# Integrated Week 2 — An equal plan that fits the actual resources

Five **35-minute** sessions combining factors, practical modelling, source-aware writing and Year 5 HASS resource questions. The 36 books and box options are fictional. Do not imply a real school has these resources or ask learners to disclose family income or needs. This route addresses parts of `AC9M5N02`, `AC9M5N09`, `AC9HS5K08`, `AC9HS5S01`, `AC9HS5S03`, `AC9HS5S05`, `AC9HS5S06`, `AC9E5LA02` and `AC9E5LY06`. See [source and review notes](../../../SOURCES-AND-REVIEW.md).

**Prepare:** [Text C](../english/MATERIALS.md), 36 counters or slips, six paper-box outlines, [factor array](../print/factor-array.svg) and [claim/evidence mat](../print/claim-evidence-mat.svg). Available six boxes each hold at most eight books; proposed four boxes of nine are **not yet available**; no costs are given. Learners can direct a helper, choose accessible digital numbers, or use the plain-text cards. There is no purchase or solicitation activity.

## Day 1 — What kind of resource is it?

1. **Question · 3 min.** Show Text C and ask, “What must a good box plan do?” Write proposed criteria without voting yet.
2. **Model · 5 min.** Explain natural resource as material supplied by the environment, human resource as people's time/skills, capital resource as made equipment used to provide a service. In this scenario, trees/fibre are a possible *source* material, volunteer sorting is human work, and a reusable book trolley or sorting box can be capital equipment for the library service. A finished box is not a raw natural resource merely because its fibre came from a tree.
3. **Guided sort · 7 min.** Sort `tree fibre / volunteer time / reusable trolley / donated books / cardboard box`. Discuss that a good may have a different role depending on use; do not force “donated books” into a single category without explaining purpose.
4. **Independent question · 12 min.** Each learner writes one investigable question about the 36-book plan and two criteria (for example equal whole-book share, capacity, availability, transport, cost). They identify which criterion can be tested from Text C and which needs new information.
5. **Partner audit · 5 min.** Partner points to evidence for a criterion or labels it “missing”.
6. **Exit · 3 min.** Key: “Can we say five boxes are cheaper?” No; prices are missing. Learner explains rather than just saying no.

## Day 2 — Equal shares and capacity

1. **Recall · 3 min.** Read the actual constraints: 36 whole books, six available boxes, at most eight each.
2. **Model · 5 min.** Build six groups of six: `6×6=36`, and six is no more than eight.
3. **Guided factor pairs · 7 min.** Use array mat to make `1×36`, `2×18`, `3×12`, `4×9`, `6×6`. Ask which pair maps to six boxes.
4. **Independent plan · 12 min.** Learners complete a card: boxes used, books each, total, spare spaces per box and whether box availability is met. Key for six boxes: 6, 6, 36, 2, yes. They may make a tactile array or choose numerical form.
5. **Check the story · 5 min.** A partner identifies a mathematically possible plan that still fails a practical constraint: four boxes of nine are not available and may exceed the known eight-book capacity of the available boxes.
6. **Exit · 3 min.** “Does `4×9=36` alone prove the four-box plan can happen now?” No; box availability/capacity differ.

## Day 3 — Change one condition, see what changes

1. **Proposal · 3 min.** Read the volunteer's five-box idea without judging the volunteer.
2. **Model · 5 min.** Divide 36 into five groups: five sevens and one left. The equal whole-book requirement fails even if five boxes cost less.
3. **Guided variation · 7 min.** Ask: “If the library permitted one partly filled box, would five boxes be possible?” Yes as a *different* requirement, e.g. `8+8+8+8+4=36`, but the shares are not equal. Capacity eight per available box fits; verify whether only five of the six could be used. Mark the change explicitly.
4. **Independent comparison · 12 min.** Learners write two plans in a table: six equal boxes and five unequal boxes. Label which satisfies `equal`, `capacity`, `available`. They may choose either if they state the governing criterion; no unstated “best” answer.
5. **Counterclaim · 5 min.** Partner says the strongest fair reason to consider fewer boxes and one reason to keep equal six. Discuss why cost cannot yet settle this.
6. **Exit · 3 min.** “What changed between the two models?” The equality requirement, not the total 36.

## Day 4 — Decide with a visible rule

1. **Criteria · 3 min.** Learners choose a decision rule: e.g. “Use boxes already available, keep whole-book shares equal, stay within capacity.” Explain why those matter to the fictional service.
2. **Model matrix · 5 min.** Draw columns `equal / capacity / available / price known`. Six boxes of six: yes/yes/yes/no. Four of nine: yes/not for the available 8-capacity boxes/no/no. Five of seven plus one extra: no/yes/yes/no.
3. **Guided source check · 7 min.** Ask who supplied each fact. Text C gives counts and availability; the class's price guess supplies nothing. Mark unknowns with `?` rather than zero.
4. **Independent recommendation · 12 min.** Learners choose a plan and justify against two criteria, acknowledge one alternative, and ask one information question. A learner may recommend not deciding yet because a safety or cost question matters.
5. **Peer challenge · 5 min.** Listener asks, “What would make you switch?” Writer identifies a changed condition or new fact.
6. **Exit · 3 min.** Teacher records whether the learner separates observed/given, calculated and unknown information. If not, return to colour-coded cards, not a repeated worksheet.

## Day 5 — A proposal that another adult can use

1. **Audience · 3 min.** The audience is a fictional librarian who can check resources; children do not promise a real decision.
2. **Plan · 5 min.** Set claim, factor fact, constraint, alternative and question in order.
3. **Rehearse · 7 min.** Each learner tests a one-minute pitch with a partner. The partner paraphrases before raising a concern.
4. **Publish · 12 min.** Create a one-page memo, accessible audio/AAC sequence or annotated array. Include a title, exact arithmetic, the given box conditions and what remains unknown. Do not invent prices. If real class work is photographed or recorded, use school permission rules and systems only.
5. **Rubric check · 5 min.** Teacher marks `math correct / constraints visible / alternative fair / missing fact named` as secure, developing or not yet observed. Ask for one targeted edit.
6. **Exit · 3 min.** “Which sentence in your memo would a librarian be able to check immediately?” A good answer points to `6×6=36` or another exact given/calculated fact, with a source.

**Teacher moves:** A child who calculates correctly but assumes a price needs a source check, not more multiplication. A child who offers a thoughtful resource criterion but cannot factor 36 needs a manipulatives/array reteach while preserving their HASS reasoning. When “fair” has different meanings, ask learners to state a criterion and its consequences rather than forcing one moral answer. Check physical accessibility of any box-handling task before class.

**Rights:** Original guide and fictional scenario © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit, source, licence and changes. ACARA codes remain under [ACARA's terms](https://www.australiancurriculum.edu.au/copyright-and-terms-of-use); ACARA does not endorse this resource. Local educator and access review pending.