Regroup Three Factors to Make an Easier Product
Find a friendly pair among the supplied factors.
About 15 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For 3×5×2, group five and two to make ten.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Multiplication of three factors can be grouped in different ways without changing the product. Look for a pair that makes a useful number such as ten. Each original factor must remain in the calculation, and only the grouping changes. This does not authorize changing multiplication into addition.
Find a friendly pair among the supplied factors. Multiply that pair first, then multiply by the remaining factor. Compare with multiplying the first pair in the original order to confirm the same result.
Keep all three factors in your rewritten calculation. Regrouping changes parentheses, not the operations or factor values. Circle the friendly pair, then write the third factor beside its product.
- Circle the friendly pair, then write the third factor beside its product.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Find a friendly pair among the supplied factors.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
For 3×5×2, group five and two to make ten. Then 3×10=30. Grouping three and five first gives 15×2=30, so both agree. The factor two is still included exactly once rather than being lost after making the friendly product. Keep all three factors in your rewritten calculation. Regrouping changes parentheses, not the operations or factor values. Circle the friendly pair, then write the third factor beside its product.
Check your reasoning
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Helpful tips
- Keep all three factors in your rewritten calculation.
- Regrouping changes parentheses, not the operations or factor values.
See the answer and explanation
20
Two times five makes ten; multiply by the remaining factor. The result is 20.
Take it further
Find 4×5×2. Expected: 40.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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