# Year 4 maths · staff key, rubric and next moves

**Teacher copy. Keep separate from [learner cards](STUDENT-CARDS.md) and [learner checks](STUDENT-CHECKS.md).** Work in the child's chosen accessible response mode. Record `first answer | reasoning or model | adult mathematical cue | access support | next move`. Reading words or moving a marker exactly as instructed is access support; saying “count six spaces” is a mathematical cue. A blank caused by missing access or time is **not yet seen**, not a misconception. These are short formative samples, not a complete Year 4 achievement-standard judgement.

## Daily exits and immediate teaching move

| Day | Worked expected response | If not yet, teach and recheck on a new example |
| ---: | --- | --- |
| 11 | One tenth after `0.5` and one tenth before `0.7` is **`0.6`** on a ten-gap 0–1 line. | Lay ten equal paper spaces between labelled 0 and 1; start at each endpoint and count gaps, not the ink marks. Recheck with `0.2` and `0.4`. |
| 12 | Seven hundredth spaces after `0.20` is **`0.27`**; it lies between `0.20` and `0.30`. | Rename endpoints 20 and 30 hundredths, lay ten equal small spaces and recheck a fresh `0.23`. |
| 13 | **`1.06 < 1.6 = 1.60`**. `1.06` needs a hundredth zoom inside `1.00–1.10`; `1.6` lies six tenths after 1. | Put both in whole/tenths/hundredths columns, then recheck `1.08` versus `1.5`. |
| 14 | **`0.49 < 0.5 = 0.50` by `0.01`**. | Build 49 versus 50 cells on two matching hundred-grids; recheck `0.39` and `0.4`. |
| 16 | **`0.5 = 0.50 = 1/2 = 5/10 = 50/100`** at one midpoint on the same whole. | Overlay matching half and ten strips; recheck `2/4` versus `5/10`. |
| 17 | **`1/4 = 0.25 > 0.2 = 0.20` by `0.05`** of the same whole. | Four equal 25-cell blocks versus two 10-cell rows; recheck `3/4` versus `0.7`. |
| 18 | **`5/5 = 10/10 = 1`** complete whole, not five wholes. | Shade every equal part in one outline, then recheck `4/4`. |
| 19 | **`0.50 = 0.5 = 1/2`** at one number-line point. | Match 50 of 100 cells to five of ten rows; recheck `0.30` versus `0.3`. |

## Thirty learner routes · worked responses

| Route | One valid checkable response |
| --- | --- |
| D11-A | `0.2` is two tenth-gaps after zero; `0.8` eight. `0.8` lies farther right. |
| D11-B | Fourth gap after zero on a ten-gap 0–1 line is `0.4`, not `0.04`. Four hundredths would be near zero on a hundredth scale. |
| D11-C | `0.1` first gap, `0.9` ninth gap. A useful instruction names 0 and 1 and counts equal spaces. |
| D12-A | `0.23` is **three** hundredth-gaps after `0.20`. |
| D12-B | Eighth tick **when the `0.20` endpoint is counted as tick one** is only the seventh travelled gap, `0.27`. `0.28` is eight gaps from the endpoint, or the ninth tick position including it. |
| D12-C | `0.21` is first gap; `0.25` fifth. `0.21 < 0.25`, four hundredth-gaps apart (`0.04`). |
| D13-A | `1.4 = 1.40 > 1.04`; fractional distances from 1 are `0.40` and `0.04`, so `1.4` is farther by `0.36`. |
| D13-B | `1.09 < 1.9 = 1.90`; nine hundredths is less than nine tenths. Their difference is `0.81`. |
| D13-C | `1.12` is two hundredth-gaps after `1.10`; `1.12 < 1.2 = 1.20` by `0.08`. |
| D14-A | `0.23` and `0.32` differ by `0.09`; `0.32` is farther right and cannot share a point on one fixed scale. |
| D14-B | `0.09 < 0.9 = 0.90`; 9 versus 90 hundredths; difference `0.81`. |
| D14-C | `0.54 < 0.6 = 0.60` by `0.06`; six hundredth-gaps separate them. |
| D15-A | `0.33` is three hundredth-gaps after `0.30`, in the fourth tick position counting endpoint. |
| D15-B | `1.09` is nine hundredth-gaps after `1.00`: 1 whole, 0 tenths, 9 hundredths. |
| D15-C | `0.79 < 0.8 = 0.80` by `0.01`; the `0.79` point comes first. |
| D16-A | `2/4 = 1/2 = 5/10 = 50/100 = 0.5 = 0.50` when outlines are the same-sized whole. |
| D16-B | `3/6 = 1/2 = 0.5`; mark the midpoint, not `0.3`. |
| D16-C | `4/8 = 1/2 = 0.5`; four of eight equal tiles are half the bar. |
| D17-A | `1/4 = 25/100 = 0.25`; shade one group of 25 cells in the 100-cell same whole. |
| D17-B | `3/4 = 75/100 = 0.75`, not `0.30`; each quarter is 25 hundredths. |
| D17-C | `2/4 = 1/2 = 50/100 = 0.50 = 0.5`, midpoint on 0–1 line. |
| D18-A | `1/5 = 2/10 = 20/100 = 0.2 = 0.20`; split **all** fifths, including the shaded one. |
| D18-B | `6/10 = 3/5 = 60/100 = 0.6`; pair each two tenth positions into one fifth. |
| D18-C | `5/5 = 10/10 = 100/100 = 1`; all parts of one whole are marked. |
| D19-A | `1/4 = 0.25 > 1/5 = 0.20` by `0.05`, for the same-sized whole. |
| D19-B | `3/5 = 0.60 < 3/4 = 0.75` by `0.15`; same numerator does not make equal shares because each part has a different size. |
| D19-C | `1/2 = 2/4 = 5/10 = 0.5 = 0.50`; both decimals mark the midpoint. |
| D20-A, **later only** | `4/5 = 8/10 = 80/100 = 0.8 = 0.80`; eighth tenth gap after zero. |
| D20-B, **later only** | `2/5 = 4/10 = 40/100 = 0.4 = 0.40`; `0.02` is two hundredths and does not match. |
| D20-C, **later only** | `1/4 = 0.25 < 1/2 = 0.50 < 3/4 = 0.75` on a fixed whole. |

