Teacher copy. Keep separate from learner cards and learner checks. 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.