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## 4.5.1a A First-Grade Class Works with Representations of Number and Counting

Students’ knowledge of number concepts and patterns grows more sophisticated as they work with different representations of number and counting. As part of the morning routine, one first-grade teacher had students represent numerical patterns in two ways. Each day they noted how many days of the school year had passed by writing the number on a strip of adding-machine tape. Every fifth day they made a circle around the number, and every tenth day they placed a square around the number. They discussed that the circles indicated counting by fives and the boxes showed counting by tens.

As another way of representing the same counting sequence, the students used a class hundred board and crossed out one number each day but highlighted every fifth day with yellow and every tenth day with red. As the days progressed, the students noticed that the highlighted numbers made a pattern of numbers ending in fives and zeros. The teacher used a calculator to show that the sequence of numbers that appeared in the display when counting by fives and by tens continued with the same pattern beyond 100.

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