Teaching article
Rotate an array and investigate what stays the same
Compare two grouping descriptions of the same array without changing its quantity.
Turn the same arrangement so its rows and columns exchange roles. The grouping description changes while the total remains available to check, making a specific multiplication relationship visible without moving to unrelated examples.
Describe the original rows. Rotate the representation. Compare the new row description and total.
Different grouping, unchanged total
Rotate or regroup the same array and compare totals. The model illustrates a multiplication relationship without implying every operation is commutative.
Three rows of four and four rows of three both contain twelve dots.
What changed and what stayed the same? Rotate a paper array rather than requiring mental rotation.
The explanation concerns multiplication, not every operation.
Resources
- Maths Puzzle Generator — Choose arithmetic or missing-number questions only when they match the number relationship being explored.
Further reading
Read next
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- Equivalent fractions: match the amount before the labels
- A bigger counter does not make a bigger collection
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