# Mathematics evidence and keyed next moves

These checks tell the teacher what to model next; they are **not** a Year 3 achievement-standard decision. Keep `exact response or model | access/prompt | mathematical idea shown | next move` for a rotating sample. The whole class attempts each exit; observe a planned few closely. Arrange a quiet individual check when independent reasoning is needed and write `not yet observed` otherwise.

| Day | Keyed check | If the response suggests a gap |
| ---: | --- | --- |
| 1 | `1 ten-thousand + 3 thousands + 0 hundreds + 2 tens + 5 ones` = **13 025** | Rebuild 13 025 beside 1 325; point to the absent hundreds. |
| 2 | **30 506** has 0 thousands and 0 tens | Say every place while a learner positions each tile. |
| 3 | **12 405 > 12 045** because hundreds differ first | Align places; compare from left and stop at first difference. |
| 4 | 18 counters is **about 20**, more than 10; exact count after estimate | Provide a visible ten benchmark, then count in groups. |
| 5A | **14 305 < 14 350** because tens 0 < 5 | Keep zero tens visible and compare both on a mat. |
| 5B | 38-counter tray: estimate first, then group 3 tens/8 ones | Do not grade closeness alone; practise interval and revision. |
| 6 | **184 + 137 = 321**, with an exchange from 4+7 ones | Use ten single pieces exchanged for one ten, then recompute. |
| 7 | **302 − 157 = 145**, with `145+157=302` as check | Count up 157→200→300→302 if exchange across zero is hard. |
| 8 | `□ + 137 = 400` → **263**; 400 is whole | Mark whole/parts before choosing subtraction. |
| 9 | Book problem **513 books**; tile problem **325 tiles** | Re-enact which group arrives/leaves, then check unit. |
| 10 | **14 370 > 14 307**; **346+178=524 tickets** | Diagnose place comparison and exchange independently. |

## Day 5 check A: place and estimate

**New place prompt:** Build **14 305** and **14 350**, say each numeral, compare, then explain which digit settles it. **Key:** both have 1 ten-thousand, 4 thousands, 3 hundreds; `0 tens < 5 tens`, so 14 350 is larger. A child who says 14 305 is larger “because 5 is greater than 0” is comparing ones before tens; ask them to point to each *place*, not rehearse a symbol. A child who reads 14 305 as 1 435 has dropped a place; rebuild in all five labelled columns.

**Estimate prompt:** show a new tray containing **38** large paper counters for a brief look. Retain the estimate before opening. Group count **3 tens and 8 singles**. Strong evidence includes a plausible interval (e.g. between 30 and 50), a reason and willingness to revise. **Do not** mark an estimate of 35 “incorrect” just because the exact count is 38. If the initial estimate is 300, compare with a visible ten; if the counting result is 37, check one-to-one organisation without treating estimation itself as weak.

**Recheck later:** use a new numeral, e.g. **16 402** versus **16 420**, and a different-size collection with a ten benchmark. Do not repeat only the answer the child has now seen.

## Day 10 check B: place plus additive model

**Place:** **14 307** has 1 ten-thousand, 4 thousands, 3 hundreds, 0 tens, 7 ones. **14 370** is greater: hundreds tie; 7 tens exceed 0 tens. Accept a well-explained equivalent expanded representation.

**Problem:** “There are 346 tickets in one box and 178 in another. How many tickets altogether?” **524 tickets.** A reasonable estimate is near 350 + 180 = 530. A place-value path: 300+100=400, 40+70=110, 6+8=14, total 524. Check `524−178=346` or another correct inverse.

**Example feedback decisions:**

- Child gets 524 with a model but omits “tickets”: ask what is being counted, keep the correct calculation.
- Child writes 414 after correctly summing hundreds/ones but dropping a ten exchange: exchange 10 tens for a hundred with cards, then try **257+164**.
- Child adds 346−178 even though boxes combine: ask them to mark the two parts and draw a whole; use **24+13** before returning to three digits.
- Child produces 524 by copying a neighbour but cannot explain any part: mark independent strategy **not yet observed** and use a private new-number check.

Reading support, translated oral explanation from an appropriate speaker, AAC or a scribe must be recorded, without confusing them with a mathematical prompt. Respond to the child's *actual* model; do not assign an ability label from a single fortnight.

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