Adding within 20

What is this skill?

Adding within 20 covers every sum up to twenty, such as 8 + 5, 9 + 9 or 6 + 7. In first grade the goal shifts from counting objects to using strategies. Children are expected to recall sums within 10 quickly and to work out bigger sums like 8 + 5 with a reliable mental method rather than counting every one on their fingers.

The most important strategy is making a ten. For 8 + 5, a child thinks: 8 needs 2 more to make 10, so split the 5 into 2 and 3; 8 + 2 = 10, and 10 + 3 = 13. Other useful strategies are doubles (6 + 6 = 12) and near doubles (6 + 7 is one more than 6 + 6, so 13), and counting on from the bigger number for small additions like 11 + 2.

Why it matters

Sums within 20 are the facts that every later calculation depends on. When second graders add 38 + 25, the ones column is 8 + 5. When third graders multiply, they rely on repeated addition. A child who has to count on fingers for 8 + 5 spends their effort on the small step and loses track of the larger problem.

The strategies matter as much as the answers. Making a ten is the same thinking children will use to add larger numbers in their heads, to make change with money, and to understand regrouping in written addition. Learning it with small numbers, where it is easy to check, makes it available later when the numbers grow.

Common mistakes

• Counting on from the smaller number, as in starting at 3 for 3 + 9 and counting on nine. It works but is slow and error-prone. Remind your child that 3 + 9 and 9 + 3 are the same, so start with 9.
• Off-by-one errors when counting on, usually from counting the starting number again. For 8 + 5, the count is "nine, ten, eleven, twelve, thirteen," five counts after 8.
• Splitting the second number incorrectly when making a ten, for example breaking 5 into 2 and 2. Practicing the pairs that make each small number (5 is 2 and 3, 4 and 1) keeps the strategy accurate.

How to help at home

• Use an egg carton cut down to ten cups, or draw two ten frames. Show 8 + 5 with counters, then slide 2 counters over to fill the first frame. The ten and the extra 3 make 13 obvious.
• Practice doubles until they are automatic: 6 + 6, 7 + 7, 8 + 8, 9 + 9. Then ask near-double questions, such as "If 7 + 7 is 14, what is 7 + 8?"
• Play a card game with two dealt cards from ace to 9; the first person to say the correct sum keeps them. Let your child explain how they worked out the trickier ones.
• When your child answers correctly, ask "How did you know?" Hearing their own strategy out loud helps it stick, and it tells you whether they are counting or reasoning.

Worked examples

These are real questions from the Tutorsaurus adding within 20 practice, with the answers worked out.

1. Example 1

   1 + 4 = ?

   Answer: 5. 1 + 4 = 5. Count on from the bigger number.

2. Example 2

   8 + 8 = ?

   Answer: 16. 8 + 8 = 16. Make a ten first: 8 + 2 = 10, then add 6 more.

3. Example 3

   6 + 10 = ?

   Answer: 16. 6 + 10 = 16. Make a ten first: 6 + 4 = 10, then add 6 more.