Counting Back Strategy for Subtraction
Counting back is one of the first subtraction strategies we learn. Start at the minuend and count downward by the size of the subtrahend.
How Counting Back Works
- Start at the minuend (larger number).
- Count backward the number of steps equal to the subtrahend.
- The number you land on is the difference.
9 − 4: start at 9, count back 4 steps: 8, 7, 6, 5
Examples
| Calculation | Start at | Count back | Answer |
|---|---|---|---|
| 8 − 3 | 8 | 7, 6, 5 | 5 |
| 15 − 5 | 15 | 14, 13, 12, 11, 10 | 10 |
| 20 − 7 | 20 | 19…13 | 13 |
Counting Back in Tens
54 − 23: start at 54, back two tens: 44, 34; back 3 ones: 33, 32, 31
When to Use It — and When Not To
Ideal for small subtrahends (1–5). For large subtrahends, counting up is faster.
50 − 48: counting back 48 steps is slow. Count up instead: 48 → 50 = 2 steps. Answer: 2.
Key Takeaways
- Start at the minuend; count backward by the subtrahend.
- Count in tens first, then ones for larger numbers.
- Best for small subtrahends (1–5).
- When numbers are close, counting up is more efficient.
Practice Questions
- Use counting back to find 11 − 4.
- Use counting back in tens then ones for 67 − 23.
- Why is counting up better for 100 − 97?
- Find 80 − 30 by counting back in tens.
- A child has 16 stickers and gives away 5. Use counting back to find how many remain.