Reach for the Star

Sample spaces and systematic lists · Optional extension

L050 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

Two fair dice are rolled. Count the outcomes with a sum of 9 and find the probability.

Reveal a worked check after attempting

(3,6),(4,5),(5,4),(6,3): 4/36=1/9.

Deep challenge

A learner lists (1,3) and (3,1) as one outcome when two distinct dice are rolled. Explain the effect.

Reveal a worked check after attempting

The outcomes are distinct ordered pairs; merging them undercounts the total and can distort probability.

Recall & Review: feedback and extension integration

Lesson L050: Sample spaces and systematic lists

Objective: List outcomes systematically and calculate probabilities from sample spaces.

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: Two fair dice are rolled. Count the outcomes with a sum of 9 and find the probability.

Deep challenge: A learner lists (1,3) and (3,1) as one outcome when two distinct dice are rolled. Explain the effect.