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First, figure out how many counters Ray has. 4 rows of 4 equals 16 counters. You can then either decide ways of making new arrays that use that total, or you could take Ray's starting array and rearrange it.
If you want to start with the number 16, you would be using factoring to figure out what arrays you can make. 16=2x2x2x2. Ray's first array was (2x2) by (2x2). Regroup, and you can make 2 by (2x2x2), or 2x8. You can also make (2x2x2)x2, or 8x2.
If you use actual counters, put them in an array of 4 by 4, and then split the array in half, either by height or width, and move the counters. This is a good way to teach basic multiplication, distributive property, and factoring.
Ray makes an array that has 4 rows of 4 counters.
This is the same 4 x 4, which means Ray has 16 counters.
He wants to make two more arrays using the same number of counters.
We need to find the factors of 16:
1 x 16
2 x 8
4 x 4
He wants more than one counter in each row.
This rules out the 1 x 16. And since 4 x 4 is already taken...
What two arrays can he make?
2 x 8 is one array, and 8 x 2 is another array.
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