3A · Chapter 4 · Lesson 3
Looking Back at Division
Interpret division as equal sharing or counting equal groups.
Today's challenge
72 counters are shared equally among 9 children. How many does each receive? Try your own method, then compare it with a model.
What you'll learn
- Interpret division as equal sharing or counting equal groups.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Multiplication facts.
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 7 equal rows with 4 counters each. How many counters?
Show answer and reasoning
Answer: 28
There are 7 groups of 4; multiply 7×4=28. Turning the array does not change the total.
- E2
There are 8 equal rows with 11 counters each. How many counters?
Show answer and reasoning
Answer: 88
There are 8 groups of 11; multiply 8×11=88. Turning the array does not change the total.
Learn the concept
Words to know
- quotient
- the result of division
- equal sharing
- divide a total into a fixed number of equal groups
Interpret division as equal sharing or counting equal groups.
Equal sharing asks how many in each of a given number of groups; grouping asks how many groups of a given size fit. Both use the same inverse multiplication.
Why this works
Division answers different kinds of equal-group questions. If 24 counters are shared among 6 children, each gets 4. If 24 counters are packed in bags of 6, there are 4 bags. Both use 24 ÷ 6 = 4, but the meaning of 6 differs, so label groups and items per group.
Check the meaning
Confirm that every group has the same amount and that the full total is accounted for.
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
72 counters are shared equally among 9 children. How many does each receive?
- Equal sharing asks how many in each of a given number of groups; grouping asks how many groups of a given size fit. Both use the same inverse multiplication.
- 9 equal groups contain 72 counters: 72÷9=8; verify 8×9=72.
- Confirm that every group has the same amount and that the full total is accounted for.
Result: 8
Understanding check 1 — your turn
28 counters are shared equally among 4 children. How many does each receive?
Reveal reasoning
Answer: 7 — 4 equal groups contain 28 counters: 28÷4=7; verify 7×4=28.
Worked example 2
Reason and verify
22 counters are shared equally among 2 children. How many does each receive?
- Equal sharing asks how many in each of a given number of groups; grouping asks how many groups of a given size fit. Both use the same inverse multiplication.
- 2 equal groups contain 22 counters: 22÷2=11; verify 11×2=22.
- Confirm that every group has the same amount and that the full total is accounted for.
Result: 11
Understanding check 2 — your turn
50 counters are shared equally among 5 children. How many does each receive?
Reveal reasoning
Answer: 10 — 5 equal groups contain 50 counters: 50÷5=10; verify 10×5=50.
Worked example 3
Reason and verify
42 counters are shared equally among 3 children. How many does each receive?
- Equal sharing asks how many in each of a given number of groups; grouping asks how many groups of a given size fit. Both use the same inverse multiplication.
- 3 equal groups contain 42 counters: 42÷3=14; verify 14×3=42.
- Confirm that every group has the same amount and that the full total is accounted for.
Result: 14
Understanding check 3 — your turn
78 counters are shared equally among 6 children. How many does each receive?
Reveal reasoning
Answer: 13 — 6 equal groups contain 78 counters: 78÷6=13; verify 13×6=78.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
66 counters are shared equally among 6 children. How many does each receive?
Show answer and reasoning
Answer: 11
6 equal groups contain 66 counters: 66÷6=11; verify 11×6=66.
- G2
98 counters are shared equally among 7 children. How many does each receive?
Show answer and reasoning
Answer: 14
7 equal groups contain 98 counters: 98÷7=14; verify 14×7=98.
- G3
32 counters are shared equally among 8 children. How many does each receive?
Show answer and reasoning
Answer: 4
8 equal groups contain 32 counters: 32÷8=4; verify 4×8=32.
- G4
63 counters are shared equally among 9 children. How many does each receive?
Show answer and reasoning
Answer: 7
9 equal groups contain 63 counters: 63÷9=7; verify 7×9=63.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
30 counters are shared equally among 6 children. How many does each receive?
Show answer and reasoning
Answer: 5
6 equal groups contain 30 counters: 30÷6=5; verify 5×6=30.
- I2
56 counters are shared equally among 7 children. How many does each receive?
Show answer and reasoning
Answer: 8
7 equal groups contain 56 counters: 56÷7=8; verify 8×7=56.
- I3
88 counters are shared equally among 8 children. How many does each receive?
Show answer and reasoning
Answer: 11
8 equal groups contain 88 counters: 88÷8=11; verify 11×8=88.
- I4
126 counters are shared equally among 9 children. How many does each receive?
Show answer and reasoning
Answer: 14
9 equal groups contain 126 counters: 126÷9=14; verify 14×9=126.
- I5
8 counters are shared equally among 2 children. How many does each receive?
Show answer and reasoning
Answer: 4
2 equal groups contain 8 counters: 8÷2=4; verify 4×2=8.
- I6
21 counters are shared equally among 3 children. How many does each receive?
Show answer and reasoning
Answer: 7
3 equal groups contain 21 counters: 21÷3=7; verify 7×3=21.
- I7
40 counters are shared equally among 4 children. How many does each receive?
Show answer and reasoning
Answer: 10
4 equal groups contain 40 counters: 40÷4=10; verify 10×4=40.
- I8
65 counters are shared equally among 5 children. How many does each receive?
Show answer and reasoning
Answer: 13
5 equal groups contain 65 counters: 65÷5=13; verify 13×5=65.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
A student says 24 ÷ 6 has to mean “24 shared among six children.” Give a different equal-group story.
Show answer and reasoning
Answer: Six objects per box, four boxes
24 objects arranged in bags of 6 form 4 bags. Division may count groups rather than their sizes.
- C2
Twenty-four crayons are put in boxes of 6. Now ask a DIFFERENT division question whose answer is 6 rather than 4.
Show answer and reasoning
Answer: How many boxes if there are 4 crayons in each? 6 boxes
Originally 24÷6=4 boxes. Change the group size to 4 crayons per box: 24÷4=6 boxes.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
36 counters are shared equally among 6 children. How many does each receive?
Show answer and reasoning
Answer: 6
6 equal groups contain 36 counters: 36÷6=6; verify 6×6=36.
- E2
63 counters are shared equally among 7 children. How many does each receive?
Show answer and reasoning
Answer: 9
7 equal groups contain 63 counters: 63÷7=9; verify 9×7=63.
- E3
96 counters are shared equally among 8 children. How many does each receive?
Show answer and reasoning
Answer: 12
8 equal groups contain 96 counters: 96÷8=12; verify 12×8=96.