# Staff-only answers, observations and next moves · Year 7 maths

Keep this separate from [learner prompts](../LEARNER.md) and [fresh checks](../STUDENT-CHECKS.md). Record `first exact response | representation and reason | access | mathematical hint if any | next move`. Accept equivalent correct methods. A blank response when access or time failed is **not yet observed**, not necessarily wrong. No check below has classroom validation or establishes a whole-year achievement judgement.

## Daily exits

| Day | Expected reasoning | Immediate next move if not yet |
| ---: | --- | --- |
| 11 | `3/4−1/8=6/8−1/8=5/8`, below3/4 on same whole. | Rebuild an eight-part strip; ask for a different subtraction. |
| 12 | `4.75+2.60=7.35`; `10.00−7.35=2.65`; estimate7–8. | Line up tenths/hundredths and check with addition on fresh decimals. |
| 13 | `1/2×3/4=3/8`, an overlap smaller than3/4. | Shade a half of a four-part strip then name eighths. |
| 14 | `2.4÷0.6=4`, because four0.6 intervals total2.4. | Mark0,0.6,1.2,1.8,2.4; count gaps, not five markers. |
| 16 | 60=`2²×3×5`, all leaves prime; `4×3×5` is numerically60 but 4 is not prime. | Split any composite leaf again and recheck84. |
| 17 | `2³×3²=8×9=72`; `3²=3×3`. | Make repeated-prime cards, then evaluate a different product. |
| 18 | `90/150=3/5` after dividing both by30; `150×3/5=90`. | Pair equal prime leaves and try another common factor, then reduce. |
| 19 | `√81=9` because `9²=81`; 81=`3⁴`. | Check a proposed root by squaring it and distinguish base from exponent. |

## Thirty route keys and acceptance criteria

| Route | Checkable result |
| --- | --- |
| D11-A | `1/2=4/8`; plus3/8 is7/8 of one strip. Result <1 and >1/2. |
| D11-B | `5/6−1/3=5/6−2/6=3/6=1/2` hour. |
| D11-C | `4/10` is false because denominators name different-size parts; `4/8+3/8=7/8`, below1. |
| D12-A | `4.75+2.60=7.35 m`; `10.00−7.35=2.65 m`; inverse 7.35+2.65=10.00. |
| D12-B | Used3.45+1.80=5.25 GB; remaining8.00−5.25=2.75 GB; sum back8.00. |
| D12-C | `6.35+2.70=9.05 km`; 8.105 is misaligned/incorrect, estimate6+3≈9 supports9.05. |
| D13-A | 3-by-4 equal grid overlap6/12=1/2. |
| D13-B | `2/5×3/4=3/10` of20 minutes =6 minutes; same whole period. |
| D13-C | `2/5×3/4=6/20=3/10`; 6/9 uses an unjustified denominator. |
| D14-A | 2.4÷0.6=4 **intervals**; four0.6 lengths=2.4; five markers if endpoints included. |
| D14-B | 1.5÷0.25=6 pieces;6×0.25=1.5. |
| D14-C | 12.5%=1/8, and48÷8=6 panels. |
| D15-A, later | `3/5+1/10=6/10+1/10=7/10`, less than1. |
| D15-B, later | `4.8÷0.8=6`;6×0.8=4.8. |
| D15-C, later | 20%=1/5;70÷5=14 tokens. |
| D16-A | Starting60 as6×10 or3×20 ends with two2s, one3, one5: `2²×3×5=60`. |
| D16-B | 84=4×21=(2×2)×(3×7)=`2²×3×7`. |
| D16-C | Split composite4 into2×2; `2²×3×5=60`. |
| D17-A | Both72 trees yield `2³×3²`;3 twos and2 threes. |
| D17-B | `2³=2×2×2=8`, `3²=9`, product72; 2×3=6 is unrelated to exponent3. |
| D17-C | 54=`2×3³` =2×27. |
| D18-A | 90=`2×3²×5`;150=`2×3×5²`; shared product2×3×5=30; 90/150=3/5. |
| D18-B | Only matching prime leaves pair: shared2,3,5; one3 remains in90, one5 in150, hence3/5. |
| D18-C | Different divisors produce 9/5, which is not equal to90/150. Divide both by30 to get3/5;150×3/5=90. |
| D19-A | `12²=144`, `√144=12`; 12=`2²×3`, so 144=`2⁴×3²`;16×9=144. |
| D19-B | 100=`10²=(2×5)²=2²×5²`; positive root10. |
| D19-C | 81=`3⁴=(3²)²=9²`; positive square root9, not3. |
| D20-A, later | 120=`2³×3×5`;8×3×5=120. |
| D20-B, later | `13²=169`; positive root13. 13 is prime if optional factor form requested. |
| D20-C, later | `2³×5²=8×25=200`, not150; true150=`2×3×5²`. |

## Day 15 held-out key

| Item | Exact answer and check | If not yet, next move |
| ---: | --- | --- |
| 1 | `2/3+1/4=8/12+3/12=11/12`, below1 and above2/3. Inverse `11/12−3/12=8/12=2/3`. | Use one 12-part whole; recheck 1/2+1/3 on a fresh strip. |
| 2 | `7.2÷0.3=72÷3=24` pieces; `24×0.3=7.2` units. | Draw groups on a simpler1.2÷0.3 model; then recheck a new decimal. |
| 3 | 10% of80=8;5%=4;15%=12 cells. Or `0.15×80=12`; whole80, `12/80=0.15`. | Rebuild one tenth and half a tenth; recheck20% of60. |

## Day 20 held-out key

| Item | Exact answer and check | If not yet, next move |
| ---: | --- | --- |
| 1 | `108=4×27=(2×2)×(3×3×3)=2²×3³`; `4×27=108`. Every leaf prime. | Stop an easier tree only at primes; recheck54 or72. |
| 2 | `196=14×14=14²`; principal positive `√196=14`. Since14=`2×7`, 196=`(2×7)²=2²×7²`;4×49=196. | Use 12²=144 and13²=169 as benchmarks, then test14×14; recheck another square. |
| 3 | `3²×5²=9×25=225`, so proposed75 equation is false. `75=3×25=3×5²`. | Expand powers into repeated primes and multiply; recheck a fresh false equality. |

## Observation codes

Use `I` for independent mathematics with access provided, `P` if a **content** prompt supplied a step, `R` for a specific mismatch and `N` for not observed because access/time was missing. Preserve first work before feedback. Aural reading, screen reader, tactile blank aid or scribe is not itself a content hint; selecting the denominator, quotient or prime leaf is. Report one next move to families, not a permanent learner type.

Original SubjectNest staff keys © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).