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Same Amount, Different Picture

factors and multiples · representing factorization with arrays and manipulatives

Show different arrays and factorizations for the same amount without changing the value.

Same Amount, Different Picture is a Grade 4 factors activity that uses arrays and manipulatives to show multiple factorizations of the same number. Students begin with a number such as 24, build an array for one factor pair, then break composite factors apart and rearrange the same total into more detailed factor structures. The quantity stays unchanged while the representation changes.

Use it when students are learning factors, divisibility, and early prime factorization ideas. Physically rearranging the same 24 objects makes it clear that 3 × 8, 3 × 4 × 2, and 3 × 2 × 2 × 2 all describe the same amount. Create a free Find a Math Game account to generate lesson support for Same Amount, Different Picture. No credit card, with 3 lifetime lesson generations.

Grades:
4
Materials:
counters

Standards alignment

4.OA.B.4 · primary

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