Practice 1
Answer and teaching response
3/4 · Each group can receive one quarter of each of three metres.
Share the leftover whole instead of discarding the remainder
Make an equal-share plan that allocates every whole and every fractional remainder, then recombine the shares to verify the total.
Get the student and teacher materialsPrepare the group
Learning goal: Produce a fair allocation with no unused amount, explaining how the number of recipients determines the fractional share of each leftover whole.
You will need: Paper rectangles to represent identical metre-long ribbons and a pencil. Ribbons can be cut into exact equal parts in this model; ignore cutting loss.
Start with this question
Five identical 1-metre ribbons must be shared equally among four groups. How much ribbon should each group receive?
1 1/4 metres per group. Give each group one whole ribbon, then cut the remaining ribbon into four equal quarter-metre parts.
- Name the total amount and the recipient count: five metres are being shared among four groups. The question asks for metres per group.
- Distribute one whole metre to each group. Four metres have been allocated, leaving one metre that still belongs in the shared total.
- Partition the remaining metre into four equal parts and give one quarter to every group. Each group now has 1 + 1/4 metres.
- Check fairness and conservation separately. All four shares are equal, and 4 × 1 1/4 = 5 metres restores the original total.
Run the 15-minute workshop
- 3 minutes. Ask learners what a remainder means when the material can be cut into smaller equal parts.
- 4 minutes. Allocate the five paper ribbons and verify both equal shares and the recovered total.
- 5 minutes. Complete the practice using a drawing of wholes first, then divide the leftovers.
- 3 minutes. Use the independent sharing task and multiply the per-group share by the number of groups.
A useful error to discuss
A learner might say: Each group gets one metre, with remainder one, so the sharing is finished.
The ribbon can be subdivided, so the remaining metre can still be shared. A whole-number remainder describes what is left before partitioning, not the final equal share.
Practise, then check independently
Try the first three tasks with the worked model. Try the final task without help. Enter a number, fraction or mixed number, such as 3/4 or 1 1/4. The number check does not assess your drawing or explanation.
Practice 2
Answer and teaching response
2 1/3 · Two metres go to each group and the remaining metre is split into thirds.
Practice 3
Answer and teaching response
2/5 · Each group receives one fifth of each of the two metres.
Independent check
Answer and teaching response
2 3/4 · Two metres each use eight metres; three remaining metres give three quarters to each group.
Transfer the idea
Would the same cutting plan work if the objects were whole sealed boxes that must remain unopened? Explain what changes.
Discuss a possible response
No. The mathematical fraction is still the equal share of the total quantity, but the physical rule prevents splitting a box. A practical allocation must report the unallocated whole boxes or change the rule; it cannot silently claim fractional boxes were distributed.
Choose the next teaching step
Look for:
- Uses the number of groups to divide every leftover whole.
- Checks equal shares and recovery of the total.
If the idea is not secure: Draw one row per group and distribute whole ribbons before cutting the leftovers.
If the learner is ready: Show a second method by cutting every original metre into fourths before sharing, and explain why the same 1 1/4-metre share results.
Materials for your group
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