Picturing Factors in Different Orders

Picturing Factors in Different Orders

Illustrative MathematicsVaries

The purpose of this task is to help students picture the multiplicative structure of the number 30 in different ways. Some of this structure is easier to communicate using grouping symbols, as it is easier to interpret 2×3×5 than 2×(3×5) in terms of equal-sized groups even though they both mean '2 times 3 times 5.' Because there are many different ways to draw the pictures called for in this task and it is the interpretation of the pictures that matters most, the task is very well suited for a whole-group discussion where students show and explain the pictures they have drawn to their classmates. The pictures shown in the solution are increasingly more abstract as they go on.

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