# Ten optional extras · home or later class work

Each fits roughly 5–10 minutes and can be done with spoken explanation or scrap paper. It is **not** a prerequisite, reward tier or second assessment. A parent need not teach a new method, print a page, share expenses or make an account. For Days 15/20, use after the first check response only.

| Day | Extra task | Self-check |
| ---: | --- | --- |
| 11 | Invent two identical boxes with `x+7` counters. Write total in two forms; test `x=1`. | `2(x+7)=2x+14`; both 16 at 1. |
| 12 | Simplify `7a−2+3a+5`; test `a=0`. | `10a+3`; both 3 at 0. |
| 13 | Find two ways to factor `12b+24` and expand each. | `12(b+2)` and `6(2b+4)` both expand correctly. |
| 14 | In `H=4+6r`, can total `H=23` describe whole refills? | `(23−4)/6=19/6`, not a whole refill. The model needs review. |
| 15 | **After check:** explain why `7d+14=7(d+2)` for any `d`. | Seven groups of `d+2`; expansion recovers `7d+14`. |
| 16 | Solve `3s−2=10` and check. | `s=4`; `3×4−2=10`. |
| 17 | With invented totals `4+2x` and `10+x`, find equality and check x=5/7. | Equality `x=6`; at 5 second is 15 versus first 14, at 7 first 18 versus second 17. |
| 18 | For whole `a≥0`, solve `2a+3<11`. | `a<4`; allowed 0,1,2,3. At 4, 11 is not less than 11. |
| 19 | Solve `18−4v≤6` and test 3/2. | `v≥3`; at 3 both sides 6, at 2 left 10, so false. |
| 20 | **After check:** give a graph/text explanation for `2x+8≤20` with whole `x≥0`. | `x≤6`, integers 0–6; 6 reaches 20, 7 exceeds it. |

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