Practice 1
Answer and teaching response
15 · Two equal parts total 10 cm, so one is 5 cm and all three total 15 cm.
Rebuild a missing whole from a known fraction
Use a labelled fragment to reconstruct its reference whole, then prove that the reconstructed whole gives the original fraction.
Get the student and teacher materialsPrepare the group
Learning goal: Produce a strip diagram that identifies one equal part, the complete whole and the units of both measurements.
You will need: Paper strips, pencil and a ruler. Lengths in the task are stated measurements; do not measure the on-screen diagram.
Start with this question
A 9 cm fragment is three quarters of a complete strip. How long was the complete strip?
12 cm. The 9 cm fragment contains three equal quarter-parts, so each quarter is 3 cm. Four such parts make the whole.
- Read the fraction as a relationship to the missing whole. The 9 cm fragment is three quarters, not the entire reference strip.
- Draw three equal boxes for the known fragment and label their combined length 9 cm. Share that length across the boxes: each box represents 3 cm.
- Add one more equal box to complete four quarters. Four copies of 3 cm produce a whole strip of 12 cm.
- Check the reconstructed whole: splitting 12 cm into four equal parts gives 3 cm per quarter, and three quarters recover the original 9 cm fragment.
Run the 15-minute workshop
- 3 minutes. Show only the three-quarter fragment. Ask learners to say what the 9 cm label measures.
- 4 minutes. Find one equal part and reconstruct the whole with a fourth matching box. Check the fragment against the new whole.
- 5 minutes. Complete the first three reconstruction cards with a labelled strip for each.
- 3 minutes. Use the independent card and check the result by rebuilding its known fragment.
A useful error to discuss
A learner might say: Take three quarters of 9 because the question contains three quarters.
Point to the label on the fragment. Nine is already the length of the selected three parts. First find one part, then build the missing whole.
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
16 · The known fragment is one of four equal 4 cm parts.
Practice 3
Answer and teaching response
36 · One sixth is 6 cm; six sixths make 36 cm.
Independent check
Answer and teaching response
16 · Each eighth is 2 cm, so eight equal parts make 16 cm.
Transfer the idea
Can the same 6 cm piece be one half of one strip and one third of another? Draw both reference wholes.
Discuss a possible response
Yes. A 12 cm whole has a 6 cm half, while an 18 cm whole has a 6 cm third. The piece stays the same; its relationship to the reference whole changes.
Choose the next teaching step
Look for:
- Distinguishes the known fragment from the unknown whole.
- Uses equal parts and checks that the stated fraction recovers the fragment.
If the idea is not secure: Provide the correct number of empty boxes and mark how many belong to the known fragment.
If the learner is ready: Choose a whole length and write two different fragment clues that both reconstruct it; include a diagram to verify each clue.
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
Unit Fraction Builders — full teaching sequence and materials