Questions: Mental Math Strategies for Subtraction

Question 1

A student needs to solve 13 - 9 quickly in their head. What is the most efficient mental strategy?

• A. Count back 9 steps from 13: 12, 11, 10, 9, 8, 7, 6, 5, 4
• B. Think: 9 + ? = 13, and use the known addition fact to find the answer
• C. Write out the problem on paper and subtract the ones column
• D. Round 9 to 10, subtract, then correct by adding 1 back

Answer: (B)

When numbers are far apart, counting back is slow and error-prone. The most efficient strategy is 'thinking addition': knowing that 9 + 4 = 13 gives you 13 - 9 = 4 instantly, using a memorized fact. Counting back 9 steps (A) works but takes much longer and risks losing count. Option D (adjust strategy) is also valid but adds an extra step. Thinking addition turns subtraction into a fact retrieval.

Question 2

A student solving 15 - 8 thinks: '15 - 5 = 10, then 10 - 3 = 7.' What strategy are they using?

• A. Counting back from 15 one step at a time
• B. Thinking addition — asking '8 + what = 15?'
• C. Decomposing 8 into 5 + 3 to subtract in two easier steps
• D. Using a related multiplication fact

Answer: (C)

The student broke 8 into 5 + 3 and subtracted in two steps — first landing on 10, then subtracting the remaining 3. This is decomposition: splitting a harder subtraction into two easier ones. Counting back (A) would involve going back 8 steps one at a time. Thinking addition (B) would mean asking '8 + 7 = 15, so the answer is 7' — valid but a different approach.

Question 3

If you know that 6 + 8 = 14, you can use that fact to solve 14 - 8 without subtracting at all.

• T. True
• F. False

Answer: True

Addition and subtraction are inverse operations — they undo each other. Knowing 6 + 8 = 14 immediately tells you that 14 - 8 = 6 and 14 - 6 = 8. This is the 'think-addition' strategy: instead of subtracting, ask 'what do I add?' and use a memorized addition fact to find the answer instantly.

Question 4

Counting back is the best mental math strategy for most subtraction problems.

• T. True
• F. False

Answer: False

Counting back works well for small differences (like 12 - 3) but is slow and error-prone for larger ones (like 15 - 8 or 13 - 9). A flexible math thinker chooses the strategy that fits the problem: counting up when numbers are close, think-addition when you know the fact family, and decomposing when crossing a ten. No single strategy is best for every problem.

Question 5

You need to solve 12 - 9 in your head. Explain a strategy other than counting back that gives you the answer quickly, and say why it works.

Model answer: Counting up: start at 9 and count forward to 12 — that's 3 steps (10, 11, 12) — so the answer is 3. Or think-addition: 9 + 3 = 12, so 12 - 9 = 3. Both work because subtraction and addition are inverse operations, and counting up is much faster than counting back 9 steps.

When two numbers are close together, counting up from the smaller number is faster than counting back from the larger. You just count the gap from 9 to 12 — three steps. Alternatively, if you know your addition facts, you recognize 9 + 3 = 12 immediately. Counting back 9 steps from 12 takes much longer and risks losing count.