Partition arrays into smaller arrays

Partitioning an array means splitting its rows or columns into smaller rectangular arrays while preserving the same total number of objects, so a multiplication situation can be represented as the sum of smaller products—for example, $6 \times 4$ as $6 \times 2 + 6 \times 2$ . This develops decomposition and the distributive relationship between a whole array and its parts; it does not require algebraic generalization or large-number factorization.

Detailed Explanation: Partition arrays into smaller arrays

An array is a group of objects arranged in equal rows and columns. To partition an array, split it into smaller rectangular arrays without moving or losing any objects.

Example: Find the total number of dots in a $6 \times 4$ array.

Start with $6$ rows and $4$ dots in each row:

6 \times 4

Split the $4$ columns into two groups of $2$ columns:

6 \times 4 = (6 \times 2) + (6 \times 2)

Now find the number of dots in each smaller array:

6 \times 2 = 12

So there are $12$ dots in each part. Add the parts:

12 + 12 = 24

Therefore,

\boxed{6 \times 4 = 24}

The two smaller arrays still contain all the dots from the original array.

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Multiplication Area Model - Teens to Total from Sum

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Partition arrays into smaller arrays

Detailed Explanation: Partition arrays into smaller arrays

Learn by doing: Partition arrays into smaller arrays

Practice with unlimited practice problems

Practice:

Multiplication Area Model - Teens to Total from Sum