Tree diagrams, completing the probability block. Starter 5/5 with no prompting: the owed exit-ticket question from 8 Sep answered well — she verified the claimant's arithmetic (15/60 = 1/4, so the value is right) and THEN gave two criticisms, sample size and the estimate wording. That is the answer-targeting habit resolving: she now checks and then answers the question asked, rather than checking instead of answering. Also P8 with replacement 9/64 simplified unprompted, 18/24 → 3/4, P4 fourth flavour 0.3 with the running total written out, and A4 4(2x+3) − 3(x−5) → 5x+27 with the negative-times-negative handled. Tree diagrams taught: branches from a point sum to 1, multiply along a path, add between paths, all four ends sum to 1. With replacement — she identified the correct paths for all four questions but initially gave only the paths, not the probabilities, needing one prompt to produce numbers; all four then correct (6/25, 6/25, 12/25, 13/25) and she used the (c)+(d)=1 check. Without replacement taught: asked only for one branch's fractions, she produced the entire correct tree unprompted including 2/4, 2/4, 3/4, 1/4. All four probabilities correct but left as twentieths. Exit ticket (4 mint, 6 toffee, without replacement) 5/5 INDEPENDENT, no hints: tree fully correct with all six probabilities labelled, then 12/90, 30/90, 48/90 and the sum-to-1 check. Left unsimplified again.
Probability strand P1–P8 is now taught in full. Move to statistics: S2 charts and tables (the "more than n" boundary misconception from the diagnostics) and S4 averages from frequency tables. Starter: one tree diagram without replacement after a gap, plus a simplifying check on a harder question rather than an easy one.
| Topic | Name | Change | Evidence recorded |
|---|---|---|---|
| P6-P7 | Developing → Secure | Tree diagrams taught 9 Sep, both with and without replacement. Exit ticket 5/5 fully independent: correct tree for 4 mint and 6 toffee without replacement, all six branch probabilities right, then both-mints, both-toffees and one-of-each all correct with the sum-to-1 check applied unprompted. Sample spaces and Venn probabilities already evidenced independently on 8 Sep. This ref is now complete — all three parts taught and evidenced. | |
| P8 | Developing → Secure | 9 Sep: multiply-along-path and add-between-paths applied correctly throughout the tree work, including multi-route questions in the exit ticket with no prompt to combine — the exact thing that needed prompting on 8 Sep. Starter P(both blue) with replacement 9/64 correct and simplified. | |
| P2-P3 | Secure → Secure | 9 Sep starter: dice rolled 60 times, lands on 3 fifteen times, claim of 1/4. Gave both the sample-size and estimate-wording criticisms unprompted, second session running. | |
| P4-P5 | Developing → Developing | 9 Sep starter: fourth flavour 0.3, with 0.3+0.25+0.15 = 0.7 then 1 − 0.7 written out as separate steps rather than done mentally. | |
| A4 | Secure → Secure | 9 Sep starter: 4(2x+3) − 3(x−5) → 5x + 27, negative-times-negative correct. Second clean independent expansion in three sittings. |