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. 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 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.