Early Math · Grades 1, 2

Addition and Subtraction Strategies Within 20

Quick answer

Facts within 20 can be found fast without counting every object. Counting on starts from the bigger number. Turning a sum around never changes it, so 3 + 8 can be found as 8 + 3. Making a ten splits one number to fill a ten first: 8 + 6 is 8 + 2 + 4, which is 10 + 4 = 14. Doubles, near doubles, subtracting through ten and using a known fact such as 8 + 4 = 12 for 12 − 8 finish the set, until the facts are known by heart.

What you'll learn

  • Add and subtract by counting on and counting back
  • Use turn-around facts and add three numbers in any order
  • Make a ten, use doubles and near doubles, and subtract through ten
  • Use an addition fact to find a subtraction fact

Count on

To find 9+29 + 2, you do not need to count all 1111. Start at 99 and count on 22: 1010, 1111.

9+2=119 + 2 = 11

To subtract a small number, count back. For 12−312 - 3, start at 1212 and count back 33: 1111, 1010, 99.

Turn it around

3+83 + 8 and 8+38 + 3 are the same. Both are 1111.

So when you add, start with the bigger number. It is much faster to count on 33 from 88 than to count on 88 from 33.

You can add three numbers in any order, too. For 2+6+42 + 6 + 4, add 6+4=106 + 4 = 10 first. Then 10+2=1210 + 2 = 12.

Make a ten

To add 8+68 + 6, fill a ten first.

Eight and six, making a ten Two ten-frames. Eight blue counters and two orange ones fill the first frame. Four more orange counters are in the second.
Eight and six, making a ten

88 needs 22 more to make 1010. So split the 66 into 22 and 44.

8+6=8+2+4=10+4=148 + 6 = 8 + 2 + 4 = 10 + 4 = 14

Why making a ten works

You still add all 66. You only add them in two steps: 22 and then 44.

The first step lands on 1010. You can add to 1010 in your head right away, because 10+410 + 4 is how we say fourteen: ten and four.

Splitting a number into parts does not change it. That is why every one of these ways gives the same answer.

Doubles and near doubles

Doubles stick in your mind fast: 5+5=105 + 5 = 10, 6+6=126 + 6 = 12, 7+7=147 + 7 = 14, 8+8=168 + 8 = 16.

A near double is one away from a double. For 6+76 + 7, think 6+6+16 + 6 + 1.

6+7=6+6+1=12+1=136 + 7 = 6 + 6 + 1 = 12 + 1 = 13

Subtract through ten

To find 13−413 - 4, take away 33 first to land on 1010. Then take away the last 11.

13−4=13−3−1=10−1=913 - 4 = 13 - 3 - 1 = 10 - 1 = 9

Use a fact you know

Adding and subtracting are linked. If you know 8+4=128 + 4 = 12, then you know 12−8=412 - 8 = 4 and 12−4=812 - 4 = 8.

So to find 12−812 - 8, ask: ”88 plus what makes 1212?”

Worked examples

Facts to know by heart

In first grade, learn every sum and difference within 1010 by heart. In second grade, learn every sum of two one-digit numbers, like 7+67 + 6 and 9+89 + 8.

The ways in this lesson are how you learn them. Use a way a few times, and soon you will know the fact with no work at all.

Common mistakes

Practice problems

  1. Count on to find 9+39 + 3.

    Answer

    1212

    Full solution

    Start at 99 and count on 33: 1010, 1111, 1212.

  2. Find 2+92 + 9. Which number should you start with?

    Answer

    1111; start with 99

    Full solution

    2+9=9+22 + 9 = 9 + 2. Start at the bigger number, 99, and count on 22: 1010, 1111.

  3. Make a ten to find 8+58 + 5.

    Answer

    1313

    Full solution

    88 needs 22 to make 1010. Split 55 into 22 and 33. 10+3=1310 + 3 = 13.

  4. Use a double to find 8+98 + 9.

    Answer

    1717

    Full solution

    8+8=168 + 8 = 16, and 99 is 11 more than 88. So 8+9=16+1=178 + 9 = 16 + 1 = 17.

  5. Find 14−614 - 6 by going through ten.

    Answer

    88

    Full solution

    Take away 44 to land on 1010. Then take away 22 more. 14−4=1014 - 4 = 10, and 10−2=810 - 2 = 8.

  6. You know 7+5=127 + 5 = 12. What is 12−712 - 7?

    Answer

    55

    Full solution

    77 plus 55 makes 1212, so 1212 take away 77 leaves 55.

  7. Add: 3+5+73 + 5 + 7.

    Answer

    1515

    Full solution

    3+7=103 + 7 = 10 makes a ten. Then 10+5=1510 + 5 = 15.

  8. Find 17−817 - 8.

    Answer

    99

    Full solution

    Ask: ”88 plus what makes 1717?” 8+2=108 + 2 = 10, and 77 more is 1717. That is 2+7=92 + 7 = 9.

  9. Find 6+56 + 5 with a near double.

    Answer

    1111

    Full solution

    5+5=105 + 5 = 10, and 66 is 11 more than 55. So 6+5=116 + 5 = 11.

  10. Eli counts on to find 7+47 + 4. He says ”77, 88, 99, 1010” and gets 1010. What went wrong?

    Hint

    What is the first number to say when you count on from 77?

    Answer

    He counted the 77. The answer is 1111.

    Full solution

    Counting on 44 from 77 means saying four numbers after 77: 88, 99, 1010, 1111.

    So 7+4=117 + 4 = 11.

Frequently asked questions

What is the make-a-ten strategy?

Split one number so the other becomes 10. For 8 + 6, split 6 into 2 and 4: 8 + 2 = 10, then 10 + 4 = 14.

What are near doubles?

Sums one away from a double. 6 + 7 is 6 + 6 + 1, so it is 12 + 1 = 13.

Does the order of numbers matter when adding?

No. 3 + 8 and 8 + 3 are both 11. It does matter when subtracting: 8 − 3 is not the same as 3 − 8.

How do I subtract through ten?

Take away enough to land on 10, then the rest. 13 − 4 is 13 − 3 = 10, then 10 − 1 = 9.

Which facts should be known by heart?

By the end of first grade, all sums and differences within 10. By the end of second grade, all sums of two one-digit numbers.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.1.OA.B.3Operations and Algebraic ThinkingApply properties of operations as strategies to add and subtract.
  • CCSS.MATH.CONTENT.1.OA.C.5Operations and Algebraic ThinkingRelate counting to addition and subtraction (e.g., by counting on 2 to add 2).
  • CCSS.MATH.CONTENT.1.OA.C.6Operations and Algebraic ThinkingAdd and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
  • CCSS.MATH.CONTENT.2.OA.B.2Operations and Algebraic ThinkingFluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.