# Year 10 mathematics · Weeks 3–4 · Days 11–20

Ten distinct **25-minute** lessons continue the opening fortnight's scatterplot and claim-scope work. Week 3 tests a numerical association and a line against invented game-map drafts; Week 4 uses a two-way table of invented game-card designs to ask “of which group?” This is a mathematics transfer alongside Year 10 English's method/denominator reading, using **different stories, numbers and check cases**. The [fictional source data](STUDENT-DATA.md), [clean learner tasks](LEARNER.md), [fresh checks](STUDENT-CHECKS.md), [teacher-targeted public key](teacher/KEY-AND-NEXT.md) and [A4/text aids](print/TEXT-ALTERNATIVES.md) are separate. The check prompts and key are public files, so they are not secure exams; adapt numbers/context if prior answer access matters.

**Prepare:** Source G and C, graph frame, residual ruler, category grid and claim audit; no personal data, products or actual game trials. Give large/reflowable text, tactile points or number strips, calculators where the goal is interpretation, sign/AAC or exact-word scribe. Each day has **three switchable evidence routes**, not fixed learner types. Record a reasoning cue separately from an access accommodation. The teacher samples short exits, not 30 individual interviews in one period. Each 25-minute schedule is 2 launch + 5 model + 7 practise + 7 choice/revision + 4 exit, except check days (2 + 3 + 10 + 6 + 4).

## Day 11 · The question determines the axes · AC9M10ST03 · AC9M10ST05

**Goal:** form a bivariate question from Source G without inventing a population claim. **25 = 2 + 5 + 7 + 7 + 4.**

- **0–2:** Ask “As draft room count rises, what happens to listed icon count in this notebook?” Name each variable and its unit.
- **2–7:** Model points (1 room, 5 icons), (1 room, 6 icons). Repeated x-values are two maps. Set x 0–5 rooms, y 0–25 clue icons on the [frame](print/scatterplot-frame.pdf).
- **7–14:** Learners identify all nine ordered pairs, decide whether the notebook is a random sample of games (no evidence), and plot/describe at least four including both one-room drafts.
- **14–21:** **Routes:** place raised coordinate pegs while a partner reads exact values; annotate large-grid axes and name two repeated x-values; write a coordinate list plus verbal direction without drawing. Each route retains both variables and the source boundary.
- **21–25:** Exit “What is the unit of y? What does the set fail to show about real players?” **Look-for:** clue icons; no gameplay test. **Next move:** if a learner swaps axes, attach the question to both axis labels and replot one pair.

**Another setting:** An invented music score page count versus stage-cue marks. **Optional/home:** sketch a fictional two-pair table with clear units; no real data gathering.

## Day 12 · Plot all drafts before naming a pattern · AC9M10ST03

**Goal:** describe direction, strength and approximate form with a visible unusual value. **25 = 2 + 5 + 7 + 7 + 4.**

- **0–2:** Retrieve the two x=1 maps without collapsing them to one dot.
- **2–7:** Plot (2,8) and (2,9), then show why repeated x does not prevent a positive overall association.
- **7–14:** Complete nine points. Describe the set as generally positive and roughly linear for x=1–4, with the x=5,y=22 draft higher than the proposed line. “Strong” is a judgement about this nine-point pattern, not all games.
- **14–21:** **Routes:** tactile dot board with axes; high-contrast plotted page and a caption; exact coordinate readout plus a spoken/signed shape description. Partners check one point against Source G.
- **21–25:** Exit “Which draft prevents an unqualified ‘exact straight-line’ claim?” **Look-for:** I at (5,22). **Next move:** if I is erased as a mistake, put it back and ask what information would justify excluding it.

**Another setting:** Imaginary storyboard panels versus caption marks. **Optional/home:** describe a pattern and an unusual point from three made-up pairs.

