These are after-lesson choices for a local timetable, small group, independent work or home. One extra at a time is enough. All contexts are invented; paper, cards, speech/AAC or large/tactile pieces work without a device, account, purchase or personal disclosure. The Day 15 and Day 20 extras happen after the fresh check.
| Day | Extra | Home/low-material route | Check and next move |
|---|---|---|---|
| 11 | Factor-pair flip: write 12's 1×12,2×6,3×4 on cards; turn each to its commuted form and decide which are new rectangles versus rotated ones. |
Six scraps. | Same factor pair can rotate; do not count it as a new distinct pair. |
| 12 | Near-prime puzzle: compare 22=2×11, 23 prime and 24=3×8/others. Explain why neighbouring labels do not prove 23's status. |
Spoken number cards. | A prime claim needs a complete factor check up to a sufficient stopping point. |
| 13 | Square border: draw 4×4, add one row and column to make 5×5; count 16+4+4+1=25. |
Graph-paper sketch or raised card border. | Growth is 9, not 8: the corner counts once. |
| 14 | Mental regroup: use 8×25=(2×4)×25=4×50=200; verify with 25+25+... if wanted. |
Spoken factor cards. | Associativity and commutativity keep the product, not a memorised shortcut with no reason. |
| 15 | After-check new label: classify 14, 19 and 81 using a factor or square witness. | Pencil or factor cards. | 14 composite; 19 prime; 81 square/composite. Do not reopen the held-out check as practice. |
| 16 | Fold and label: make one paper whole into halves, then quarters; mark 1/2 and 2/4 at the same crease. | One strip, no printer. | Equal physical whole and equal folds are checked. |
| 17 | Gap debate: compare 1/3 and 1/4 on one 12-gap line: gaps 4 and 3; give the difference. | Twelve marks on scrap or tactile notches. | 1/3 exceeds 1/4 by 1/12 of the same whole. |
| 18 | Another beyond-one name: show 4/3=1 1/3=16/12 and decide its position relative to 3/2=18/12. |
Two identical unit strips. | 4/3 is left of 3/2 by 2/12=1/6 of one unit. |
| 19 | Wrong-line clinic: intentionally place 3/4 at tick 3 on a 12-gap line, then repair it to tick 9 and explain why. | Draw 12 gaps or say the count. | Numerator 3 counts quarters, not single twelfth gaps. |
| 20 | After-check equivalence gallery: choose one pair among 2/4=1/2, 3/6=1/2, 6/8=3/4; draw/describe two matching bars and one same-point line. |
Paper, no device. | Same whole; equal-area/equal-length shares; names coincide. |
Teacher note: If an extra exposes a misconception, recheck with a different number or fraction in the next lesson. Do not infer a fixed learner type from a preferred mode. These cards have not been classroom tested. Original SubjectNest extras © NeuroForgeIO Pty Ltd 2026, CC BY 4.0.