# Ten optional 8–12-minute maths extras

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](https://creativecommons.org/licenses/by/4.0/).