Questions: Mental Math Strategies for Addition

Question 1

A student needs to add 8 + 6. Which strategy would be most efficient?

• A. Start at 1 and count all the way up to the total
• B. Break 6 into 2 + 4, give the 2 to the 8 to make 10, then add 4
• C. Start at 6 and count on 8 more steps
• D. Memorize the answer without using any strategy

Answer: (B)

Making 10 is the most efficient strategy here because 8 is only 2 away from 10. Breaking 6 into 2 + 4, using the 2 to complete the 10, then adding the leftover 4 gives 14. Option C (counting on from 6) would work but requires more steps — counting on is most efficient when adding a small number to a large one. The key insight is that you choose the strategy that fits the numbers.

Question 2

When adding 3 + 9 using the counting-on strategy, a student should:

• A. Start at 3 and count forward 9 steps: 4, 5, 6, 7, 8, 9, 10, 11, 12
• B. Start at 9 and count forward 3 steps: 10, 11, 12
• C. Add the two digits together like normal: 3 + 9 = 12
• D. Use doubles: 3 + 3 = 6, so 3 + 9 must be 12

Answer: (B)

The counting-on strategy works best when you start from the larger number and count on the smaller amount. Starting at 9 and counting 3 steps (10, 11, 12) requires only 3 mental moves. Starting at 3 and counting 9 steps is more work and more error-prone. This is why the commutative property matters: 3 + 9 = 9 + 3, so you can always flip to start from the bigger number.

Question 3

When you use the 'making 10' strategy on a problem like 7 + 5, you are changing the total amount being added.

• T. True
• F. False

Answer: False

Making 10 works by rearranging the pieces without changing the total. You borrow 3 from the 5 to make 7 into 10, leaving 2 from the 5. The expression becomes 10 + 2 = 12. The total is still 12 — you've only changed the *form* of the addition to pass through 10, which is easier to compute. Numbers are flexible: you can pull them apart and rearrange without changing the sum.

Question 4

A flexible mental math thinker uses the same strategy for most addition problem.

• T. True
• F. False

Answer: False

The key insight is that different problems suit different strategies. 9 + 3 is perfect for counting on (just 3 steps from 9). 8 + 7 is best handled by making 10 (8 + 2 + 5 = 15) or near-doubles (8 + 8 = 16, so 8 + 7 = 15). 6 + 6 calls for the doubles fact directly. A good mental math thinker reads the problem and picks the strategy that makes the computation simplest — not the same strategy every time.

Question 5

Explain why 'making 10' works as a strategy. What makes 10 special, and what allows you to rearrange numbers without changing the answer?

Model answer: Ten is special because our number system is built in groups of ten — adding to and from 10 is very fast. Making 10 works because of the associative property: you can regroup the addends without changing the total. When you break 5 into 2 + 3 to solve 8 + 5, you rewrite it as (8 + 2) + 3 = 10 + 3 = 13. The total stays the same; you've just rearranged the pieces into a shape that's easier to compute.

This is the deepest idea in early mental math: numbers are flexible. They can be broken apart and recombined in any order without changing their sum. Recognizing this flexibility — rather than treating addition as a fixed procedure — is what separates a fluent mental math thinker from one who is stuck counting on fingers.