# Mathematics teacher notes and keys: original fictional data

All numbers below are **invented classroom data**, not observations, quotes, prices or financial advice. **This is the teacher master and includes answers plus a fresh Day 10 item: do not distribute the whole file before assessment.** Give learners the separate [student data cards](STUDENT-DATA.md) for Days 1–9. The same contexts are used in the [English reading set](../english/MATERIALS.md) and [integrated guides](../integrated/week-01.md). Students can work on paper using the [scatterplot frame](../print/scatterplot-frame.svg) and [cost comparison board](../print/cost-comparison.svg), or with their [plain-text equivalents](../print/TEXT-ALTERNATIVES.md). No account or screen is required. A digital graph may be used locally as an optional check.

## Table A: model cart (fictional simulated readings)

A **0.50 kg** model cart is assigned eight simulated trials. The listed force is **net force**, not an unmeasured push. Accelerations vary slightly around the ideal model `a = F_net / m`. No experiment was actually conducted; the variation was authored to allow discussion of measurements, repeated trials and limits.

| Trial | Net force (N) | Simulated acceleration (m/s²) |
|---:|---:|---:|
| 1 | 1 | 1.8 |
| 2 | 1 | 2.1 |
| 3 | 2 | 3.8 |
| 4 | 2 | 4.2 |
| 5 | 3 | 5.9 |
| 6 | 3 | 6.2 |
| 7 | 4 | 7.8 |
| 8 | 4 | 8.1 |

Plot force on horizontal axis from 0–4 N and acceleration vertically from 0–10 m/s², matching the printable frame and learner card. The pattern is **strong positive, approximately linear** for this constructed set. Paired averages are 1.95, 4.00, 6.05 and 7.95 m/s², versus ideal 2, 4, 6 and 8 m/s². A scatterplot and an association statement do **not** by themselves establish that a wheel finish caused a change. Force and mass would need to be held comparable for a finish comparison, with a valid local method. No wheel-finish comparison data are supplied.

## Table B: fictional travel planning transfer

Six invented route-distance/duration pairs, in km and minutes: `(2,7), (4,13), (6,18), (8,26), (10,31), (12,35)`. They show a positive roughly linear association in this invented set. Route, stops and traffic are not specified; do not make a real transport estimate. A text-only comparison can order pairs and describe direction without seeing the plotted dots.

## Table C: fictional 10-month device-hire brief

An **adult fictional household** is comparing two simplified month-to-month device-hire plans for study and creative work. Both plans are assumed to meet the **same fictional minimum access, safety and service requirements**; that assumption would need checking in life. There is no exit fee in this simplified exercise. Monthly payments are due for each complete month; `m` is a whole number from 0 to 12. A $1,000 cap for the first 10 months is a practice constraint, not advice about anyone's budget.

| Plan | Setup cost | Monthly cost | Total model |
|---|---:|---:|---|
| A | $240 | $80 | `A(m)=240+80m` |
| B | $480 | $50 | `B(m)=480+50m` |

Key values: at month 0, A $240 and B $480; at month 4, A $560 and B $680; at month 8, both **$880**; at month 10, A **$1,040**, B **$980**; at month 12, A $1,200, B $1,080. Equality: `240+80m=480+50m`, so `30m=240`, `m=8`. A is cheaper for whole months 0–7; tie at 8; B cheaper for 9–12. Under $1,000, A permits at most **9 complete months** (cost $960) and B at most **10** (cost $980), within the 0–12 model. At the stated 10-month horizon, B fits the cap and A does not. The model omits taxes, actual terms, device performance, repair outcomes, energy use and legal rights. A real choice needs current, verified sources and advice appropriate to the person.

## New check data (do not model before Day 10)

Two different **fictional** plans for an invented creative device: `X(m)=180+90m`, `Y(m)=420+60m`, with whole months 0–12. Equality at `180+90m=420+60m` → `30m=240` → **8 months**, cost **$900**. At 10 months X **$1,080**, Y **$1,020**. With a $1,000 practice cap at 10 months, neither fits. At month 9, X $990 and Y $960, both fit. Students should state the model's missing conditions rather than present it as a real offer.

## Access, verification and rights

Use a ruler or grid, large-print coordinates, raised axes with pins/cord placed by an adult, typed tables, speech/AAC, or partner-operated plotting under the learner's direction. For equations, a student can dictate the inverse steps and verify by substitution. Record the support supplied. Do not classify learners by a fixed “learning style”. An inaccessible graph is not evidence of weak statistical reasoning.

Original fictional data, examples and explanatory text © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit the source, link the licence and indicate changes. The [ACARA descriptions](../../../CURRICULUM-CROSSWALK.md) retain separate attribution and terms.