Reach for the Star

Frequency trees and probability models · Optional extension

L075 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

Of 80 people, 45 cycle. Of those who cycle, 27 are adults. Find the conditional proportion of adults among cyclists.

Reveal a worked check after attempting

27/45=3/5.

Deep challenge

A frequency tree has root 60 and first branches 28 and 31. Diagnose the issue and state a possible repair.

Reveal a worked check after attempting

Branches total 59, so one person is unaccounted for; verify data and correct one count or add an unknown branch of 1.

Recall & Review: feedback and extension integration

Lesson L075: Frequency trees and probability models

Objective: Interpret frequency trees and compare model predictions with observed data.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the outcomes systematically, used the correct probability rule and checked that the probabilities or frequencies were consistent.

Even Better If (EBI)

I will show the sample space, branch or set reasoning explicitly, state any dependence or condition and check totals before giving the final probability.

Stretch and deep challenge

Stretch: Of 80 people, 45 cycle. Of those who cycle, 27 are adults. Find the conditional proportion of adults among cyclists.

Deep challenge: A frequency tree has root 60 and first branches 28 and 31. Diagnose the issue and state a possible repair.