← GCSE Mathematics

Session 19

2026-09-11 · 2026-W37

What happened

S2 charts and tables — the June misconception targeted directly. Starter 5/5 with nothing prompted: P(both red) without replacement 42/90 → 7/15 simplified unprompted, which is the step that had slipped on every hard question for a week; map scale 1:25 000 with 4 cm → 100 000 cm → 1 km, carrying the conversion all the way; error interval 12.35 ≤ w < 12.45 with correct inequality notation and the variable named; £12.53 change; and a sampling criticism where she volunteered both the small-sample and the bus-stop-bias points when only one was asked. Grouped frequency table (test scores, 30 students): 6/7. Total 30, "more than 9" = 19 — the exact boundary that was attempted and got wrong in the June diagnostics, now correct. "9 or more" she answered as "between 19 and 27", which is not the expected answer but is better reasoning than the expected answer: she spotted that the 5–9 group hides how many scored exactly 9. The exam convention that questions always fall on group boundaries was then explained. "At least 15" = 8 and "fewer than 10" = 11 both correct. Only slip: gave a count (19) where a fraction was asked for, then wrote 19/30 and correctly identified that it does not simplify. Bar chart (pets, 40 children) 4/4 including the more-than-1 versus at-least-1 pair. Exit ticket (puzzle times, 60 people, grouped with inequality notation) 5/5 INDEPENDENT: 39, 42, 7/20 simplified, 1/10, and a correct if thin explanation of why an exact time cannot be read off grouped data. She read 10 < t ≤ 15 correctly without the notation being taught, placing 15 in that group — question 2 answered 42, not 30.

Planned next

S4 averages from frequency tables — mean, median, mode and range from a list, then the estimated mean from grouped data using midpoints. The diagnostic note says mean from a chart was left blank while reverse mean was fine, so build from the reverse-mean strength. Starter: one drawn FREQUENCY tree (the P1 loose end, distinct from the probability tree drawn 10 Sep), and one grouped-table boundary question after a gap.

What this session changed

TopicNameChangeEvidence recorded
S2Gap → DevelopingTaught 11 Sep. The June misconception ("more than n" including the group containing n) corrected and then evidenced across three separate contexts: grouped table 6/7, bar chart 4/4, exit ticket 5/5 independent. Read 10 < t ≤ 15 notation correctly without being taught it. Also identified unprompted that grouped data hides individual values.
P6-P7Secure → Secure11 Sep starter: P(both red) without replacement, 42/90 → 7/15, simplified unprompted on the hardest question of the starter. The simplifying step that was missing on 8 and 9 Sep and on the drawn tree of 10 Sep.
N15Developing → Secure11 Sep starter: 12.4 kg to 1 d.p. → 12.35 ≤ w < 12.45, inequality notation correct and variable named. Second clean independent answer after 2 Sep; the notation gap from the 19 Aug exit check now looks closed.
R1-R3Secure → Secure11 Sep starter: map scale 1:25 000, 4 cm apart → 1 km, conversion carried through from centimetres to kilometres rather than stopping at 100 000 cm. Ageing check passed after roughly 11 weeks.
N16Secure → Secure11 Sep starter: three shirts at £14.99 plus a jacket at £42.50, change from £100 → £12.53. Ageing check passed.
P4-P5Developing → Secure11 Sep starter: council surveying 25 people at a bus stop — gave both the sample-size and the location-bias criticisms when only one was asked. Third session running with correct sampling reasoning.