48 books are placed equally on shelves. Each shelf holds 8 books. How many shelves are needed? What is unknown in this problem?
AThe total number of books (48)
BThe number of books per shelf (8)
CThe number of shelves
DWhether to multiply or divide
Every division word problem has three quantities: total, number of groups, and size of each group. Here, the total is 48 books, the group size is 8 books per shelf, and the number of shelves (groups) is unknown. Identifying the unknown is the key step — once you know which of the three quantities is missing, the equation writes itself: 48 ÷ 8 = 6 shelves.
Question 2 Multiple Choice
A student reads: 'There are 6 bags with 9 apples in each bag. How many apples in all?' The student writes 54 ÷ 6 = 9. What went wrong?
ANothing — the student correctly identified this as a division problem
BThe student used multiplication facts, which don't apply here
CThe student divided instead of multiplied — the total isn't given, so this is a multiplication problem
DThe student swapped the dividend and divisor
This problem gives you the number of groups (6 bags) and the group size (9 apples each) and asks for the total — that is a multiplication problem: 6 × 9 = 54. Division is used when the total is given and a group or size quantity is unknown. The student confused the structure by treating a known total as something to solve for.
Question 3 True / False
In a division word problem, the dividend is always the total being divided.
TTrue
FFalse
Answer: True
The dividend is the whole amount — the total being split into groups. In 48 ÷ 6 = 8, the 48 (dividend) is the total. Identifying the total correctly is the most important step in setting up a division equation. Students who swap the dividend and divisor (e.g., writing 6 ÷ 48) get answers that don't make sense in context.
Question 4 True / False
In a grouping division problem, the known quantity is the number of groups, and the unknown is how many items go in each group.
TTrue
FFalse
Answer: False
This describes a sharing (partitive) problem, not a grouping problem. In grouping (measurement) division, you know the group SIZE and you're finding the number of groups. Example: '24 apples packed into bags of 6 — how many bags?' You know total (24) and group size (6); the number of groups (4) is unknown. The two interpretations are often confused, but recognizing which quantity is unknown is key.
Question 5 Short Answer
What are the three quantities in every division word problem, and how do you determine which operation to use once you've identified them?
Think about your answer, then reveal below.
Model answer: The three quantities are: (1) the total — the whole amount being divided; (2) the number of groups; (3) the size of each group. In a division problem, the total is always known and one of the other two quantities is unknown. If you know total and group size, divide to find number of groups. If you know total and number of groups, divide to find group size. If the total is unknown, multiply instead.
This three-quantity framework is the diagnostic tool that lets you set up any word problem correctly. Before writing an equation, students should label: 'What is my total? What is my group size? What is my number of groups? Which one am I solving for?' That analysis determines both the operation and the correct arrangement of numbers in the equation.