Reading one table two ways
Keeping track of which group forms the denominator, when the question changes it three times.
Notes and data
A school surveyed 300 students about how they travel to school:
Walk: 90 students, of whom 27 also cycle sometimes Cycle: 60 students Bus: 120 students, of whom 18 also walk sometimes Car: 30 students
Answers in order, explanations withheld, and a report on where the chain broke.
- 4.1PercentagesFoundation
What percent of all surveyed students travel by bus?
- A40%
- B30%
- C25%
- D60%
Show the answer and reasoningHide the reasoning
40%
The denominator here is every student surveyed: 120 / 300 = 0.40, which is 40 percent.
- 4.2Two-way frequenciesStandard
Builds on: Question 1 used every student as the denominator; this one does not, and noticing the switch is the whole task.
What percent of the students who walk also cycle sometimes?
- A30%
- B9%
- C45%
- D22.5%
Show the answer and reasoningHide the reasoning
30%
The denominator has changed: the question asks about walkers, not all students. 27 / 90 = 0.30, which is 30 percent. Dividing 27 by 300 gives 9 percent, which answers a question nobody asked.
- 4.3Two-way frequenciesChallenge
Builds on: The distinction drilled in questions 1 and 2 between a count and a share of a chosen group.
A student claims that more bus riders walk sometimes than walkers cycle sometimes. Is the claim correct?
- ANo: 18 bus riders walk sometimes, against 27 walkers who cycle sometimes.
- BYes: bus riders are the largest group, so they contribute more of everything.
- CYes: 18 out of 120 is a larger share than 27 out of 90.
- DIt cannot be decided from the table.
Show the answer and reasoningHide the reasoning
No: 18 bus riders walk sometimes, against 27 walkers who cycle sometimes.
The claim is about counts, so the counts settle it: 18 is fewer than 27. The second choice reasons from group size rather than the figures, and the third compares shares when the claim was about numbers — and 18/120 is 15 percent against 30 percent anyway.