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Using Counting to Add Digits Up to 20

This lesson introduces counting strategies for adding whole numbers up to 20. Students learn to count all objects in two groups and, more efficiently, to count on from the larger number, building a foundation for fluent addition facts.

What Does Counting to Add Mean?

Before students memorize addition facts, they learn to find sums by counting. Counting to add means using numbers in order, one at a time, to figure out how many objects there are in total. This is one of the very first strategies used for adding with digits up to 20, and it builds the number sense needed for every addition strategy that comes after it.

There are two common counting strategies for addition: counting all and counting on. Both strategies work for any two numbers that add up to 20 or less, but one is quicker once you understand how numbers are ordered.

Counting All: Combining Two Groups

Counting all means counting every single object in both groups, starting from 1, to find the total. For example, to add \( 7 + 5 \), a student would count 7 blue dots one at a time, then keep counting the 5 orange dots without starting over, all the way to 12.

Counting every dot from 1 to 12 shows that \( 7 + 5 = 12 \).

Counting all works well, but it takes longer as numbers get bigger, because every object must be counted from the very beginning.

Counting On: A Faster Way to Add

Counting on is a shortcut. Instead of counting both groups from 1, a student starts at the larger number and counts up by the smaller number. To find \( 8 + 5 \), start at 8 and count on 5 more: 9, 10, 11, 12, 13. This is much faster than counting all 13 objects one by one.

Counting on from 8 to 13 shows that \( 8 + 5 = 13 \).

A number line makes counting on easy to see, and it is the same idea used in using a number line to add up to 20.

Steps for Counting On

Follow these steps whenever you add two numbers with counting on:

Look at both numbers and find the larger one. This is your starting point.
Say the starting number out loud or hold it in your head.
Count on, one number at a time, for as many counts as the smaller number.
The last number you say is the sum.

For \( 12 + 6 \), start at 12 and count on 6 more: 13, 14, 15, 16, 17, 18. So \( 12 + 6 = 18 \).

Worked Examples

Example 1: Find \( 9 + 4 \). Start at 9 (the larger number) and count on 4 more: 10, 11, 12, 13. So \( 9 + 4 = 13 \).

Example 2: Find \( 6 + 8 \). Even though 6 is written first, always start at the larger number, 8, and count on 6 more: 9, 10, 11, 12, 13, 14. So \( 6 + 8 = 14 \).

Example 3: Find \( 14 + 5 \). Start at 14 and count on 5 more: 15, 16, 17, 18, 19. So \( 14 + 5 = 19 \).

Why Counting Strategies Matter

Counting all and counting on give every student a reliable way to solve addition problems even before facts are memorized. With practice, these counting steps become faster and more automatic, which leads directly into recalling addition facts up to 20 from memory. Counting is the bridge between touching objects one by one and confidently knowing that numbers combine to make a sum.

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