Number Play

One of the most unexpected things that has happened with homeschooling is the way that this second chance at learning math has really revolutionized the way that I understand and approach math: I always wondered why it is that kindergarten books start out with patterns, thinking that those had very little to do with math. Boy did I miss the boat:

Patterns are the heart and soul of math.
And they're fascinating.

So today, I'm helping Dragon with his math, and it's patterns, and they're driving him crazy.

I had a look at that third one, and saw that it's increaing by odd numbers:

1+3=4
4+5=9
9+7=16

So it's a pattern of "interval", I told him. And he was confused. So I asked him, "What's an interval?" And he said it's the space between. Yep. I also reminded him to get out his notebook so he's got some scratch paper to play around with, which he did.

And he noticed a different pattern, as he was looking over his multiplication chart:

2x2=4
3x3=9
4x4=16

So it's a multiplication pattern, squaring, and traveling diagonally down the center of the multiplication table. Which is cool. Both patterns fit.

5x5=25
6x6=36

He starts figuring out the next numbers in the sequence; it's pretty obvious, really, looking at the multiplication table. So I wondered what comes next when you do it my way. Maybe I should have predicted what happened, but I didn't:

16+9=25
25+11=36

It's pretty cool. I would never have predicted a relationship between this adding of odd numbers thing to square numbers. Makes me want to explore these numbers more, though I wouldn't know how to go about doing it. I love that our math program (we use MEP) sometimes causes these spontaneous discoveries that we can play with.

Numbers are so much cooler and more interesting than I ever suspected in school.