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Build simple arrays

An array is an organized arrangement of objects in equal rows and equal columns, allowing a quantity to be seen as equal groups and counted efficiently. Learners connect the number of rows, the number in each row, and the total through skip-counting or repeated addition, and recognize that turning an array changes its orientation but not its total. The focus is on small whole-number arrays; formal multiplication algorithms and larger fact generalizations are beyond this scope.

Detailed Explanation: Build simple arrays

An array is a neat arrangement of objects in equal rows and equal columns.

Example: Make an array with 12 dots.

  1. Put the dots in 3 equal rows.
  2. Put 4 dots in each row.
∙∙∙∙∙∙∙∙∙∙∙∙\begin{array}{cccc} \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet & \bullet \end{array}

Now count by rows:

4+4+4=124+4+4=12

So, the array has 3 rows, 4 dots in each row, and 12 dots altogether.

You can turn the array. It will have 4 rows with 3 dots in each row:

∙∙∙∙∙∙∙∙∙∙∙∙\begin{array}{ccc} \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet \end{array}

Count again:

3+3+3+3=123+3+3+3=12

Turning an array changes the rows and columns, but the total stays the same.

Learn by doing: Build simple arrays

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