Questions: Multi-Step Word Problems

Question 1

A school had 125 students. Then 38 new students joined. Then 15 students moved away. A student writes the equation 125 − 38 + 15. What is wrong?

• A. Nothing — addition and subtraction can be done in any order.
• B. The operations are reversed: students joining should be addition (+38), and students moving away should be subtraction (−15). The correct expression is 125 + 38 − 15.
• C. This problem requires multiplication, not addition and subtraction.
• D. You cannot mix addition and subtraction in the same equation.

Answer: (B)

Reading carefully reveals what each event means as an operation. Students 'joining' increases the total (addition). Students 'moving away' decreases the total (subtraction). Writing 125 − 38 + 15 reverses those operations, giving 102 instead of the correct answer 148. This is a reading error, not an arithmetic error — the key skill in multi-step problems is correctly translating each event into the right operation before calculating.

Question 2

Why should you write down an intermediate answer after completing each step in a multi-step problem?

• A. Because the rules of arithmetic require it.
• B. Because the answer from one step becomes the starting number for the next step — recording it creates a clear handoff and a checkpoint where you can verify reasonableness before continuing.
• C. Because teachers want to see your work written out.
• D. Because each step's answer is a final answer to a separate problem.

Answer: (B)

In multi-step problems, the output of one step is the input of the next. Recording the intermediate answer makes that handoff explicit and gives you a natural checkpoint: does this intermediate value make sense before I proceed? Students who try to chain all steps in their head in one go frequently lose track and make errors that are hard to locate.

Question 3

In a multi-step word problem, checking whether your final answer is reasonable can catch errors where you used the right arithmetic but applied the operations in the wrong order.

• T. True
• F. False

Answer: True

A reasonableness check is the last line of defense against procedural errors. If a problem involves a student who started with 48 cards, gained some, then gave some away, an answer of 200 is obviously unreasonable given the numbers involved — even if the individual arithmetic steps were correct. Reasonableness checking catches order-of-operations errors that the arithmetic itself won't flag.

Question 4

A multi-step word problem usually requires exactly two steps — one addition and one subtraction.

• T. True
• F. False

Answer: False

Multi-step problems can have any number of steps, and the operations can be any combination of addition and subtraction (or, in later grades, multiplication and division). The defining feature is simply that the problem cannot be solved with a single operation. The number and type of steps depends entirely on the events described in the problem.

Question 5

How do you decide which operation (addition or subtraction) to use for each step in a multi-step word problem?

Model answer: Look at what is happening in each event of the story. If something is being gained, added, combined, or increased — use addition. If something is being lost, used up, given away, or decreased — use subtraction. Reading each sentence and asking 'does this make the total bigger or smaller?' helps assign the right operation before calculating. Drawing a quick picture of each event can also make it visible whether the amount is growing or shrinking.

This is the translation skill at the heart of word problems. The arithmetic itself is straightforward; the challenge is mapping real-world language ('joined,' 'spent,' 'gave away') onto mathematical operations. Building this careful, event-by-event reading habit is what makes multi-step problems consistently solvable.