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Multiplication practice

Commutative multiplication arrays

Compare an array with its turned orientation to show that reversing the factors preserves the total number of objects.

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Write one equation for each orientation. Compare the factors and products, then explain why the number of objects stays the same.

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Learning objective

What this activity builds

Explain the commutative property using transposed rows and columns.

Worked example

A 3-by-8 array is turned to make an 8-by-3 array. What equations describe it?

3 × 8 = 24 and 8 × 3 = 24

Turning the same 24 objects exchanges the row and column counts without changing the total.

Teaching notes

Make the practice count

  • Rotate a physical array or the paper instead of redrawing a different collection.
  • Use the word factors for the exchanged values and product for the unchanged total.

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Worksheet settings

Rows in each array
Objects in each row
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Math SheetNameScore/ 24TeacherDateCommutative Multiplication ArraysRead the array and its transpose. Show how swapping factors preserves the total.1.Write both factor orders.____ × ____ = ________ × ____ = ____2.Write both factor orders.____ × ____ = ________ × ____ = ____3.Write both factor orders.____ × ____ = ________ × ____ = ____4.Write both factor orders.____ × ____ = ________ × ____ = ____math-sheet.comPage 1 / 1

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