Questions: Multiplication Word Problems

Question 1

'Mia has 4 times as many stickers as Tomás. Tomás has 6 stickers. How many stickers does Mia have?' A student writes 4 + 6 = 10. What is the error?

• A. The student added correctly but should then multiply the result by 4
• B. '4 times as many' signals a multiplicative comparison — the answer is 4 × 6 = 24, not an addition
• C. The student forgot to include Mia's stickers in the total
• D. 'Times as many' means divide, so the answer should be 6 ÷ 4

Answer: (B)

'Times as many' signals that one quantity is a multiple of another — it is a comparison using multiplication. Mia's amount equals Tomás's amount taken 4 times: 4 × 6 = 24. Adding 4 and 6 treats 'times' as if it meant 'more,' which confuses additive comparison ('4 more than') with multiplicative comparison ('4 times as many'). These are different operations with very different results.

Question 2

'There are 8 rows of chairs with 7 chairs in each row.' Which setup correctly identifies the two factors?

• A. 8 is the group size and 7 is the number of groups
• B. 7 is the total and 8 tells you how many to add
• C. 8 is the number of groups and 7 is the group size
• D. This is a comparison problem, not an equal-groups problem

Answer: (C)

The 'rows' are the groups (8 of them), and the chairs in each row are the group size (7 each). Number of groups × group size = total: 8 × 7 = 56. Option A reverses the roles, which doesn't change the product here (multiplication is commutative) but reflects faulty understanding of the structure — understanding the structure matters especially for multi-step problems and division.

Question 3

Drawing a picture of equal groups before writing an equation can help you correctly identify which number is the group size and which is the number of groups.

• T. True
• F. False

Answer: True

Diagrams externalize the structure of the problem. Drawing 6 circles (groups) with 8 dots in each (group size) makes the multiplication structure visible before any numbers are written. This prevents the common error of confusing the two factors, especially in problems where the wording is ambiguous.

Question 4

'Jaylen collected 3 times as many rocks as Priya' means Jaylen collected 3 more rocks than Priya.

• T. True
• F. False

Answer: False

'3 times as many' is multiplicative: if Priya has 7 rocks, Jaylen has 3 × 7 = 21. '3 more than' is additive: Jaylen would have 7 + 3 = 10. These are entirely different relationships. 'Times as many' always signals multiplication, never addition.

Question 5

What is the difference between an equal-groups multiplication problem and a comparison multiplication problem? Give one signal phrase that helps identify each type.

Model answer: An equal-groups problem describes several collections each containing the same number of items — the multiplication structure is explicit (e.g., '6 bags with 8 apples each'). A comparison problem states that one quantity is a multiple of another without describing physical groups (e.g., '4 times as many'). Signal phrases for equal groups include 'each,' 'per,' 'groups of,' and 'rows of.' Signal phrases for comparison include 'times as many' and 'times as much.'

Recognizing the problem type before writing an equation is the central skill. Both types call for multiplication, but students who only recognize equal-groups situations will miss comparison problems — or incorrectly add when they see 'times.'