Operations & Algebraic Thinking

Arrays & Repeated Addition

Using rectangular arrays to write a repeated-addition equation.

Foundational15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Odd & Even Numbers

Rows and Columns

Objects arranged in neat rows and columns, like eggs in a carton or chairs in a classroom, are called an array. Counting an array is a shortcut for a repeated addition problem — and it's your first real step toward multiplication.

Definition — Array

A group of objects arranged in equal rows and equal columns, with the same number of objects in every row. The total in an array can be found by adding the same number repeatedly, once for each row.

To find the total in an array, count how many objects are in one row, then add that same number once for every row in the array. This turns counting a whole array, one object at a time, into a much shorter repeated-addition equation.

Worked Example — Writing a Repeated Addition Equation

An array has 3 rows with 4 objects in each row. Since each row has 4 objects, add 4 once for every row: 4 + 4 + 4 = 12. The array has 12 objects in all.

Worked Example — Finding the Total of a Larger Array

An array has 5 rows with 3 objects in each row. Add 3 once for every row: 3 + 3 + 3 + 3 + 3 = 15. The array has 15 objects in all.

Tip

Count the number of rows first, and let that tell you exactly how many times to add the row's amount — an array with 5 rows needs the row amount added exactly 5 times.

Common Mistakes

Adding the wrong number of times, such as adding a row of 4 only three times for an array that actually has four rows.
Match the number of times you add to the number of rows in the array exactly — count the rows first, then repeat the addition that many times.
Mixing up rows and columns, using the number of objects in a column as the repeated amount instead of the number in a row.
Pick one consistent direction — count how many objects are in a single row, then add that amount once per row.

Key Takeaways

An array arranges objects into equal rows and columns.
The total in an array can be found with repeated addition — adding one row's amount once for every row.
Repeated addition of equal groups is the foundation multiplication builds on in later grades.

Summary

Arrays connect counting to repeated addition, the idea multiplication grows out of in later grades. The next unit shifts from operations back to place value, extending what you know about tens and ones into the hundreds.

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