Math Doodles is an app for iPad and iPhone. It is a ton of fun.
I was initially nonplussed but playing with Tabitha turned me around in a hurry.
Tabitha was playing the Connect Sums game by herself and guessing haphazardly. In this game, the player is shown a 4-by-4 grid of numbers, and is offered a target number. The goal is to click on numbers in the grid until you reach the target number. Then the numbers you used disappear and a new target is offered. Et cetera.
Haphazard guessing didn’t seem to be a particularly valuable activity for Tabitha, so I sat down with her. Our first target number was 12.
Me: What do you know about twelve?
Tabitha (five): That it has a 1 and a 2.
Me: Yes. Why does it have a 1?
T: Because when you count to twelve and write it, there’s a 1.
Me: I see. Actually it’s because twelve is made of 10 and 2. So if you can make 10, you can make 12.
T: Ten is two 5s. So 5-5-2.
Our next target number was 8.
Me: What do you know about 8?
T: That it’s two circles; one on top of the other.
Me: Yes. But what do you know about how much eight is?
T: I don’t know.
Me: Do you know a number that eight is more than, or less than?
T: It’s more than 6, but less than 10.
Me: Yes. How much less than 10?
T: Two less.
Me: Nice. So a minute ago, you did ten as 5 and 5. Now we need two less than that. Do you know what’s 2 less than 5?
T: Three. So 5 and 3.
Our next target number was 9.
Me: What do you know about 9?
T: One more than 8. So 5-3-1.
Our final target number in this round was 7.
T: That’s one less than 8.
Me: Yeah. But we don’t have a 5 this time.
T: Uh huh! Two and three!
Me: Oh nice. Two and three to get five. Then two more.
There was a whole lot of learning going on there. Of particular interest to me was her shift from numeration (how we write a number) to quantity (how much a number represents). In our first two rounds, she told me what the numbers looked like; she was telling me how to write numbers. In the third round, she told me about quantity when I asked. And in the last round, she knew to start with quantity.
Playing the game a few days later, when she was a bit less patient, we got stuck on the target number 11 on a board that had only 4s and 3s remaining. I couldn’t see how to use what she already knew to build towards 11 as 4-4-3.
I can, however, see that various decompositions of 10 are really useful, and that halves would be as well.
We’ll have to talk about those things.
I’ll let you know how it goes.