## Day 15 held-out check · decimal lines

| Item | Worked response | What to record |
| ---: | --- | --- |
| 1 | From `0.30` to `0.40` there are ten equal `0.01` gaps; `0.36` is **sixth** gap after `0.30`, at seventh tick position if the left endpoint is position one. | Correct endpoints, equal-gap count and `0.36` location. |
| 2 | `1.07` is **seventh** gap after `1.00` in the `1.00–1.10` zoom: **1 whole, 0 tenths, 7 hundredths**. | Beyond-one whole, correct zoom and place names. |
| 3 | **`0.68 < 0.7 = 0.70`**. Difference `0.02` or **two hundredths**. | Same-whole comparison, not printed-digit-length heuristic. |
| 4 | Sixth gap after zero on ten equal 0–1 gaps is **`0.6` or `0.60`**, not `0.06`. `0.06` is six hundredths, nearer zero than one tenth. | Repairs claim and distinguishes tenths from hundredths. |

These values were held out of the Days 11–14 scripts and cards. The Day 15 practice routes are explicitly **after** the check. Do not let a displayed teacher key reveal the outcomes before the first response.

## Day 20 held-out check · equal shares

| Item | Worked response | What to record |
| ---: | --- | --- |
| 1 | `2/5 = 4/10 = 40/100 = 0.4 = 0.40`. Each of **five** equal fifths splits into two tenths, so the **two** shaded fifths become **four** shaded tenths. | Same whole, related denominators and exact decimal. |
| 2 | `0.4` is the **fourth gap after zero** on a 0–1 line with ten equal gaps. | Fraction and decimal occupy one point. |
| 3 | `2/5 = 0.40 < 1/2 = 0.50` by **`0.10` = 10 hundredths = one tenth** of the same whole. | Reasoned comparison and exact unit difference. |
| 4 | The note is false. `2/10 = 1/5 = 0.2`, while **`2/5 = 4/10 = 0.4`**. Splitting every fifth doubles both the total count of parts and the shaded count. | Identifies error and preserves amount using related denominators. |

`2/5` and its linked decimal were not modelled in the Days 16–19 scripts or learner choices. The Day 20 practice cards are for after the retained check.

## Formative rubric and next teaching

Score **each focus separately**: Day 15 (equal scale, hundredth placement, decimal order, repair); Day 20 (fixed whole, equivalent grouping, decimal location, comparison/repair). This is a planning note, not a high-stakes grade or an end-of-year judgement.

| Evidence | Record | Next teaching move |
| --- | --- | --- |
| Accurate first model and reason without a mathematical cue | `I`, exact example and response mode | Try a different value/denominator and ask the learner to explain a peer's model. |
| Correct only after a prompt such as “count spaces” or “split every part” | `P`, the exact prompt and later revision | Reteach with a tactile or drawn same-whole model; fade the cue and resample a fresh case. |
| Specific conflict between mark, symbol and explanation | `R`, preserve original and repaired work | Use the matched repair below, then a new number or fraction. |
| No accessible opportunity, interrupted check or unfinished response | `N`, state why | Offer a quieter accessible attempt; a blank is not mathematical evidence. |

**Matched repairs:** Count *spaces* with endpoints named when a learner counts ticks. Align same-sized grids and place digits into whole/tenths/hundredths columns if decimals are ordered by string length. To repair a wrong fraction equivalence, split **every** part of a fixed whole and recount both numerator and denominator. If a picture uses unequal parts, rebuild the whole before naming fractions. For a number-line claim, demand a labelled endpoint and equal scale. Family feedback should name the next small task, never a fixed learning-style or ability label.

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