Arrays and Repeated Addition

Have you ever noticed how things like eggs in a carton or muffins in a baking pan are lined up perfectly? When we arrange objects into equal rows and columns, we call it an array. Arrays make it much easier to count things quickly using repeated addition!

What is an Array?

An array is a group of objects arranged in a neat grid.

• Rows go straight across from left to right.
• Columns go up and down.

For an array to work, every row must have the exact same number of objects.

Writing Repeated Addition for an Array

Let's look at an example. Imagine you have a grid of dots with 4 rows, and there are 3 dots in each row.

Instead of counting the dots one by one ($1, 2, 3, 4...$), we can add the rows together!

• Row 1 has $3$ dots.
• Row 2 has $3$ dots.
• Row 3 has $3$ dots.
• Row 4 has $3$ dots.

We can write a repeated addition sentence to find the total: $3 + 3 + 3 + 3 = 12$

There are $12$ dots in total.

Drawing an Array from an Equation

You can also build an array if you are given a repeated addition sentence. Look at this equation: $5 + 5 + 5 = 15$

This tells us we need to add the number $5$ three times. To draw this as an array:

1. Draw $5$ objects in a row.
2. Make $3$ rows just like that.

You now have $3$ rows of $5$, which gives you an array of $15$ objects in total!

A Stepping Stone to Multiplication

Why do we learn about arrays and repeated addition? Because it is the secret trick to learning multiplication! When you say "$3 + 3 + 3 + 3 = 12$", you are really saying "$4$ rows of $3$ equals $12$." Very soon, you will write this as: $4 \times 3 = 12$

Practicing with arrays helps you see exactly how multiplication works!