# Integrated Week 1 — Would that repair plan really save money?

Five **35-minute** sessions. The imaginary Fix-It Club has two model plans; no real offer or purchase is involved. Students combine algebra, source reading and an economics question about how price structures could influence choices. These sessions address parts of `AC9M8A02`, `AC9M8A03`, `AC9E8LA04`, `AC9E8LY03`, `AC9E8LY06`, `AC9HE8K01`, `AC9HE8S01`, `AC9HE8S02`, `AC9HE8S03`, `AC9HE8S04`, `AC9HE8S05`. Exact source notes and review limits are in [the ledger](../../../SOURCES-AND-REVIEW.md).

**Before class:** display [Text A](../english/MATERIALS.md) with its **FICTIONAL** source label, the [model table](../mathematics/MATERIALS.md) and [print graph](../print/plan-graph.pdf) or [text equivalent](../print/TEXT-ALTERNATIVES.md). Each learner needs an independent way to represent a choice. Do not ask students to reveal household finances, real repairs or access to services.

## Day 1 — What is the actual decision?

1. **Frame · 3 min.** Read the headline once, then small print. Ask which words are a claim and which are calculable conditions.
2. **Model inquiry · 5 min.** Teacher asks: “For which whole numbers of repairs is each model total lower?” Name `n`, the intended decision, and unknowns (parts, quality, access).
3. **Criteria · 7 min.** Groups propose criteria: total price at an expected repair count, coverage, wait and service quality. Only the first is answerable from the supplied numbers; mark others `unknown`, never `$0`. Ask what a change in demand *might* mean for the club's allocation of repair slots or parts, while noting that no demand or stock data were given.
4. **Independent formulation · 12 min.** Learners make a decision card with their chosen *fictional* count `n=0,2,6 or 8`, a predicted lower model cost, why that count matters to a hypothetical user and a question for a real provider. It is fine to choose “no recommendation until terms are known”.
5. **Peer audit · 5 min.** Partner checks that the user was hypothetical and the question is answerable by a provider rather than invented.
6. **Exit · 3 min.** Key: Plan A's $18 is fixed; a lower $7 marginal charge does not alone prove lower total.

## Day 2 — Price changes the choice by count

1. **Retrieve · 3 min.** Learners write `A(n)=18+7n`, `B(n)=10n` from source, or point to each term on an accessible card.
2. **Model · 5 min.** Calculate at two repairs: $32 and $20, B lower by $12.
3. **Guided table · 7 min.** Calculate at zero and eight repairs: zero A$18/B$0; eight A$74/B$80. Ask when the preferred **model cost** changes.
4. **Independent recommendation · 12 min.** Learners choose one of those counts and write two sentences: exact model numbers and a limit. A learner who prefers quality over $6 must say that quality is not in the data.
5. **Compare · 5 min.** Pairs explain why both “A is cheaper” and “B is cheaper” can be valid at different counts, but neither is true for every count.
6. **Exit · 3 min.** “At eight repairs, how much lower is A's model total?” Key: $6.

## Day 3 — A crossing point with an honest domain

1. **Orient · 3 min.** Read the graph axes as repairs (x) and total dollars (y), not time and price per item.
2. **Model · 5 min.** Plot `(0,18)` and `(2,32)` for A; `(0,0)` and `(2,20)` for B.
3. **Guided extend · 7 min.** Groups plot `(4,46)/(4,40)`, `(6,60)/(6,60)` and `(8,74)/(8,80)`.
4. **Independent explanation · 12 min.** Learners explain the crossing at six using graph *and* substitution. Mark whole-number x-values as possible purchases; a line between dots is a visual trend, not a half repair.
5. **Check · 5 min.** Partner tests a point either side: `n=5` B lower; `n=7` A lower. If a graph is inaccessible, use coordinate table or tactile tape paths.
6. **Exit · 3 min.** Key: at six repairs, each model costs $60, so no plan has lower stated total.

## Day 4 — Which missing term could change the answer?

1. **Claim · 3 min.** Display “At eight repairs, A is the best option.” Ask what the model actually proves.
2. **Model boundary · 5 min.** Teacher rewrites: “A's **listed model total** is $6 lower at eight repairs; parts, eligibility, wait and quality are unknown.”
3. **Scenario cards · 7 min.** Compare two original *hypothetical additions* separately, without treating them as real: if A had a $9 parts fee for the set, A would be $83 versus B $80; if both had the same $9 fee, A remains $6 lower. This shows assumptions can matter.
4. **Independent sensitivity check · 12 min.** Learners calculate both additions and write which change affects the ordering. They label every new fee as *what-if*, not a quoted price.
5. **Peer challenge · 5 min.** Ask “Which fact would you verify first before a real decision?” A valid answer is actual parts terms or service equivalence.
6. **Exit · 3 min.** Key: $83 versus $80 reverses the eight-repair result only in the **A-only $9 what-if**.

## Day 5 — A recommendation a listener can inspect

1. **Audience · 3 min.** Learners address a fictional club editor who could fix the headline; no real business is contacted.
2. **Plan · 5 min.** Organise claim, exact count and cost, algebra/graph check, one missing term and a revised headline.
3. **Rehearse · 7 min.** Partner restates the count and recommendation; if they cannot, move the count earlier.
4. **Create · 12 min.** Make a one-page note, annotated graph or accessible spoken/AAC version. Include at least one value below six, equality at six, and one above six; label all amounts as the fictional model.
5. **Rubric · 5 min.** Teacher records `math check / source attribution / condition and limit / audience clarity` as secure, developing or not yet observed. Ask for one precise revision.
6. **Exit · 3 min.** “What would make the flyer less misleading?” A defensible line: “Plan A's per-repair charge is lower, with an $18 joining cost; compare total at your count.”

**Teacher next moves:** If a learner swaps fixed and variable terms, substitute zero repairs. If algebra is right but the copy promises universal savings, compare zero and eight. If reading is difficult but the cost reasoning is sound, provide the source aloud and record constructs separately. Human review must check any local price examples before substitution. No student spending data is needed.

**Rights:** Original guide, hypothetical fees and wording © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/); credit, source, licence and changes. ACARA curriculum links remain under [ACARA's terms](https://www.australiancurriculum.edu.au/copyright-and-terms-of-use); ACARA does not endorse SubjectNest.