To solve 53 − 28 mentally, Carlos thinks: 'I'll count up from 28 to 53. First I jump to 30 — that's 2. Then I jump to 50 — that's 20. Then I jump to 53 — that's 3. My answer is 25.' Is Carlos correct, and what strategy is he using?
AWrong — to subtract, you must count backward, not forward
BCorrect — he is using the counting-on strategy, turning the subtraction problem into a series of additions
CWrong — you cannot mix tens jumps and ones jumps in the same problem
DCorrect — but only because 28 happens to be close to a multiple of ten
Carlos is correct and his method is elegant. The counting-on strategy reframes 53 − 28 as 'what do I add to 28 to reach 53?' Each hop adds a friendly amount and targets a landmark number. 28 → 30 is +2, 30 → 50 is +20, 50 → 53 is +3. Total: 2 + 20 + 3 = 25. This works for any subtraction problem — not just when numbers are close to tens — and is often faster and more accurate than counting backward.
Question 2 Multiple Choice
To solve 71 − 29 using the round-and-adjust strategy: you round 29 up to 30, compute 71 − 30 = 41, then...
AStop — 41 is the final answer
BSubtract 1 more to get 40, because rounding up means adding more
CAdd 1 back to get 42, because you subtracted 1 too many when you used 30 instead of 29
DSubtract 29 from 41 to double-check
When you round 29 up to 30, you are subtracting a larger number than the original problem asks for. 71 − 30 takes away one more than 71 − 29 does. To correct for this overshoot, you add 1 back: 41 + 1 = 42. The rule is: if you rounded UP (subtracted more than needed), ADD back the difference. If you had rounded DOWN (subtracted less than needed), you would subtract the difference.
Question 3 True / False
In the counting-on strategy for subtraction, you count backward from the larger number to the smaller number.
TTrue
FFalse
Answer: False
Counting on means starting at the smaller number and counting FORWARD (adding) to reach the larger number. For 45 − 18, you start at 18 and count up to 45 — you never subtract at all. This is the key insight: subtraction can be turned into addition. Counting backward from the larger number is a different strategy (counting back) that is only efficient when the number being subtracted is very small.
Question 4 True / False
When using the round-and-adjust strategy, if you round the subtracted number UP before computing, you need to ADD back the difference to get the correct answer.
TTrue
FFalse
Answer: True
If you subtract a number that is bigger than what the problem asks, your answer will be too small. You over-subtracted, so you compensate by adding back the extra. For example, 65 − 19: round 19 up to 20, compute 65 − 20 = 45, then add back 1 (because 20 is 1 more than 19), giving 46. The adjustment always corrects for the difference between the rounded number and the original.
Question 5 Short Answer
Explain why the counting-on strategy turns a subtraction problem into an easier addition problem. Use 62 − 57 as your example.
Think about your answer, then reveal below.
Model answer: Subtraction asks 'how much is left after taking away?' but counting on asks the equivalent question 'how much do I need to add to get from the smaller number to the larger?' For 62 − 57, instead of trying to subtract 57 from 62, count up from 57 to 62: 57 → 60 is +3, 60 → 62 is +2. Total added: 5. So 62 − 57 = 5. The two numbers are close together, so only a few small hops are needed — far easier than borrowing or counting back 57 steps.
The key insight is that subtraction and addition are two sides of the same relationship: a − b = ? is the same question as b + ? = a. Counting on exploits the fact that small hops to landmark numbers are much easier to track mentally than large backward counts. This strategy is especially powerful when the two numbers are close together (small difference) or when one number is near a multiple of ten.