Questions: Subtraction Within 100

Question 1

Which strategy is most efficient for solving 84 - 79?

• A. Use the standard borrowing algorithm, regrouping the tens digit
• B. Count up from 79 to 84: 79 + 5 = 84, so the answer is 5
• C. Subtract tens then ones: 84 - 70 = 14, then 14 - 9 = 5
• D. Count back by ones from 84 until you reach 79

Answer: (B)

When two numbers are close together, counting up is far more efficient than any subtraction algorithm. Instead of borrowing or counting back, you ask: 'What do I add to 79 to get 84?' 79 + 5 = 84, so the answer is 5. The other strategies all reach the correct answer but require significantly more steps. Strategy selection — choosing the right tool based on the numbers — is what subtraction fluency actually looks like.

Question 2

Before computing 91 - 47, a student estimates '90 - 50 = 40, so my answer should be around 40.' She then computes and gets 54. What should she conclude?

• A. Her estimate was too rough; trust the computation since 54 is the precise answer
• B. Her computation is likely wrong — 54 is too far from 40, and she should recheck her work
• C. Her estimate of 40 was wrong; the correct answer is 54
• D. Estimation and computation can give different answers depending on the strategy used

Answer: (B)

The actual answer to 91 - 47 is 44, so the estimate of ~40 is accurate. The computed answer of 54 is 10 too high — a regrouping error. Estimation is a built-in check: when the computed result is far from the estimate, it flags an error before it becomes a wrong answer. The student should recompute, not discard the estimate.

Question 3

The standard borrowing algorithm is the most accurate subtraction method and should be used for most problem within 100.

• T. True
• F. False

Answer: False

All correct strategies give the same accurate answer. The issue is efficiency, not accuracy. For problems like 83 - 78 where numbers are close, counting up takes 5 steps while borrowing takes many more. Fluent students select the strategy that fits the numbers: counting up for close numbers, the standard algorithm or subtract-tens-then-ones for larger differences. Using borrowing for every problem is like taking the longest route when a shortcut exists.

Question 4

Subtraction is not commutative: 72 - 48 and 48 - 72 give different results.

• T. True
• F. False

Answer: True

Unlike addition and multiplication, subtraction order matters. 72 - 48 = 24, while 48 - 72 gives a negative number — a completely different result. This makes subtraction fundamentally different from addition, which is why students should never flip the order of a subtraction problem. A common regrouping error is subtracting the smaller digit from the larger regardless of which is on top — which implicitly treats subtraction as commutative when it isn't.

Question 5

Explain why counting up is often a better strategy than borrowing for subtraction, and describe the type of problem where it works best.

Model answer: Counting up reframes subtraction as addition: instead of computing 81 - 76, you ask 'what must I add to 76 to reach 81?' (answer: 5). It works best when the two numbers are close together, because the gap is small and takes only a few steps to bridge. When numbers are far apart, borrowing or subtracting by place value is more efficient.

The counting-up strategy also reinforces the inverse relationship between addition and subtraction — they are two ways of describing the same gap between numbers. Flexible students recognize which strategy minimizes their work. 81 - 76 takes 5 steps to count up; borrowing here requires regrouping and multiple digit operations. 91 - 34 is far apart, so borrowing or subtract-tens-then-ones is faster.