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.
Overthinking my teaching 