Here is an example of an open arrary model for division. Solve 1,525 / 12.
Using benchmark numbers, how many groups of 12 are in 1,525? I know that 1000 x 12 is 12,000. That is way too big. If I multiply 100 x 12, that is 1200. That is less than 1525. I can put the 100 above the rectangle array and then put 1200 in a sectioned off portion of the array. On my scratch paper, I need to subtract 1200 from 1525. I now have 325 left. I cannot make another 100 groups, so I choose a smaller benchmark number. I can make 10 groups of 12 which is 120. Again, I put the 10 above the rectangle and put 120 in another sectioned off portion of the array and also subtract it from my balance of 325. I repeat this process until I cannot make any more groups of 12. The quotient is the total of the partial quotients that are above the array. The remainder (if any) is my remaining balance.
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