P6–P7 sample spaces and Venn diagrams. Starter 4.5/5. A4 5(3x−2) − 4(2x−3) → 7x + 2 with all four terms written out unprompted, including −4 × −3 = +12 — the exact sub-skill that failed on 2 Sep, now passed independently with working shown. N4 HCF of 84 and 360 → 12, the harder-numbers question the loose end asked for. P1 gym frequency tree (120 people) all four boxes correct, answer 35 — but listed, not drawn; she explained she has no camera to show a drawn tree, which is a practical constraint rather than avoidance. P4-P5 spinner with two equally likely colours → P(green) = 0.25, two steps, correct. Q5 (company claims P(faulty) = 0.04 from 2 in 50): gave the small-sample criticism correctly but could not produce the second — said "I don't know" when pushed on the wording. This is the second failure of the same point after Aaron on 2 Sep; taught again with a hook — worked out from the setup means probability, found by experiment means estimate. Sample spaces taught: two-dice total, 36 outcomes, 6 ways to make 7, probability correct though given as 0.167 rather than 6/36 = 1/6 (exact-value habit prompted). Venn diagrams taught: French/German class of 30 built correctly, 12 / 6 / 8 / 4, DRAWN not listed, with the regions checked against the total. Session ended before the probability-reading questions off the Venn, so P(French) versus P(French only) — the whole-circle trap — is untested.
Resume at reading probabilities off the Venn diagram: P(French), P(both), P(neither), P(German only) from the class of 30 — the whole-circle versus only trap. Then P8, add versus multiply. Starter: one more "criticise this claim" question to retest the estimate wording (third attempt), and one exact-value probability to reinforce fractions over decimals.
| Topic | Name | Change | Evidence recorded |
|---|---|---|---|
| P6-P7 | Gap → Developing | Taught 7 Sep. Two-dice sample space: 36 outcomes, 6 ways to total 7, probability correct (given as 0.167, prompted to leave it exact). Venn built correctly for the class of 30: 12 French only, 6 both, 8 German only, 4 neither, regions checked against the total. Drawn rather than listed. | |
| A4 | Developing → Secure | 7 Sep starter: 5(3x−2) − 4(2x−3) → 7x + 2, all four terms written out unprompted including −4 × −3 = +12. Independent retest with working shown, exactly the bar set when it was demoted on 2 Sep. | |
| N4 | Developing → Secure | 7 Sep starter: HCF of 84 and 360 → 12, correct non-calculator. The uglier-numbers question the loose end called for, after 12/18 on 2 Sep. Two independent correct answers across separate sittings. | |
| P1 | Developing → Developing | 7 Sep starter: gym frequency tree (120 people) all four boxes correct, answer 35, unaided. Third correct tree across three separate sittings. | |
| P4-P5 | Developing → Developing | 7 Sep starter: spinner with red 0.2, blue 0.3 and two equally likely colours → P(green) = 0.25. Two-step, correct, independent. | |
| P2-P3 | Developing → Developing | 7 Sep starter Q5: company claims P(faulty) = 0.04 from 2 faulty in 50. Small-sample criticism given correctly; could not produce the second criticism and said "I don't know". Second failure of the estimate-wording point after Aaron on 2 Sep. |