Practice 1
Answer and teaching response
3/4 · The cuts use 1 1/4 metres, leaving 3/4 metre.
Plan two cuts and account for the offcut
Check whether a stock length can supply two unlike-fraction pieces, then account for the unused part in a complete cutting record.
Get the student and teacher materialsPrepare the group
Learning goal: Produce a cut list that preserves the original length, uses compatible fractional units and distinguishes remaining material from a shortage.
You will need: Pencil, paper and a drawn strip. These are exact-length mathematics models; assume no material is lost during cutting.
Start with this question
A 2-metre strip must provide pieces of 3/4 metre and 2/3 metre. Is there enough material, and how much remains?
Yes. The required pieces total 17/12 metres, leaving 7/12 metre from the original 24/12 metres.
- Keep one measurement unit throughout: every length is measured in metres. Estimate first: each required piece is below one metre, so their sum is below the 2-metre stock.
- Choose twelfths so both piece lengths can be represented with equal units. Three quarters is 9/12 and two thirds is 8/12.
- Add the required lengths to get 17/12 metres. Subtract that total from 2 metres, or 24/12, to obtain an offcut of 7/12 metre.
- Check the entire record: 9/12 + 8/12 + 7/12 = 24/12. Both required pieces and the offcut together must recover the original stock.
Run the 15-minute workshop
- 3 minutes. Predict whether the two required pieces fit before calculating an exact offcut.
- 4 minutes. Draw a strip in twelfths, mark both cuts and account for the remaining section.
- 5 minutes. Complete the first three cut records, distinguishing a leftover length from a shortfall.
- 3 minutes. Use the independent plan and add all outputs back to the original stock.
A useful error to discuss
A learner might say: Add the numerators and denominators to find 5/7 metre of required material.
Quarters and thirds are different-sized units. Rename them as equal twelfths before counting; a total smaller than either large piece would also contradict the estimate.
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
7/12 · The stock is 18/12 and the cuts use 8/12 + 3/12, leaving 7/12.
Practice 3
Answer and teaching response
1/4 · The required 1 1/4 metres exceed the stock by 1/4 metre; there is a shortage rather than an offcut.
Independent check
Answer and teaching response
11/12 · The cuts use 15/12 + 10/12 = 25/12 metres, leaving 11/12 of the original 36/12.
Transfer the idea
If a real cutting process removes a small length at every cut, can this exact model be used unchanged to order material? Explain what information is missing.
Discuss a possible response
No. The model explicitly assumes no cutting loss. A practical plan needs the loss per cut and the number of cuts, then includes that extra material before deciding whether the stock is sufficient.
Choose the next teaching step
Look for:
- Uses one length unit and equivalent fractions before adding.
- Accounts for every piece and interprets a shortage correctly.
If the idea is not secure: Use a pre-partitioned strip with a common denominator, label the stock first and shade each required length once.
If the learner is ready: For the worked two-piece plan, find the shortest exact stock length with no offcut: 17/12 metres, or 1 5/12 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
Common Denominator Kitchen — full teaching sequence and materials