Keep each learner's equation, unit, estimate and explanatory sentence. Log calculator/spreadsheet and prompts. These quick checks are not formal QCAA assessment instruments, an A–E grade or financial advice. Missing real-world costs remain unknown. The source data are all fictional.
| Day | Key | Diagnostic next move |
|---|---|---|
| 1 | 2h=$48; 5h=$120; 6h=$144 at $24/paid h | If learner adds 24 to hours, write/cancel units and build equal groups. |
| 2 | Saturday rate $30/h; 2h=$60; 4h=$120; 6h=$180 | If 1.25 is added as dollars, break it into 1 + 0.25 and find 25% of $24. |
| 3 | Extra rate $36/h; 8h=$204; 9h=$240; 10h=$276 under stipulated rule | If all hours use $36, colour first seven and extra hours separately. |
| 4 | $80 at 15% off gives $12 discount and $68 new; $45 at 20% gives $9 and $36; $100 at 5% gives $5 and $95 | If discount/new price swapped, estimate whether reduced total is below old price. |
| 5 | Fresh Check A below | Compare independent work with rate/unit/check criteria. |
| 6 | Small $2.30/sheet, large $2.25/sheet; 8 needed: $18.40 vs $27; 24 needed: $55.20 vs $54 | If learner chooses unit-price winner at 8, make whole-pack count visible. |
| 7 | Large after 10% rise $29.70; two $59.40; small three $55.20, lower by $4.20. $50 fee +8%=$54 | If percent applied to total incorrectly, identify which price changes first and why. |
| 8 | Fixed $235, balance $245; plus two large: planned $289/remaining $191; plus three small: planned $290.20/remaining $189.80 | Check planned + remaining = $480; separate given costs from unknown delivery. |
| 9 | 2 Saturday hours $60, 5 hours $150; 6 hours $180 | If output has no formula, change hours and ask what operation the cell must perform. |
| 10 | Fresh Check B below | Diagnose pack count, unit price, percentage base or missing condition separately. |
Day 5 check A
Fresh fictional card: “An imaginary pop-up arts group states a base of $28 per paid hour and a Saturday multiplier of 1.25 under this invented arrangement. One example has three paid weekday hours; another has four paid Saturday hours. No travel, break or deduction rule is given.” Ask for (a) Saturday $/h, (b) both stated totals, (c) difference and which stated total is larger, (d) one reason the numbers alone do not settle a real preference. Require an estimate, equation and units; allow the agreed calculator setting.
Key: $28×1.25=$35/paid h. Weekday 3×28=$84. Saturday 4×35=$140. Saturday stated total is $56 greater. The two shifts have different paid hours, so “greater total” is not “higher take-home value”; missing terms include duties, travel, breaks, access or deductions. Do not apply real award rates. A valid estimate is 4×about $35≈$140, larger than three×about $30≈$90.
Day 10 check B
Fresh fictional card: “Art Relay supplies unopened packs of 10 badges for $22 or 15 badges for $31.50. A fictional project needs exactly 30 badges. It cannot buy part packs or return extras. Delivery and storage are unquoted. Then imagine only the 15-badge pack rises 10%.” Ask for both unit prices, two feasible exact-30 whole-pack routes, lower original stated outlay and difference, new 15-pack price/two-pack total, which route is lower after the rise, and one missing condition.
Key: 10-pack: $22÷10=$2.20/badge; 15-pack: $31.50÷15=$2.10/badge. Three 10-packs cost $66; two 15-packs cost $63, so 15-pack route is $3 lower originally. Rise: 0.10×31.50=$3.15; new 15-pack=$34.65; two=$69.30. Three 10-packs at $66 are now $3.30 lower. Delivery/storage unknown. A learner may consider mixed packs, but 10+? cannot make 30 with one 15 and only 10-pack multiples; other overbuy combinations need explicit extra cost and do not defeat the stated exact routes. Do not infer a real supplier offer.
Four-criterion feedback and recheck
| Construct | Secure in these tasks | Developing | Next teaching move/recheck |
|---|---|---|---|
| Model selection | Reads which rate/pack/percentage base applies and marks invented assumptions | Uses real-world assumptions or applies one rate to all hours | Rewrite givens in a two-column given / unknown table; recheck with a new number |
| Calculation and units | Correct operation, currency/unit labels and whole-pack feasibility | Arithmetic perhaps correct but wrong unit or impossible split pack | Draw grouping, estimate range, calculate again with units |
| Interpretation | Compares the requested total at the requested quantity and states difference | Chooses only lowest unit price or says “best” without quantity | Test 8 versus 24 sheets, then give a fresh quantity |
| Reasonableness/technology | Gives estimate or second route and explains formula/model limit | Copies calculator output without checking base/condition | Change one input; predict direction, then verify and describe why |
Mark secure / developing / not yet observed per construct. Recheck one week later with a new fictional wage or pack context after targeted teaching; do not simply repeat the same answer. For a reader who needs text read aloud, record that access so the arithmetic is not confused with independent reading. For a learner with maths difficulty, allow a structured equation card while noting the support. A formal QCAA task needs separate local design and approval.
Optional domain-switch keys
For the fictional practice cards: (1) garden six-pack $15÷6=$2.50/pot; ten-pack $23÷10=$2.30/pot. For exactly six pots, one six-pack costs $15, $8 less than one ten-pack's $23 even though the ten-pack is cheaper per pot. (2) sports hall original 3×$18=$54; new hourly what-if $18×1.10=$19.80, so three hours cost $59.40, up $5.40. (3) transport four rides cost 4×$4.80=$19.20, so the $18 pass is $1.20 lower on stated price; two rides cost $9.60, so individual rides are $8.40 lower than the pass. Real route coverage and eligibility remain unknown.
Rights: Original checks and rubric © NeuroForgeIO Pty Ltd 2026, SubjectNest, CC BY 4.0; credit, link and indicate changes.