Teacher worked key… | Year 11 Specialist Maths · T1 W1–2 · Answer And…

The checks 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

|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.
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.
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

|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.
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.
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 governs local curriculum and assessment. This key evaluates only the stated invented finite problems.