things- the set that I picked for him (about mid elementary) is starting off with some geometric concepts. We haven't done too much with geometry, so he's learning things like "a square is a rhombus, but a rhombus isn't necessarily a square." Fred does a few lessons that seem geared toward logic and analysis (not a lot of math facts and rote)- so far, I'm liking the series quite a lot.