First we dump out all his money and divide it into piles of different kinds of coins. Then Natty has Aleks count small stacks of coins. They start with stacks of four quarters, then stacks of five nickels. Then stacks of ten pennies. Aleks mostly has pennies and this is where the counting starts to be more than just counting. Over and over he counts to ten.
At one point, he stops at 9 and asks, "Why is 9 three 3s?" My jaw drops. I explain that this is addition and multiplication - that once you know all the numbers, there are easier ways of counting, mainly "counting by." I explain that you can count by 1s - 1, 2, 3, 4, 5... You can count by 2s - 2, 4, 6, 8... You can count by 10s - 10, 20, 30, 40, 50... And you can count by 3s - 3, 6, 9, 12, 15 - and this is how we know three 3s are 9. He finishes counting to 10 and starts over with more pennies. A moment later he asks, "Why is 4 two 2s?" I reiterate the counting by.
When they get to stacks of 10 dimes, Natty has Aleks try to count above the highest he can count normally - 13 - by explaining how the teens and twenties and so on work. He seems to get, if only momentarily, the concept of putting "twenty" or "thirty" in front of the lesser numbers. It was a big day for numbers for him. After all that counting, he forgot about Optimus Prime and decided to watch Harry Potter instead.
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