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Year 8 / Term 1 / Weeks 01 02 / Mathematics

Development draft · local review needed

Mathematics checks, calculations and reteach routesYear 8 Maths · T1 W1–2 · Assessment guide

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Teacher copy · prompts and answer keys

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.

Keep an evidence ledger: problem / exact response / representation / independence and supports / what to teach next. A copied pair result is not independent evidence. Short checks cover only this fortnight's content descriptions.

Day Exit answer If not yet secure
1 In A(n)=18+7n, 7 is the per-repair charge. Test zero repairs to distinguish fixed from variable.
2 At eight repairs A=$74, B=$80, so A is $6 lower in the model. Substitute one value in each formula; label dollars.
3 (6,60) means six repairs cost $60 under either model. Match ordered pair to table row and axis labels.
4 At five repairs A=$53, B=$50; A is not lower. Substitute on both sides of the equality; do not rely on graph alone.
5 New art-studio model See Check A.
6 20 responses are not automatically representative. Compare selection from all numbered cards with standing at one location.
7 Bicycle shares A=15%, B=20%; gap 5 percentage points (one person). Build two 20-cell grids; avoid “five people” error.
8 C's 80% arithmetic is correct for C; the whole-population inference is unsupported. Label denominator group on each percentage.
9 Two same-size random model samples can differ; here 15% and 20%. Use two token draws or tables without promising a particular outcome.
10 Fresh arts-club sample See Check B.

Day 5 check A

Fresh fictional prompt: “An imaginary art studio offers C: $12 entry and $5 per visit, or D: no entry cost and $8 per visit. A visit is a whole non-negative count. Write expressions, find when totals are equal, check by substitution, and say which total is lower for 3 and 6 visits. Name one assumption that would need checking before a real choice.”

Answer key: C(v)=12+5v, D(v)=8v. Equality: 12+5v=8v, so 12=3v, v=4; both $32. At v=3, C $27, D $24, so D lower by $3. At v=6, C $42, D $48, so C lower by $6. Valid assumptions: comparable access/quality, no omitted fees, same eligible visit, current actual terms. If a student finds 4 only from graph, ask for substitution. If a student writes 12v+5, use zero visits to expose the wrong fixed term.

Day 10 check B

Fresh fictional prompt: “In a made-up population of 100, 60 students are interested in an arts-club music-room session. Two constructed simple random samples of 20 find 11 and 14 interested. A constructed convenience sample of 20 at a music-club meeting finds 18 interested. Calculate each sample proportion. Which sample is most likely to overrepresent interested students, and why? Can either one random sample prove the exact population share in a real unknown population? Write a bounded report and an ethical next step.”

Answer key: random A 11/20=55%; random B 14/20=70%; meeting 18/20=90%; model population 60/100=60%. The meeting sample is selected where interested people are likely, so it is biased for whole-school inference. Two equal-size random samples differ by 15 percentage points here; neither proves an unknown real population's exact proportion. This exercise's 60% population is given solely for simulation. A sound next step is a school-approved, voluntary and privacy-conscious random selection across the whole imagined population, with access for all response modes, or to review decision criteria before more collection. Do not infer a student's actual interests.

Four-criterion feedback rubric

Criterion Secure in this check Developing Next move
Linear structure Fixed and rate terms correct; domain named; equality verified Swapped terms, missing fixed cost or unchecked intersection Substitute zero, then one; build table before solving
Numerical accuracy Correct totals, fractions and percentage-point comparison Arithmetic or units slip with sound setup Use calculator/counters to isolate calculation from model reasoning
Data method Names population, random/convenience selection and plausible bias Treats sample size alone as fairness Simulate selection from numbered cards versus meeting/rack location
Bounded conclusion Distinguishes model/sample result from real decision or unknown population Reports sample percentage as universal fact Add “among these 20” and ask what a new source could change

Mark secure / developing / not yet observed separately. A learner can be strong at interpreting a model while still needing arithmetic support, or vice versa. Recheck with altered numbers after reteaching, not a memorised repeat. Do not grade speed, handwriting, accent or willingness to disclose private information.

Rights: Original assessment © NeuroForgeIO Pty Ltd 2026, SubjectNest, CC BY 4.0; credit, source and changes required.