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Day 17 · ‘Of’ changes the denominator · AC9M10ST04 · AC9M10P01Year 10 Maths · T1 W3–4 · Day 17 lesson

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Year 10 / Mathematics / Term 1 / Weeks 03 04

Part of the full two-week lesson sequence. Check the pack guide and taught point before teaching.

Open for this lesson: Pack guide · Fresh learner checks · Aids and text routes.

Teacher copy: This page may include teaching prompts or answer keys. Answer keys in this public library can be viewed by anyone. Give learners a clean prompt, use checks as formative evidence, and change a case locally when prior access matters.

Learner prompts

Goal: compare a row conditional proportion with an all-register proportion. 25 = 2 + 5 + 7 + 7 + 4.

0–2: Ask “18 of which cards?” before converting to a percent.
2–7: If one design is chosen uniformly from this constructed register, model P(two-sided | Puzzle)=18/24=3/4=75%; without the given condition, P(two-sided)=30/50=60%. Explain given Puzzle narrows the denominator; it does not mean a causal probability for future cards.
7–14: Learners compute Story two-sided 9/18=50% and No-theme two-sided 3/8=37.5%; label every group. Compare row rates without saying theme caused side count.
14–21: Routes: fraction strips with 24/50 totals; annotated two-way grid; symbolic fractions and a spoken/signed given/of sentence. All routes state numerator, denominator and scope.
21–25: Exit “Is 18/50 the same question as 18/24?” Look-for: no; Puzzle-and-two-sided among all versus two-sided given Puzzle. Next move: hold the numerator tile still while physically changing the reference-group frame.

Another setting: Fictional puzzle-card designs by two categories. Optional/home: invent a safe two-way table and read one given sentence; no family survey.

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