## Day 13 · A residual measures mismatch, not cause · AC9M10ST03 · AC9M10ST01

**Goal:** compare all nine drafts to the proposed `M(x)=3x+2` and keep claims scoped. **25 = 2 + 5 + 7 + 7 + 4.**

- **0–2:** Say the line is the notebook's proposal, not a fitted physical law.
- **2–7:** At x=2 the line predicts 8; drafts C/D list 8/9, residuals 0/+1. Define `record − model`, with clue-icon units.
- **7–14:** Learners fill the [residual ruler](print/residual-ruler.pdf): A–I residuals 0,+1,0,+1,0,+1,0,+1,+5. At x=5, 22−17=+5. Discuss how one chosen line can describe the x=1–4 cluster but miss I.
- **14–21:** **Routes:** move 0/+1/+5 number tiles next to draft letters; fill a table and calculate by hand; use a calculator then explain one subtraction orally/AAC. Every route states the sign and unit.
- **21–25:** Exit “Does +5 show why I differs?” **Look-for:** no, only numerical mismatch. **Next move:** change a causal sentence into a question about the design decision.

**Another setting:** Invented picture-book scene counts versus caption counts. **Optional/home:** find one residual from an original mini-table.

## Day 14 · Which maps did the notice select? · AC9M10ST01 · AC9M10ST05

**Goal:** audit Source G2's quantifier, selection and possible bias. **25 = 2 + 5 + 7 + 7 + 4.**

- **0–2:** Read “every”, “guarantees”, “without exception” aloud; identify what a strong claim would require.
- **2–7:** Contrast x=1 values 5/6 with x=2 values 8/9: equal x can have different y. More decisively, proposed line predicts 17 at x=5 but I lists 22. A selected A/C/E/G sequence supports the exact rule only for those four drafts, not all nine.
- **7–14:** Learners compare the four selected drafts with the full notebook and plan a fairer next dataset: define draft source, inclusion rule, units and gameplay question separately. No real participants are recruited.
- **14–21:** **Routes:** highlight selected/unselected cards; arrange nine tactile cards into retained/omitted piles; write a short source-claim-limit audit. Each must name at least one omitted conflicting record and a sampling limit.
- **21–25:** Exit “What is the denominator of maps in the source and in the cherry-picked set?” **Look-for:** nine versus four. **Next move:** if learner calls four random, ask for an actual selection procedure.

**Another setting:** Fictional rehearsal diagrams selectively showing cue density. **Optional/home:** invent a five-item dataset and write a headline that tells its scope.

## Day 15 · Fresh Check A: new paired-data claim · AC9M10ST03 · AC9M10ST01

**Goal:** transfer axis, association and residual audit to a distinct fictional cue-board case. **25 = 2 + 3 + 10 + 6 + 4.**

- **0–2:** Explain this is a public fresh practice check, not a secure test or real-world study.
- **2–5:** Offer exact read-aloud, large/tactile axes, calculator, AAC or scribe; do not explain the new points.
- **5–15:** Learners independently answer [Check A](STUDENT-CHECKS.md); collect first work.
- **15–21:** Discuss the general routine `variable / model / residual / scope` after collection. **Routes:** number tiles; annotated graph; verbal/typed source audit. Do not overwrite first-response evidence.
- **21–25:** Teacher uses the [public key](teacher/KEY-AND-NEXT.md) to target one next skill. **Next move:** recheck later with different numbers if a response was cued or previously seen.

**Another setting:** An invented animation frame schedule after assessment. **Optional/home:** explain why a point can be unusual without being wrong.

## Day 16 · Build the whole two-way table · AC9M10ST04

**Goal:** distinguish two categorical variables, cells, margins and a missing label. **25 = 2 + 5 + 7 + 7 + 4.**

- **0–2:** Introduce Source C: 50 invented designs, not players. Theme and side count are categorical variables.
- **2–7:** Locate Puzzle/two-sided 18, Puzzle row total 24 and two-sided column total 30. Explicitly add 18+9+3=30 and 24+18+8=50.
- **7–14:** Learners reconstruct a blank [category grid](print/two-way-grid.pdf) from Source C, including **No theme assigned**; check all margins by two directions.
- **14–21:** **Routes:** sort labelled count tiles into tactile rows/columns; fill a large-print matrix; dictate a cell and margin audit to an exact-word scribe. Each route checks two cells and the grand total.
- **21–25:** Exit “What does 30 count? What does 50 count?” **Look-for:** two-sided designs versus all designs. **Next move:** if a learner excludes no-theme cards, point to their known side counts.

