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Here are some ideas for using counters to investigate number patterns.

Collection of Counters Make different square arrays using nine counters.

Discuss the patterns formed.

[hint: 1,3,5/ 1,2,3,2,1/ 4,4,1 etc]

What would a 2,2,2,2,1 look like?

Continue the patterns for 16 counters in 4 by 4 arrays.

What is noticed now?
Can anyone explain the patterns seen?

Can anyone devise a different pattern? What about 25 counters in 5 by 5 arrays? Or 36 counters in 6 by 6 arrays?