3A · Chapter 4 · Lesson 7
Word Problems — Part 1
Translate one-step equal-group stories into multiplication or division.
Today's challenge
Each of 3 shelves holds 17 equally sized boxes. How many boxes altogether? Try your own method, then compare it with a model.
What you'll learn
- Translate one-step equal-group stories into multiplication or division.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Equal-group and array models.
Prerequisite competency: 3A-C04-L01
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
There are 5 equal rows with 11 counters each. How many counters?
Show answer and reasoning
Answer: 55
There are 5 groups of 11; multiply 5×11=55. Turning the array does not change the total.
- E2
There are 6 equal rows with 9 counters each. How many counters?
Show answer and reasoning
Answer: 54
There are 6 groups of 9; multiply 6×9=54. Turning the array does not change the total.
Learn the concept
Words to know
- equal groups
- groups each containing the same number
- product
- the result of multiplication
Translate one-step equal-group stories into multiplication or division.
Label the number of groups and the number per group. Draw matching bars or an array, then multiply.
Why this works
First identify the number of equal groups and the number in each. Nine rows with seven seeds in each row contain 9 × 7 = 63 seeds. If four seeds do not sprout, there are 63 − 4 = 59 sprouts. If rows have different sizes, a single equal-groups multiplication does not describe them.
Check the meaning
If the groups are not equal, a single multiplication sentence does not represent the situation.
Concrete → Pictorial → Abstract
- Build: Use counters, grid paper, or labeled bundles to represent the story or quantity.
- Draw: Sketch an array, place-value exchange, or equal-unit bar; label what is known.
- Calculate: Write an equation matching the representation and solve.
- Verify: Use an inverse operation or a second strategy to check.
For advanced students: if you can already explain this concept, start with the independent or challenge set.
Worked examples and immediate checks
Explain each step aloud or in writing. Work the fresh question before revealing its solution.
Worked example 1
Reason and verify
Each of 3 shelves holds 17 equally sized boxes. How many boxes altogether?
- Label the number of groups and the number per group. Draw matching bars or an array, then multiply.
- The total is 3 equal groups of 17: 3 × 17 = 51.
- If the groups are not equal, a single multiplication sentence does not represent the situation.
Result: 51
Understanding check 1 — your turn
Each of 4 shelves holds 15 equally sized boxes. How many boxes altogether?
Reveal reasoning
Answer: 60 — The total is 4 equal groups of 15: 4 × 15 = 60.
Worked example 2
Reason and verify
Each of 5 shelves holds 24 equally sized boxes. How many boxes altogether?
- Label the number of groups and the number per group. Draw matching bars or an array, then multiply.
- The total is 5 equal groups of 24: 5 × 24 = 120.
- If the groups are not equal, a single multiplication sentence does not represent the situation.
Result: 120
Understanding check 2 — your turn
Each of 6 shelves holds 22 equally sized boxes. How many boxes altogether?
Reveal reasoning
Answer: 132 — The total is 6 equal groups of 22: 6 × 22 = 132.
Worked example 3
Reason and verify
Each of 7 shelves holds 8 equally sized boxes. How many boxes altogether?
- Label the number of groups and the number per group. Draw matching bars or an array, then multiply.
- The total is 7 equal groups of 8: 7 × 8 = 56.
- If the groups are not equal, a single multiplication sentence does not represent the situation.
Result: 56
Understanding check 3 — your turn
Each of 8 shelves holds 6 equally sized boxes. How many boxes altogether?
Reveal reasoning
Answer: 48 — The total is 8 equal groups of 6: 8 × 6 = 48.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Each of 4 shelves holds 14 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 56
The total is 4 equal groups of 14: 4 × 14 = 56.
- G2
Each of 6 shelves holds 21 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 126
The total is 6 equal groups of 21: 6 × 21 = 126.
- G3
Each of 8 shelves holds 5 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 40
The total is 8 equal groups of 5: 8 × 5 = 40.
- G4
Each of 10 shelves holds 13 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 130
The total is 10 equal groups of 13: 10 × 13 = 130.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Each of 13 shelves holds 5 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 65
The total is 13 equal groups of 5: 13 × 5 = 65.
- I2
Each of 4 shelves holds 12 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 48
The total is 4 equal groups of 12: 4 × 12 = 48.
- I3
Each of 6 shelves holds 19 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 114
The total is 6 equal groups of 19: 6 × 19 = 114.
- I4
Each of 8 shelves holds 26 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 208
The total is 8 equal groups of 26: 8 × 26 = 208.
- I5
Each of 10 shelves holds 10 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 100
The total is 10 equal groups of 10: 10 × 10 = 100.
- I6
Each of 12 shelves holds 18 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 216
The total is 12 equal groups of 18: 12 × 18 = 216.
- I7
Each of 3 shelves holds 25 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 75
The total is 3 equal groups of 25: 3 × 25 = 75.
- I8
Each of 6 shelves holds 9 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 54
The total is 6 equal groups of 9: 6 × 9 = 54.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
A shelf holds 7 boxes, but the boxes have different numbers of toys. Why is 7 × one box size not necessarily the total?
Show answer and reasoning
Answer: The groups are not equal
Multiplication as equal groups requires the same amount per group. Otherwise count or add the actual different sizes.
- C2
A farmer plants 9 equal rows of 7 seeds, and 4 seeds fail to sprout. How many sprout?
Show answer and reasoning
Answer: 59
9×7=63 planted; 63−4=59 sprout. The plants that failed do not change the original group structure.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Each of 9 shelves holds 10 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 90
The total is 9 equal groups of 10: 9 × 10 = 90.
- E2
Each of 11 shelves holds 17 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 187
The total is 11 equal groups of 17: 11 × 17 = 187.
- E3
Each of 13 shelves holds 24 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 312
The total is 13 equal groups of 24: 13 × 24 = 312.