# Year 7 mathematics: keyed formative checks and next moves

These tasks sample the **opening fortnight**, not the Year 7 achievement standard. Keep four fields per learner: exact representation/calculation; explanation; access and prompts; next teaching move. Use a rotating focus roster; an unseen or partner-copied answer is `not yet observed` for independent reasoning. Accept a different correct strategy with a coherent unit and check.

| Day | Keyed exit | Next move for a common misconception |
| ---: | --- | --- |
| 1 | `1/4 = 0.25 = 25%` of the same whole | If 0.4, partition the whole into four equal parts, then hundredths. |
| 2 | `0.25 < 3/8 (=0.375) < 0.5` | If 3/8 is read as 3.8, use eighths on a 0–1 strip and write 0.375. |
| 3 | `7/10 = 0.7 = 70%` | If 7%, contrast 7 of 10 with 7 of 100 cells. |
| 4 | `12.684` to a tenth = **12.7** | If 12.6, check hundredths digit 8 and proximity to 12.7. |
| 5A | `2/5 = 0.4 = 40%`; lies between 0.25 and 0.5 | Rebuild as 4/10, then 40/100; do not teach a memorised conversion only. |
| 5B | `0.65 < 3/4 (=0.75)`; `12.684 → 12.7` to tenths | If 0.65 > 3/4, use hundredths on equal-length bars. |
| 6 | `3/4 − 1/8 = 5/8` | If numerator and denominator are subtracted separately, express 3/4 as 6/8 first. |
| 7 | `$25.00 − $21.35 = $3.65`; inverse totals $25 | If $4.35, align cents and use a 100-cent exchange. |
| 8 | 30% of 50 = **15** | If 30, name 50 as whole and use 10% of 50 = 5. |
| 9 | $120 − $38.40 − $46.75 = **$34.85** | If $35.15, add costs to $85.15, then subtract and add back. |
| 10 | `3/5=0.6=60%`; `7.486→7.49` hundredths; remaining **$37.45** | Diagnose equivalence, rounding and money model **separately**. |

## Day 5 check A — equivalent forms, order and precision

**Prompts:** (1) Show `2/5` as decimal and percentage, and place it between 0.25 and 0.5. (2) Compare 0.65 with 3/4 using a numeric reason. (3) Round 12.684 to one decimal place. **Key:** `2/5 = 4/10 = 0.4 = 40%`; `0.65 < 0.75`; `12.7`.

**Worked response decisions:** “Two fifths equals 0.25 because it has a 2 and 5” signals digit matching, so represent five equal segments and shade two, then ask for a *new* 3/5. “0.65 is less than 3/4 because 65 hundredths < 75 hundredths” is convincing. “12.68” is accurate rounding to **hundredths**, but the requested place was tenths; repeat the instruction and point to the tenths digit before a new number such as 8.247 → 8.2. Record whether a cue was necessary.

## Day 10 check B — representation, rounding and model

**Prompt 1:** Rename `3/5` in decimal/percent and locate it on a 0–1 line. **Key:** 0.6, 60%, to the right of 1/2. **Prompt 2:** round 7.486 to hundredths. **Key:** 7.49; the thousandths digit 6 makes hundredths 8 round to 9. **Prompt 3:** $100 minus $26.80 and $35.75, with a model and inverse check. **Key:** costs $62.55; remainder $37.45; `$62.55 + $37.45 = $100.00`.

**Example next moves:**

- Student writes `3/5 = 0.35`: use 3 of 5 equal parts, then 6 of 10; ask whether 0.35 being below one half is plausible for 3/5.
- Student rounds to 7.48: compare 7.486 to 7.48 and 7.49 on a hundredth line, then round an unseen 4.273 to hundredths.
- Student obtains `$37.45` but no model: ask for an equation or bar showing total and two costs; do not call the strategy independently known yet.
- Student writes `$162.55` after adding costs to the starting budget: identify whether $100 is a whole or an extra part; return to a simple $10 whole with two small costs.
- Student uses a calculator under an access plan after showing a coherent model: record the model and tool, then check interpretation; do not silently reclassify the solution as unaided calculation.

The next lesson should use a **different** but structurally similar example. Feedback names what happened today and what to try next, not a fixed ability tier. A correct calculation with no unit in a money story needs the unit added; it does not erase the arithmetic evidence.

**Rights:** Original assessment/keys © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit, link and indicate changes.