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Build rectangular arrays

A rectangular array represents a collection arranged in equal rows and equal columns, so the total can be determined by counting rows of equal length or columns of equal height and described with repeated addition or a multiplication equation. The arrangement makes the factors and total visible, including that turning an array around preserves the total while interchanging the factors; the focus is on whole-number arrays within basic multiplication ranges, not area formulas or generalized arrays.

Detailed Explanation: Build rectangular arrays

An array is a group of objects arranged in equal rows and equal columns.

Example: Make an array with 12 counters.

  1. Put the counters in 3 equal rows, with 4 counters in each row:

    ● ● ● ●
    ● ● ● ●
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  2. Count by rows using repeated addition:

4+4+4=124+4+4=12
  1. Write the multiplication equation:

3×4=123\times4=12

This means 3 rows of 4 make 12.

  1. You can turn the array around:

    ● ● ●
    ● ● ●
    ● ● ●
    ● ● ●

    Now there are 4 rows of 3, so:

3+3+3+3=123+3+3+3=12 4×3=124\times3=12

Both arrays have the same total, 12. Turning an array around switches the factors, but the total stays the same.

Learn by doing: Build rectangular arrays

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Multiplication - From Grid Model to Answer


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