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Interpret multiplication as an array

Multiplication can be interpreted as a rectangular array of equal rows or equal columns: one factor names the number of rows and the other the number in each row, while the product counts all objects. Rotating the array exchanges the factors without changing the product, making the commutative property visible and supporting multiplication facts and later area reasoning; the focus is on whole-number arrays with products within 100, not generalized matrices.

Detailed Explanation: Interpret multiplication as an array

An array is a rectangle made of equal rows or equal columns.

To read an array:

  1. Count the number of rows.
  2. Count how many objects are in each row.
  3. Write a multiplication equation.
  4. Count the total number of objects.

Example: A garden has 3 rows of 4 flowers.

Draw the array:

🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸\begin{array}{cccc} 🌸 & 🌸 & 🌸 & 🌸 \\ 🌸 & 🌸 & 🌸 & 🌸 \\ 🌸 & 🌸 & 🌸 & 🌸 \end{array}
  • There are 33 rows.
  • There are 44 flowers in each row.
  • So the multiplication equation is
3×4=123 \times 4 = 12

There are 12 flowers altogether.

If you turn the array, it has 4 rows of 3 flowers:

4×3=124 \times 3 = 12

The total stays the same. This shows that the order of the factors can change:

3×4=4×33 \times 4 = 4 \times 3

Learn by doing: Interpret multiplication as an array

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Multiplication - From Grid Model to Answer


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