Explore · fraction group measurement
How many 2/5-liter-sized groups are in 2 liters? Count a partial final group as a fraction of a group.
Great Inheritance Mathematics Term A · Independent learning
Dividing a Whole Number by a Fraction
Learning target: Interpret whole-number division by a proper fraction as measurement of group size.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
Find 3 × 2/3.
Understand the idea
Interpret whole-number division by a proper fraction as measurement of group size.
Whole-number division by a proper fraction measures how many fractional-size groups fit in the total quantity. The answer may be a whole or fractional number of groups. Check by multiplying group count by size per group.
Vocabulary focus: sharing interpretation, measurement interpretation, inverse multiplication. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Dividing by numerator and denominator separately.
Model to study: Measurement/group-size bar model.
Worked examples
Worked examples 1 · fraction group measurement
How many 5/6-liter-sized groups are in 7 liters? Count a partial final group as a fraction of a group.
Solution: 42/5 groups
Why: Each group is 5/6 L. The group count is 7 ÷ 5/6 = 7×6/5 = 42/5. Multiply the group count by 5/6 L to check it equals 7 L.
Worked examples 2 · fraction group measurement
How many 2/3-liter-sized groups are in 5 liters? Count a partial final group as a fraction of a group.
Solution: 15/2 groups
Why: Each group is 2/3 L. The group count is 5 ÷ 2/3 = 5×3/2 = 15/2. Multiply the group count by 2/3 L to check it equals 5 L.
Worked examples 3 · fraction group measurement
How many 2/5-liter-sized groups are in 3 liters? Count a partial final group as a fraction of a group.
Solution: 15/2 groups
Why: Each group is 2/5 L. The group count is 3 ÷ 2/5 = 3×5/2 = 15/2. Multiply the group count by 2/5 L to check it equals 3 L.
Check understanding
Check understanding 1 · fraction group measurement
How many 2/6-liter-sized groups are in 7 liters? Count a partial final group as a fraction of a group.
Check understanding 2 · fraction group measurement
How many 2/3-liter-sized groups are in 2 liters? Count a partial final group as a fraction of a group.
Guided practice
Guided practice 1 · fraction group measurement
How many 3/4-liter-sized groups are in 6 liters? Count a partial final group as a fraction of a group.
Guided practice 2 · fraction group measurement
How many 2/4-liter-sized groups are in 3 liters? Count a partial final group as a fraction of a group.
Guided practice 3 · fraction group measurement
How many 4/6-liter-sized groups are in 6 liters? Count a partial final group as a fraction of a group.
Independent practice
Independent practice 1 · fraction group measurement
How many 2/6-liter-sized groups are in 4 liters? Count a partial final group as a fraction of a group.
Independent practice 2 · fraction group measurement
How many 4/5-liter-sized groups are in 2 liters? Count a partial final group as a fraction of a group.
Independent practice 3 · fraction group measurement
How many 2/3-liter-sized groups are in 7 liters? Count a partial final group as a fraction of a group.
Independent practice 4 · fraction group measurement
How many 2/5-liter-sized groups are in 7 liters? Count a partial final group as a fraction of a group.
Independent practice 5 · fraction group measurement
How many 3/4-liter-sized groups are in 4 liters? Count a partial final group as a fraction of a group.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “6 ÷ 2/3 = 4; I multiplied instead of counting how many 2/3-size groups fit.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: How many 2/3-liter-sized groups are in 6 liters? Count a partial final group as a fraction of a group.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). How many 2/4-liter-sized groups are in 4 liters? Count a partial final group as a fraction of a group.
Exit check
Exit check 1 · fraction group measurement
How many 5/6-liter-sized groups are in 3 liters? Count a partial final group as a fraction of a group.
Exit check 2 · fraction group measurement
How many 3/6-liter-sized groups are in 5 liters? Count a partial final group as a fraction of a group.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.