An Active Week - and MATH!

This week F returned (again) to the California Science Center, where he took his grandparents on a tour of the amazing things there that he loves.

We sat together on the couch one evening going through 3rd grade math problems which he does in his head. Three digit subtraction with regrouping and zeroes... "easy." Multiplication and division... "easy."

He learned to add fractions with the same denominator. "Easy." He loves fractions. He also already relates fractions to percentages. I think we'll be moving on soon, though he still operates in the concrete mode a lot, but hey, so do I.

We have been using the World Cup to create word problems. So his father asked him at CPK to think about a problem and then by the time he was done eating he could explain his answer. The question was: if two teams from each group go on to the second round, and the second round has 16 teams, how many teams started in the first place?

First he tried to think it out by trying to determine which operators he would need. He decided it would be multiplication or division. But he didn't know quite how to put the numbers (abstract) in an order that would result in a simple answer. So... he drew a box (concrete) for each group of four teams, filled in two random boxes as the winners of the round robin, counted out how many boxes/groups he needed (8), then counted the total squares (32). So we then launched into the lesson about the other ways to do it - 16x2, 8x4, whatever, he was already mentally able to see how it all worked and was very excited about it. Then he drew the leaderboard showing how the single elimination games would eventually play out.

So then his father asked... if every team plays every other team in its group one time in the round robin, and then it becomes single elimination, how many games does the winning team end up playing? That was easy --3+1+1+1+1. And then... if each game is 90 minutes, and they play 7 games, how many minutes do they have to play? He counted by 90s. BY 90s, people! So naturally we then showed him the abstract for that. He has understood multiplication as a function of addition since early 1st grade, maybe earlier, but now he's starting to put the concrete and the abstracts together. Half a year of 3rd grade math before the check arrived.

And I pointed out that there was a pattern to single elimination - 16 teams to 8 to 4 to 2 to 1 winner. So he said "divide by twos." It's obvious to us adults, but he hasn't even officially learned multiplication yet, much less division....

Then we did some multiplication with "magic zeros" so he can shortcut any multiplication with an even tens like 7 x 90 = (7 x 9) x 10. "Easy."

Is it time for 4th grade yet? It's going to be a challenge to get him to practice these things while hack-schooling, but he's very, very good at applying math to real problems so we'll just sneak it in as much as we can.