R.1 Counting back to subtract using number lines - up to 20

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Counting Back to Subtract

Counting back is a way to subtract by starting at a number and saying the numbers in reverse order. Each number you say takes one away.

Examples:

Problem: 12 − 1 = ?
Solution: Start at 12. Count back one number: 11. So, 12 − 1 = 11.
Problem: 15 − 3 = ?
Solution: Start at 15. Count back three numbers: 14, 13, 12. So, 15 − 3 = 12.

Helpful Hint

When subtracting, always move toward smaller numbers step by step without skipping.

Fingers help keep track of how many steps you subtract. Think of the starting number in your head, then fold down one finger for each count back.

Examples:

Problem: 13 − 2 = ?
Solution: Start at 13. Fold down 1 finger (12), then another (11). So, 13 − 2 = 11.
Problem: 9 − 4 = ?
Solution: Start at 9. Fold down 4 fingers: 8, 7, 6, 5. So, 9 − 4 = 5.

Helpful Hint

Say each number out loud as you count back on your fingers to stay on track.

A number line shows subtraction by moving left. Start at the larger number and hop left one step for each number you subtract.

Examples:

Problem: 18 − 5 = ?
Solution: Start at 18. Hop back 5 steps: 17, 16, 15, 14, 13. So, 18 − 5 = 13.
Problem: 14 − 6 = ?
Solution: Start at 14. Hop back 6 steps: 13, 12, 11, 10, 9, 8. So, 14 − 6 = 8.

Helpful Hint

Each hop on the number line shows one subtraction step. Always move to the left.

Sometimes it is easier to subtract in parts. Break apart a number to make the subtraction simpler.

Examples:

Problem: 16 − 7 = ?
Solution: Break 7 into 6 and 1. Start at 16. Subtract 6 first (16 − 6 = 10). Then subtract 1 more (10 − 1 = 9). So, 16 − 7 = 9.
Problem: 19 − 8 = ?
Solution: Break 8 into 9 − 1. Start at 19. Subtract 9 to get 10, then add 1 back: 10 + 1 = 11. So, 19 − 8 = 11.

Helpful Hint

Breaking apart numbers helps make subtraction easier, especially when working with numbers close to 10.

Subtraction is part of everyday life. We can use strategies like counting back, using fingers, or number lines to solve story problems.

Examples:

Problem: Sarah had 12 balloons. 5 floated away. How many are left?
Solution: Start at 12. Count back 5: 11, 10, 9, 8, 7. So, 12 − 5 = 7.
Problem: There are 17 ducks in a pond. 8 swim away. How many ducks remain?
Solution: Start at 17. Count back 8: 16, 15, 14, 13, 12, 11, 10, 9. So, 17 − 8 = 9.

Try This

Create your own subtraction story. Use a number line, fingers, or breaking apart numbers to solve it.