# Teacher worked key · keep separate until first response

The [checks](../STUDENT-CHECKS.md) are public by URL and their answers are public here. They are **not secure QCAA school instruments**. Do not turn them into a QCAA unit result. Record whether support was neutral reading/motor access or a content hint. Mark a correct count and method separately from spelling, drawing neatness or speed.

## Day 5 · new File G

1. `|D∪C|=19+14−6=27` people. Neither `36−27=9`. Four disjoint regions: drawing only `19−6=13`, both `6`, coding only `14−6=8`, neither `9`. Check `13+6+8+9=36`. The union is `13+6+8=27`.
2. Exactly one booking from disjoint categories gives `2+3=5` bookings. `2×3=6` would count one indoor **and** one outdoor session as a pair, contrary to the one-booking rule.
3. Model: “The two station sets overlap, so adding 19+14 would count six people twice; the booking lists do not overlap, so their options add directly.” Other correct reasons that name overlap/exclusivity are valid.

**Next instruction:** If the learner gets 33 maker participants, move six “both” counters from two written lists into a shared region, then count people once. If they multiply bookings, ask what one completed booking contains. If arithmetic slips but model is sound, retain conceptual credit and use counters to repair the calculation.

## Day 10 · new Files H/I

1. `|A∪C∪M|=15+14+12−6−5−4+2=28` people. None `36−28=8`. Exact regions: all three **2**; A&C only `6−2=4`; A&M only `5−2=3`; C&M only `4−2=2`; A only `15−4−3−2=6`; C only `14−4−2−2=6`; M only `12−3−2−2=5`. Seven regions sum `2+4+3+2+6+6+5=28`. Each set reconstructs (A 15, C 14, M 12). Alternative check accepted by the prompt: for example A&C only 4 and A only 6, plus formula union 28 and none 8; all regions nonnegative.
2. Poster route `3×2=6`; audio route `2×3=6`. Exclusive alternatives sum to `6+6=12` complete routes. `3×2×2×3=36` would describe a combined selection containing both poster attributes **and** audio attributes, a different product. A bare `6×6=36` has the same wrong paired-route interpretation.
3. Reasonableness: H's union 28 is no larger than universe 36 and no smaller than its largest single set 15; seven regions are nonnegative and total 28. I has six distinct poster leaves and six audio leaves, with no leaf shared, so total 12. A different valid explicit check earns credit.

**Next instruction:** If H gives 26, inspect whether the centre 2 was restored after all pair subtractions. If a pair-only cell is 6 rather than 4, revisit the statement that pairs include the centre. If I gives 36, ask whether the story allows one outcome to be both route types. A method explanation can be correct even if one arithmetic operation was mistyped; reteach the arithmetic without discarding the reasoning.

## Daily feedback map

| Day | Evidence to accept | Next step if absent |
| --- | --- | --- |
| 1 | A's 25 with both subtracted once | Place five both-tokens in overlap first. |
| 2 | B's 8 both and 8 neither as distinct regions | Change universe while holding union 32 to separate meanings. |
| 3 | C's 22, centre restored | Recount a triple token through 3 add/3 subtract/1 add. |
| 4 | D's 7 one-session outcomes | List actual outcomes; compare a two-session pair. |
| 5 | G's 27 union, 9 neither and 5 bookings | Separate overlap from exclusive branches. |
| 6 | E's 12 paired labels | Draw three branches with four leaves each. |
| 7 | F's 6+4=10 with branch meaning | Label AND inside, OR across. |
| 8 | C's seven nonnegative regions and set rebuild | Put the centre in before the pair-only cells. |
| 9 | Method chosen for overlap/add/product/mixed | Ask what a wrong method's outcomes would be. |
| 10 | H's 28/8 and I's 12 with checks | Separate three-set correction from branch count. |

The official [QCAA Specialist Mathematics 2025 v1.4 syllabus](https://www.qcaa.qld.edu.au/downloads/senior-qce/syllabuses/snr_maths_specialist_25_syll.pdf) governs local curriculum and assessment. This key evaluates only the stated invented finite problems.