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Fraction Classroom · 2.4.0 · Student pages

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.

Anonymous group code: __________   Date: __________

The first piece, second piece and offcut account for all 24 twelfths in the 2-metre stock. No cut loss is assumed.PartLength in metresTwelfth unitsFirst piece3/49/12Second piece2/38/12Offcut7/127/12Original stock224/12
The first piece, second piece and offcut account for all 24 twelfths in the 2-metre stock. No cut loss is assumed.

Build the idea

model. A 2-metre strip must provide pieces of 3/4 metre and 2/3 metre. Is there enough material, and how much remains?

  1. 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.
  2. Choose twelfths so both piece lengths can be represented with equal units. Three quarters is 9/12 and two thirds is 8/12.
  3. 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.
  4. Check the entire record: 9/12 + 8/12 + 7/12 = 24/12. Both required pieces and the offcut together must recover the original stock.

Worked example: Yes. The required pieces total 17/12 metres, leaving 7/12 metre from the original 24/12 metres.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. From 2 metres, cut pieces of 1/2 metre and 3/4 metre. Enter the remaining length in metres.

p2. From 1 1/2 metres, cut 2/3 metre and 1/4 metre. Enter the remaining length in metres.

p3. You have 1 metre but need separate pieces of 3/4 metre and 1/2 metre. How many additional metres are needed?

e1. From a 3-metre strip, plan cuts of 1 1/4 metres and 5/6 metre. Enter the offcut length and check that all pieces recover 3 metres.

Transfer the idea

transfer. 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.