← GCSE Mathematics

Session 6

2026-09-04 · 2026-W36

What happened

P4–P5 probabilities summing to 1, and sample-size reasoning. DATE UNCONFIRMED — logged retrospectively on 7 Sep; 4 Sep is inferred from the conversation, not verified. Amend if wrong. Starter 4/5 first pass: frequency tree (swimming, 200 people) correct and unaided; biased spinner 24/150 → 4/25 simplified; £36 after 25% off → £48; V = kr³ → cube root taken correctly, closing a loose end open since 13 Aug. A4 6x²+8x LEFT BLANK, then produced 2x(3x+4) correctly once walked through in three steps — she could do it and wrote nothing. P4 taught: 1 − P(A) on decimals and fractions, including P(yellow) = 5/12 via a common denominator unprompted; combined P4 and expected-frequency question 0.35 × 60 = 21 correct. P5 sample-size reasoning: the Priya sampling question answered in full for both marks (bias and sample size), well explained in her own words. Chen coin question — correct expected-versus-observed reasoning (10 expected, 13 observed) but concluded "the coin is not biased" rather than "no evidence of bias"; the distinction was taught. Exit ticket 4/5: 0.88, 0.3 and 27 white counters all correct and unaided; Q4 initially blank then fully correct once prompted to add the five probabilities; Q5 attempted but answered a different question — she checked Aaron's arithmetic instead of criticising his method. Two behavioural patterns flagged: written-reasoning questions are becoming the new skip category, and answer-targeting recurred three times.

Planned next

P6–P7 sample spaces and Venn diagrams. Retest the theoretical-probability versus relative-frequency wording with a fresh "criticise this claim" question.

What this session changed

TopicNameChangeEvidence recorded
P4-P5Gap → DevelopingTaught 4 Sep. 1 − P(A) correct on decimals and fractions incl. 5/12 via common denominator unprompted; 0.35 × 60 = 21. Exit ticket 4/5 — Q4 correct only after a prompt, Q5 answered the wrong question. Taught and tested same session.
A5Secure → Secure4 Sep starter: V = kr³ made r the subject, cube root taken correctly. Three weeks after the 19 Aug exit check where she divided by r twice. Loose end closed.
A4Developing → Developing4 Sep starter: 6x²+8x left BLANK. Produced 2x(3x+4) correctly once walked through in three steps, so this is a starting failure, not a method failure. Stays developing.
P1Developing → Developing4 Sep starter: swimming frequency tree (200 people) correct and unaided, two days after teaching. Corroborates the 4/4 exit ticket but is not a spaced check.
P2-P3Developing → Developing4 Sep starter: biased spinner 24/150 → 4/25, correct and simplified. Second independent relative-frequency question, differently framed. Practice Q4/Q5 now completed (see amended session 3).
R9Secure → Secure4 Sep starter: £36 after a 25% reduction, original price £48, correct non-calculator.