Mathematics · Days 11–20 | Year 10 Maths · T1 W3–4 · Lessons

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, clean learner tasks, fresh checks, teacher-targeted public key and A4/text aids 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.
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: 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; 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 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 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: 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, 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 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.