**Another setting:** Imaginary plant-label designs by colour and fold type, not real plants. **Optional/home:** draw a 2×2 table from four invented cards.

## Day 17 · ‘Of’ changes the denominator · AC9M10ST04 · AC9M10P01

**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.

## Day 18 · The unassigned category still counts · AC9M10ST04 · AC9M10ST01

**Goal:** preserve known second-variable data when the first label is missing. **25 = 2 + 5 + 7 + 7 + 4.**

- **0–2:** Source C's eight no-theme designs have known side counts. Missing theme is not missing side count.
- **2–7:** Remove that row as a demonstration only: named-theme two-sided count is 27 of 42 (≈64.3%); restore the row for the all-design claim of 30/50=60%. Both fractions answer different questions.
- **7–14:** Learners complete a two-column claim audit: 27/42 named-theme designs versus 30/50 all designs. Circle the excluded three two-sided and five one-sided designs.
- **14–21:** **Routes:** physically remove/restore eight marked cards; shade the no-theme table row and write both fractions; dictate a two-sentence comparison with denominator labels. No route guesses why labels are absent.
- **21–25:** Exit “Could 27/42 be described as ‘all designs’?” **Look-for:** no; eight were excluded. **Next move:** if learner treats no-theme as zero, restore its 3 and 5 cells.

**Another setting:** Imaginary theatre costume sketches with undecided colour but known sleeve type. **Optional/home:** explain to a fictional designer why unknown in one field need not erase a row.

## Day 19 · Test the headline with a fresh paper classification · AC9M10ST01 · AC9M10ST04 · AC9M10ST05

**Goal:** conduct a small constructed bivariate classification, compare with Source C and report limits. **25 = 2 + 5 + 7 + 7 + 4.**

- **0–2:** Read C's “three quarters of all” claim. Only Puzzle gives 18/24=75%; all gives 30/50=60%.
- **2–7:** Teacher models one item from the [12-card mini-deck](STUDENT-DATA.md#optional-constructed-mini-deck-for-day-19): Puzzle/2 goes in that cell. Keep the mini-deck separate from the 50-card source.
- **7–14:** Learners sort or transcribe all 12 card records into a new two-way table and check row/column totals. This is actual **paper classification of invented records**, not a real sample of games or people.
- **14–21:** **Routes:** tactile word cards; large-print category grid; typed table and text audit. Each reports the new mini-deck's two-sided count and whether it verifies C's 50-card prevalence (it does not). Write a cautious replacement headline with source and denominator.
- **21–25:** Exit “What did we actually do, and what did we not observe?” **Look-for:** classified 12 constructed records; observed no real choices. **Next move:** if mini-deck counts are silently added to 50, draw a source boundary around each set.

**Another setting:** Imaginary map-symbol cards by type and colour. **Optional/home:** invent a 2×2 mini-deck on paper; do not gather other people's information.

## Day 20 · Fresh Check B: new category and report · AC9M10ST04 · AC9M10P01 · AC9M10ST01

**Goal:** transfer two-way table, conditional denominator and claim-scope judgement to a new invented sticker-card case. **25 = 2 + 3 + 10 + 6 + 4.**

- **0–2:** State that this public check is new relative to lessons but can be read in advance; locally adapt if prior access matters.
- **2–5:** Offer exact read-aloud, tactile grid, calculator, AAC or scribe without explaining the fresh totals.
- **5–15:** Learners independently answer [Check B](STUDENT-CHECKS.md), preserving first work.
- **15–21:** General reflection after collection: `which cell / which group / what absent category / what claim?` **Routes:** count tiles; shaded table; spoken/signed fraction audit.
- **21–25:** Teacher reads the [public key](teacher/KEY-AND-NEXT.md) and picks a next step based on the learner's actual evidence. **Next move:** fresh local case for later reassessment if prior prompt access mattered.

**Another setting:** Invented craft-template cards with a different two-way register. **Optional/home:** explain `given` versus `all` using a made-up fraction, no real survey.