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Fraction Classroom · 2.4.0 · Teacher answers & responses

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.

Ribbon lengths in metres. Each cross represents one piece; repeated crosses must each contribute their length to the inventory.01/4××1/2×3/4××1
Ribbon lengths in metres. Each cross represents one piece; repeated crosses must each contribute their length to the inventory.

Build the idea

model. The line plot represents five ribbon pieces. What is their combined length?

  1. Read the horizontal labels as lengths in metres. Each cross means one piece at that length, not one metre of ribbon.
  2. Write one measurement for every cross. Preserve both quarter-metre pieces and both three-quarter-metre pieces; repeated values still represent different objects.
  3. 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.
  4. 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.

Worked example: 2 1/2 metres: 1/4 + 1/4 + 1/2 + 3/4 + 3/4 = 10/4. Each mark contributes a separate measured piece.

Practise and explain

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

p1. For the displayed plot, how many ribbon pieces are there? Enter the count.

Answer: 5

Teacher response: There are two quarter-metre, one half-metre and two three-quarter-metre pieces.

p2. What is the total length in metres of the two 3/4-metre pieces?

Answer: 1 1/2

Teacher response: The two separate pieces contribute 3/4 + 3/4 = 6/4 metres.

p3. Using the plot, find the difference in metres between the longest and shortest piece.

Answer: 1/2

Teacher response: Subtract 1/4 metre from 3/4 metre; frequency does not change the length of a single piece.

e1. A new stock has three 1/4-metre pieces and one 1/2-metre piece. Draw its line plot and enter the combined length in metres.

Answer: 1 1/4

Look for:

  • Preserves the frequency of each measurement.
  • Labels a count as pieces and a length as metres.

Teacher response: Three quarter units and two more quarter units make five quarters.

Transfer the idea

transfer. Two stock boxes contain the same total ribbon length. Must their line plots be identical? Give a counterexample.

Answer: 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.

Run the 15-minute workshop

teach-1. 3 minutes: Match the five listed pieces to five crosses. Check that every piece appears exactly once.

teach-2. 4 minutes: Build a stock list from the plot and find the combined length using quarter units.

teach-3. 5 minutes: Use the same plot for the practice inventory questions; require units for every result.

teach-4. 3 minutes: Complete the independent new-stock question and check that its list includes repeated lengths.

Respond to the learner

misconception. Add the three different axis labels once each to get the total ribbon.

Teacher response: 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.

support. Write the length under every cross before combining equal fractional units.

extend. 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.

Teaching notes