### Late Night Math

It's 10 o'clock on Saturday night and Supriya is having trouble falling asleep. So what do Manisha and Supriya do to amuse themselves? Math of course!

First Supriya did counting by 2s. She has a good handle on this and she wrote down numbers all the way up to 104. Then she did counting by 3s. Instead of starting with 3 (as I would have done), she started with 1, and so wrote down the series as 1, 4, 7, 10, up to 43.

Last night (after 9 o'clock of course) I wanted to build on that. I had her count by 2s and write the numbers up to 10. So she had 2, 4, 6, 8, 10. On another sheet of paper I made two columns, one called "Parting" numbers and the other "No Parting." That terminology, by the way, was her own invention for even and odd numbers -- even numbers can be "parted" into 2 and odd can not be. We let her keep those terms because she owned them

*and*the concepts (which is much more important).

I started with 1. Supriya said non-parting. 2, parting. 3, non-parting. 4, parting. Something clicked inside her head and her eyes shone with understanding. She could see that the numbers alternate. We went up to 11. So now I had in the even column: 2, 4, 6, 8, 10. I pointed to that earlier sheet of paper with counting by 2s. Voila! It was the same numbers again. She was thrilled at the magic of it.

**Adding 3 Numbers**

Westford Public Schools put out their curriculum benchmarks by grade-levels. For Grade Level 1, one entry for Math reads "Add up to 3 single-digit addends". Supriya has a very good handle on adding two numbers, so I decided to go for three. It took her about 2 seconds to do "7 + 5 + 3" in her head. "8 + 8 + 8" took a little longer. First she came up with 16. I told her she had done the first part. She went back, used pieces of foam lying on the floor as tokens and came up with the right answer. Her basics are clearly sound and she owns the concepts.

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