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Fraction Classroom · 2.5.0 · Student pages

Compare participation when the groups have different sizes

Keep a group's participation fraction separate from its participant count and choose the quantity that actually answers a survey question.

Anonymous group code: __________   Date: __________

The reference totals differ. Group A's larger fraction does not make its participant count larger than Group B's.GroupWhole groupFractionParticipantsA16 learners3/412 learnersB24 learners2/316 learners
The reference totals differ. Group A's larger fraction does not make its participant count larger than Group B's.

Build the idea

model. In Group A, 3/4 of 16 learners choose drawing. In Group B, 2/3 of 24 learners choose drawing. Which group has more drawing participants?

  1. Read exactly what is being compared. More participants asks for a count of learners; a larger fraction asks for the proportion of a specified whole.
  2. Find one quarter of Group A's 16 learners: 4. Three such groups give 12 drawing participants. Record both 3/4 and 12 instead of replacing one quantity with the other.
  3. Find one third of Group B's 24 learners: 8. Two such groups give 16 participants, so Group B has four more people choosing drawing.
  4. Check the counts against their group totals and compare the fractions separately if needed. Three quarters exceeds two thirds, yet twelve is below sixteen because the reference groups have different sizes.

Worked example: Group B has more participants: 16 compared with Group A's 12. Group A has the larger participation fraction, but that fraction refers to a smaller group.

Practise and explain

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

p1. Support: 1/4 of a group of 20 learners chooses drawing. Enter the participant count.

p2. Core: 2/3 of a group of 18 learners participates. Enter the participant count.

p3. Challenge: Group C has 1/2 of 30 learners participating; Group D has 3/4 of 20 participating. Enter the difference in participant counts, and explain why their fractions differ.

e1. Independent check: Group E has 3/4 of 24 learners participating; Group F has 2/3 of 21. How many more participants are in E? Enter the count and record both totals.

Transfer the idea

transfer. A report says one half of one group and one half of another participate. What additional information is needed to compare participant counts?