Reach for the Star | GCSE Mathematics

L075: Frequency trees and probability models

Objective

Interpret frequency trees and compare model predictions with observed data.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Frequency trees and probability models
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for frequency trees and probability models.

Core practice

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

Reasoning

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

Exam-style

A probability problem is presented with two stages. Complete the representation, calculate the probability and explain any assumption.

WWW / EBI

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.