# Public teacher-targeted worked key · Weeks 5–6

This file is **public by URL**, not an access-controlled store. The [learner checks](../STUDENT-CHECKS.md) are new relative to the lesson cards, but are **formative only, not secure school or QCAA Unit 1–2 assessment instruments**. Collect and keep first independent responses before giving content feedback. If prior access matters, set local replacement values. Record an access support separately from a mathematical hint. All models are fictional; no legal wage, actual exchange quote, tax treatment, investment return or purchasing recommendation follows.

## Core daily results and response moves

| Day | Worked result and source boundary | Next move when evidence is weak |
| --- | --- | --- |
| 21 | Card H: regular `8×$28=$224`; additional rate `$28×1.5=$42/hour`; additional `2×$42=$84`; total `$308`. A made-up factor does not establish a legal overtime rate. | If all 10 hours are multiplied by 1.5, split the 8/2 hour counts before adding. |
| 22 | Card I: regular `6×$31=$186`; additional rate `$31×1.25=$38.75/hour`, additional `$77.50`; fixed once-only allowance `$24`; total `$287.50`. | If allowance is hourly, label it “$24 once for shift” and rebuild total from three layers. |
| 23 | Card J: `25%×$80=$20`; stated price `$100`; gross price gap `$20`, not known net profit. | Ask which value is the percentage base and what costs are omitted. |
| 24 | Card K: gap `$90−$72=$18`; mark-up `$18/$72×100=25%`; gross margin `$18/$90×100=20%`. | Place the same $18 above each different denominator and name it. |
| 25 | Check A below. | Reteach the weak rate-unit or percentage-base step with unseen local data; do not rewrite first evidence. |
| 26 | Card L: up `$12.50/$125×100=10%`; return down `$12.50/$137.50×100≈9.09%`. These are invented figures, not inflation data. | Underline “from” and write that starting amount under each fraction. |
| 27 | Card M stipulated rate: AUD `$250×0.64=USD $160`; USD `$96÷0.64=AUD $150`. Reverse checks recover AUD250/USD96. No live rate or fee conclusion. | Label source and target units above arrows before choosing × or ÷. |
| 28 | Card N1: `50×$0.84=$42` annual model dividend; `$0.84/$24×100=3.5%` yield. Full portfolio check: `$42/(50×$24)×100=3.5%`. No future payout guarantee. | Align one-share dividend with one-share price or both portfolio totals. |
| 29 | Card N2: Cedar `$30/$2=15` P/E; Slate `$36/$3=12` P/E. Ratios are not percentages or a buying recommendation. | Reverse-multiply by EPS and request one missing risk/growth/accounting input. |
| 30 | Check B below. | Recheck source-unit direction, per-share versus portfolio bases and ratio interpretation with fresh local inputs. |

## Check A · worked first response

1. Regular `7×$33=$231`. Additional rate `$33×1.5=$49.50/hour`; 2 additional hours yield `$99`. Once-only `$17` allowance. Gross fictional shift total `$231+$99+$17=$347`. A check is `$33×9=$297` if all 9 hours were regular, plus the additional-hours premium `2×($49.50−$33)=$33` and the allowance `$17`, giving `$347`.
2. Item gap `$110−$88=$22`. Mark-up base **cost**: `$22/$88×100=25%`. Margin base **selling price**: `$22/$110×100=20%`. Reverse checks `$88×1.25=$110` and `$110×0.20=$22`.
3. Accept a checked sum/estimate with rate labels and a scope statement: no actual award, tax, deductions, other business expense or contract is supplied. Neither result proves net pay or net profit.

**Response branch:** If a learner gets `$33×1.5×9`, separate seven regular and two additional hours. If $17 is multiplied by hours, re-label it “one fixed shift allowance.” If mark-up and margin both use $88, ask what “of the selling price” names. Capture first work before coaching.

## Check B · worked first response

1. Given **invented** AUD1 = USD0.72: `AUD $175×0.72=USD $126`; `USD $54÷0.72=AUD $75`. Reverse `USD $126÷0.72=AUD $175`; no live rate or fee is established.
2. Annual dividend on 45 shares: `45×$1.28=$57.60`. Yield `$1.28/$32×100=4%`; full-portfolio check `$57.60/(45×$32)×100=4%`.
3. P/E `$32/$2.50=12.8` as a **ratio**, not 12.8%. One ratio and a dividend cannot reveal future earnings, risk, debt or suitability, so no purchase conclusion is justified.
4. Accept missing real-world exchange date, live rate, fee/spread or provider condition; for shares accept payout uncertainty, price changes, future earnings, risk or individual circumstances. Do not ask for learner's personal finances.

**Response branch:** If USD54 is multiplied by 0.72, label the given ratio `USD per AUD` and reverse the arrow. If 45 is mistakenly included in per-share yield, pair 45 dividends with 45 prices or use one of each. If P/E is given as a percentage, cancel `$ per share` units and name it a ratio. Preserve first response, content hints and access supports as distinct notes.

## Twenty optional swap results

These correspond, in order, to the two learner prompts under each [day heading](../PRACTICE-SWAPS.md). They offer a second numerical route or a next-day recheck; they are not QCAA formal assessment. All claims remain within stipulated invented inputs.

| Day | Swap 1 | Swap 2 |
| --- | --- | --- |
| 21 | Film-set: regular `$150`, additional `$112.50`, total `$262.50`. | Museum: regular `$120`, additional `$60`, total `$180`; multiplier applies to the one additional hour. |
| 22 | Audio: regular `$130`, additional `$65`, allowance `$15`, total `$210`. | Festival: regular `$168`, additional `$36`, allowance `$12`, total `$216`. |
| 23 | Badge: gap `$12`, price `$60`. | Prop: gap `$7`, price `$42`. |
| 24 | Zine: gap `$10`, mark-up `25%`, margin `20%`. | Kit: gap `$18`, mark-up `20%`, margin `16.67%` rounded. |
| 25 | Exhibition: gap `$15`, mark-up `25%`, margin `20%`. | Scene: regular `$60`, additional `$30`, total `$90`. |
| 26 | Ticket: up `$10`, `25%`; return down `$10`, `20%`. | Materials: up `$15`, `20%`; return down `$15`, `16.67%` rounded. |
| 27 | Travel: AUD100 → USD75; USD45 → AUD60. | Digital rights: AUD180 → USD108; USD72 → AUD120. |
| 28 | Library shares: annual dividend `$10`, yield `2%`. | Garden shares: annual dividend `$51.20`, yield `4%`. |
| 29 | Press: `P/E=7`, check `7×$4=$28`. | Studio: `P/E=15`, check `15×$3=$45`; no recommendation follows. |
| 30 | Ticket conversion: AUD90 → USD72; USD64 → AUD80. | Publisher: annual dividend `$6`, yield `2%`, `P/E=5`. |

## Criterion view, not a grade

Note whether a learner identified the named base and unit, selected a valid operation, checked it, explained a model limitation and worked independently with their chosen access support. A dollar total without its period or denominator is incomplete evidence. These two checks sample small parts of Unit 1 Topic 1; they do **not** establish mastery of the full topic, replace the school's assessment program or measure classroom effectiveness. A spreadsheet file being supplied does not show an individual learner used it.