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Stage 3 of 20

Single-Digit Subtraction

Understand single-digit subtraction as taking away, comparing, and finding a missing addend using fact families, number lines, and precise checks.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Interpret subtraction as removal, difference, and a missing-part question
  • Use related addition facts to calculate differences within 9
  • Count back or count up when either route is efficient
  • Verify a subtraction equation by recombining the parts

Why This Matters

Subtraction is used to describe change, compare quantities, and recover a missing part. These meanings later support change-making, measurement differences, equations with unknowns, and borrowing across place-value columns.

Connecting subtraction to addition turns two separate lists of facts into one network. A single bond such as 4 + 5 = 9 supplies 9 − 4 = 5 and 9 − 5 = 4 as well.

The Reasoning Behind Single-Digit Subtraction

Subtraction describes several closely related situations. In 9 − 4, four objects may be removed from nine, or 9 and 4 may be compared to find the gap between them. Both interpretations produce 5. Thinking about the situation prevents the minus sign from becoming a command with no meaning.

Every subtraction fact can be read as a missing-addend equation. The question 8 − 3 asks, “Three plus what makes eight?” Because 3 + 5 = 8, the difference is 5. This inverse relationship grows directly from the part-part-whole bonds used in Stage 1: if 3 and 5 compose 8, removing either part reveals the other.

Counting back models removal. To solve 7 − 2, begin at 7 and make two backward jumps: 6, then 5. Counting up models distance and can be better for close numbers: for 9 − 7, move from 7 to 8 and then 9, a gap of two. A good number sense choice minimizes the number of tracked steps.

Unlike addition, subtraction is not commutative. Changing 9 − 4 to 4 − 9 changes the question and moves beyond this stage’s nonnegative facts. The first number names the whole or starting quantity; the second names the amount removed or the lower endpoint of a comparison.

Checking restores the removed part. If 9 − 6 = 3, then 3 + 6 must equal 9. This check tests the structure of the equation, not merely a repeated subtraction attempt. Doubles and number bonds from earlier stages make many checks immediate: 8 − 4 is 4 because 4 + 4 makes 8.

Where You Will Use Single-Digit Subtraction

If nine library books are on a cart and four are shelved, the missing part is the number still on the cart: 4 plus 5 reconstructs the original 9. In a comparison, a score of 9 is two points above a score of 7, found by counting up from 7.

The same symbol can therefore answer “how many remain?” and “how many more?” Identifying which story is present helps determine whether to picture removal or a gap.

See the Strategy in Action

Read the strategy, then prove you can use it: every example ends with a matching problem on new numbers that you answer and check right here. Answer it and press New numbers for as many fresh problems as you like.

Think of the missing partner

9 − 4

  1. 1 I ask which number joins 4 to make 9.
  2. 2 I know the bond 4 + 5 = 9.
  3. 3 Therefore the missing part is 5.

9 − 4 = 5

Your turn — try it on new numbers

6 − 2 = ?

Count back a short distance

7 − 2

  1. 1 I start at 7 without counting 7 as a step.
  2. 2 Two backward jumps land on 6 and then 5.

7 − 2 = 5

Your turn — try it on new numbers

3 − 1 = ?

Count up to compare

9 − 7

  1. 1 The numbers are close, so I start at 7.
  2. 2 I move to 8, then 9: that is two jumps.

9 − 7 = 2

Your turn — try it on new numbers

8 − 5 = ?

Use a double fact

8 − 4

  1. 1 I recognize 8 as two equal groups of 4.
  2. 2 Removing one group of 4 leaves the other group.

8 − 4 = 4

Your turn — try it on new numbers

5 − 1 = ?

Self-Check: Errors to Avoid

Reversing the numbers

In 8 − 3, start with the whole 8 and remove 3. Do not switch the numbers just because 3 is smaller; check the result by adding it back to 3.

Counting the start as one

For 6 − 2, saying “6, 5” records only one backward move. Begin the count after 6: first 5, second 4.

Using addition without matching the whole

The check for 9 − 5 is not any fact containing 5. Find the number that makes exactly 9: 5 + 4 = 9, so the correction is 4.

Pro Tips

  • • Turn each uncertain subtraction into “the second number plus what makes the first?”
  • • Count back for a small amount removed and count up for nearby endpoints.
  • • Keep the first number visible as the whole while reasoning about its parts.
  • • Check by adding the difference and subtrahend in either order.

Practice Exercises

Work each problem mentally, then type the answer and check it. Nothing is marked correct until you enter a value that actually equals the result, and every problem keeps its mental-steps note in reach if you get stuck.

  1. 1. 9 − 3 = ?
  2. 2. 8 − 5 = ?
  3. 3. 7 − 2 = ?
  4. 4. 6 − 4 = ?
  5. 5. 9 − 8 = ?
  6. 6. 5 − 3 = ?
  7. 7. 8 − 2 = ?
  8. 8. 7 − 5 = ?
  9. 9. 9 − 6 = ?
  10. 10. 4 − 1 = ?
  11. 11. 6 − 3 = ?
  12. 12. 8 − 7 = ?
  13. 13. 5 − 2 = ?
  14. 14. 7 − 4 = ?
  15. 15. 9 − 5 = ?
  16. 16. 8 − 4 = ?
  17. 17. 6 − 1 = ?
  18. 18. 3 − 3 = ?

Drill Stage 3 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses single-digit subtraction with answers that stay positive. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

5 − 3 = ?

Stage 3 Questions

Does subtraction always mean taking objects away?

No. It can also compare two quantities or measure the distance between numbers. All three meanings calculate a difference.

Why can addition check subtraction?

Addition reverses the separation: the difference plus the removed part reconstructs the original whole.

Should I count back or think addition?

Choose the route with fewer mental steps. Known fact families are fast; counting up or back remains a sound strategy when a fact is uncertain.