Dividing by a negative in inequalities was opened and taught in full by testing numbers, and the bracket expansion that cost marks on Wednesday was right 3/3 alone and 3/3 inside an inequality. Ran 09:14-10:27 on the Friday consolidation block; non-calc; typed, four drawings on paper by photo; one item per message; chunks to 09:45, 10:06, 10:27 with 2-min breaks. Cold: 3 squared, 5 squared, 2 cubed right in under 2 min; x greater than 3 drawn right; 8, 9, 10 named for x greater than 7. Dividing by a negative: tested x = 5 (fits) and x = -5 (does not; sum typed after a prompt), divided to x less than -3, saw -5 does not fit, chose x greater than -3 herself; say-back right; asked 'please explane this more', given the flipped-line picture, then -3 greater than -7 right. Hinted: -3x at least 12 gave x at most -4 after a prompt for the full line. Unaided on paper: -4x greater than 8 gave x less than -32 (sign and ring right, division fixed when asked); -5x at most 20 gave x greater than -4 open ('or equal' dropped, fixed after one question); -3x less than -9 gave x greater than 3, all right. Brackets: 2 hinted 2/2; 4(x-1), 7(2x+3), -2(x+6) alone 3/3. 4(x-1) less than 8 solved in three valid lines, drawn right. 60 pounds up 15 percent gave 69, the new price, working shown, no pound sign. Changing ratio 4:5 with 20 blue, scaffolded: one part 4; red answered 5 then 16 after a prompt; 24 then 8 added right. Fresh 3:7 with 21 yellow: 9 right, answer only, lines after two prompts. 32 asks, 32 answered, 0 blank; 24 right first time, 5 after one prompt, 3 part right. Session 99's dividing-by-a-negative item is completed. Not run: listing integers after solving; a changing-ratio item alone; HCF from index form.
FIRST, cold, one per message, 5 min: one inequality with a negative divisor and an at-most sign (-2x at most 10) solved and drawn on paper - watch that the 'or equal' survives the flip and the ring is filled; one expansion with a negative outside (-3(x - 4)) written as one line with the sign between the terms (A4). Then the changing-ratio method on her own, owed since Wednesday's paper (R7-R8): one worked example of 'blue stays 5 parts' with her writing each line, then two alone with both lines written before the answer, 10 min each. Then listing integers after solving an inequality (A22, untaught): solve, draw, list. For later: a timed order-of-operations item with a square in it (N1-N3, N6-N7: 3/3 cold untimed today, untested timed); the pound sign on a money answer (N11-N12); HCF from index form (N4, not urgent). Homework 8 is with Dad for marking.
| Topic | Name | Change | Evidence recorded |
|---|---|---|---|
| A22 | Developing → Developing | 16 Oct, non-calc. Dividing by a negative taught by number tests, rule chosen herself. Cold: x greater than 3 drawn right; 8/9/10 for x greater than 7. Hinted -3x at least 12: x at most -4 after a prompt. Unaided on paper, 4 items: -3x less than -9 and 4(x-1) less than 8 fully right; -4x greater than 8 had 8 divided by -4 as 32 (fixed when asked); -5x at most 20 dropped the 'or equal' (fixed after one question). 2/4 clean. Listing integers after solving untaught. | |
| A4 | Secure → Secure | 16 Oct, non-calc, typed: 3(x+5), 5(x-2) with the hint 'both terms' 2/2; then 4(x-1), 7(2x+3), -2(x+6) alone 3/3 (last typed -2x + -12, tidied). Both terms multiplied unprompted on all three, including the 14 Oct item 4(x-1) which had been 4x-1 under time. Then 4(x-1) less than 8 expanded right unaided inside an inequality. | |
| A17 | Developing → Developing | 16 Oct, non-calc, unaided: 4(x-1) less than 8 solved 4x-4 less than 8, 4x less than 12, x less than 3, 3/3 lines valid, 2 min. Bracket expansion inside a solve now right untimed; the 14 Oct timed version was 4x-1. | |
| N6-N7 | Developing → Developing | 16 Oct, cold, non-calc, typed, before any other item: 3 squared = 9, 5 squared = 25, 2 cubed = 8, 3/3 right first time in under 2 min. The 14 Oct timed paper had 3 squared as 6. Untimed only today. | |
| N11-N12 | Developing → Developing | 16 Oct, non-calc, typed, 'read the last line back first': coat 60 pounds up 15 percent, new price: 60/10 = 6, 6/2 = 3, 60 + 6 + 3 = 69. New price given, not the increase (the 14 Oct error), working on every line, no pound sign, 2 min, 1/1. | |
| R7-R8 | Secure → Secure | 16 Oct, non-calc, typed. Changing ratio 4:5 with 20 blue, scaffolded one step per message: one part = 4 right; red answered 5 (parts count) then 16 after a prompt; 6:5 gave 24 then 8 added, right. Fresh 3:7 with 21 yellow unaided: 9 right, answer only, lines only after two prompts. The 14 Oct item (0/4) now done with support; nothing yet alone. |