Practice 1
Answer and teaching response
5 · There are two quarter-metre, one half-metre and two three-quarter-metre pieces.
Count every ribbon in a fraction line plot
Turn repeated measurement marks into a usable stock record, then check both the number of pieces and their combined length.
Get the student and teacher materialsPrepare the group
Learning goal: Produce an inventory that preserves repeated measurements and distinguishes a piece count from a total length.
You will need: Pencil and paper. The illustrative ribbon lengths are 1/4, 1/4, 1/2, 3/4 and 3/4 metre; assume no stretching or cutting loss.
Start with this question
The line plot represents five ribbon pieces. What is their combined length?
2 1/2 metres: 1/4 + 1/4 + 1/2 + 3/4 + 3/4 = 10/4. Each mark contributes a separate measured piece.
- Read the horizontal labels as lengths in metres. Each cross means one piece at that length, not one metre of ribbon.
- Write one measurement for every cross. Preserve both quarter-metre pieces and both three-quarter-metre pieces; repeated values still represent different objects.
- Rename the half metre as two quarters and add all ten quarter units. Four quarters make a metre, so ten quarters make 2 1/2 metres.
- Check two totals separately: there are five pieces and 2 1/2 metres. A total of three lengths would signal that repeated measurements were omitted.
Run the 15-minute workshop
- 3 minutes. Match the five listed pieces to five crosses. Check that every piece appears exactly once.
- 4 minutes. Build a stock list from the plot and find the combined length using quarter units.
- 5 minutes. Use the same plot for the practice inventory questions; require units for every result.
- 3 minutes. Complete the independent new-stock question and check that its list includes repeated lengths.
A useful error to discuss
A learner might say: Add the three different axis labels once each to get the total ribbon.
Point to each cross and match it to a separate row in the inventory. The labels name possible lengths; the marks tell how many actual pieces have each length.
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
1 1/2 · The two separate pieces contribute 3/4 + 3/4 = 6/4 metres.
Practice 3
Answer and teaching response
1/2 · Subtract 1/4 metre from 3/4 metre; frequency does not change the length of a single piece.
Independent check
Answer and teaching response
1 1/4 · Three quarter units and two more quarter units make five quarters.
Transfer the idea
Two stock boxes contain the same total ribbon length. Must their line plots be identical? Give a counterexample.
Discuss a possible response
No. One 1-metre piece and two 1/2-metre pieces both total 1 metre but produce different plots and different piece counts. The inventory must keep that distinction.
Choose the next teaching step
Look for:
- Preserves the frequency of each measurement.
- Labels a count as pieces and a length as metres.
If the idea is not secure: Write the length under every cross before combining equal fractional units.
If the learner is ready: Move one 3/4-metre piece out of the original stock and update both the plot and the combined length, which becomes 1 3/4 metres.
Materials for your group
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.
Continue with the complete lesson
Repeated Fraction Groups — full teaching sequence and materials