# Three genuine practice routes each day

Pick one A/B/C. Every route reaches the **same mathematical goal** while changing representation, context or type of reasoning. Use speech, AAC, labelled manipulatives, typed steps or a neutral scribe for any route. A text/tactile version of every A4 aid is [here](print/TEXT-ALTERNATIVES.md). Day15 and Day20 routes begin **after** the independent check.

| Day | A · build or represent | B · explain or apply | C · inspect a tempting error | Common evidence |
| ---: | --- | --- | --- | --- |
| 11 | Build two groups of `a+5`; expand `2(a+5)` and test `a=3`. | Script four equal rows of `b+3`; expand `4(b+3)` and test `b=2`. | A note says `5(c+2)=5c+2`. Locate the skipped multiplication, correct and test `c=1`. | Distribution to both terms and a matching substitution. |
| 12 | Sort terms in `3t+8+4t−2`; simplify and test `t=2`. | Explain `5r−4+2r+9` after regrouping; test `r=1`. | A note says `6p+3−2p+7=4p+4`. Correct and test `p=2`. | Coefficient and signed constants grouped accurately. |
| 13 | Split `8n+16` into eight equal groups; write and re-expand. | Explain `5p+20` as equal groups; check at `p=2`. | Critique `9q+18=9(q+18)`; fix by expanding back. | Common factor, bracket form and inverse expansion. |
| 14 | For fictional `C=10+4n`, find `n` when `C=30`; check and state domain. | For fictional `L=6+3m`, find `m` when `L=21`; explain a model limit. | A note solves `K=7+2h`, `K=19` as `h=12`. Locate the missing inverse step, check and state the whole-count domain. | Rearranged subject, substitution, domain/assumption. |
| 15 | **After check:** expand and collect `5(a+2)+a`; verify at `a=2`. | **After check:** describe equal groups in `8b+16`, then expand the bracket back. | **After check:** inspect `3(c+4)+c=4c+4`; repair with a value check. | Equivalent transformation, not memorised held-out values. |
| 16 | Solve `2x+5=14` with the balance mat; give fraction and decimal, substitute. | Dictate steps for `5y−4=13`; check exact answer. | A note gives `4z+6=17`, `z=11`; repair and substitute. | Same change to both sides, rational value and verification. |
| 17 | Compare `8+3n` and `20+n`; solve, plot crossing and check. | Explain fictional `5+5p` versus `20+2p`; find, verify and describe the graph crossing. | A note says `4+6k=18+4k` at `k=3`; test, correct and describe the graph crossing. | Exact crossing, both substitutions, whole-batch model limit. |
| 18 | Solve fictional `4n+7≤27` for non-negative whole `n`; mark boundary and test 5/6. | Explain `3t+8<23` for whole `t≥0`; list allowed counts and test 4/5. | A note says `2r+9≤21` allows `r=7`; test then repair solution set. | Inequality, boundary inclusion and domain. |
| 19 | Solve `14−2t≥4`, draw/tell number line and test 5/6. | Explain `21−3m>9` with inverse steps and checks 3/4. | A note keeps the sign in `10−4u≤2` and concludes `u≤2`; test, then repair. | Direction reversal and checks around boundary. |
| 20 | **After check:** solve `6+2p=18`, then test that answer against `16−2p≥8`; explain the combined condition. | **After check:** solve `5+3q=17+q`, then test the crossing against `18−2q≥8`. | **After check:** inspect `3k+5≤20 ⇒ k≥5` alongside `2k+4=14 ⇒ k=5`; correct/test the inequality, then decide whether the equation answer is allowed. | Equation plus inequality verification using different values. |

The [staff key](teacher/ANSWER-AND-NEXT.md) has worked answers and next moves. These three routes are not ranked by ability. Original SubjectNest routes © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).