See Multiplication in Arrays

Count by rows or by columns — same total: order doesn't change the product

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About This Practice

One dot array, two ways to count: by rows it is rows × columns, by columns it is columns × rows — and both reach the same total. That is exactly where the commutative property of multiplication comes from. Adjust the rows and columns with + and − buttons and discover why 3 × 4 = 4 × 3.

Adjust the rows and columns of a dot array with + and − buttons. Counting by rows gives rows × columns, counting by columns gives columns × rows — both reach the same total, showing why 3 × 4 = 4 × 3.

EasyEstimated Time: 10minarraycommutativefactorstimes table

How to Play

  1. Use the + and − buttons to set the rows and columns of the array.
  2. Count by rows: how many in each row, how many rows? Work out rows × columns.
  3. Count by columns: how many in each column, how many columns? Work out columns × rows.
  4. Compare the two results — is the total the same?
  5. Try more combinations and check that swapping the factors never changes the product.

Learning Objectives

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