# Teacher copy · worked answers, feedback and next moves

Keep this file separate from [learner cards](../STUDENT-CARDS.md) and [fresh checks](../STUDENT-CHECKS.md). Record **actual task, child's first answer, method, access route, adult prompts, revision and next move**. A mathematical idea shown through tactile cards, AAC, speech, handwriting or typing has the same status when the target is number reasoning. A correct calculator display without a chosen operation/scale check is incomplete evidence of this fortnight's target. A missing answer can mean access or time failed; mark **not yet observed**, offer a usable route and gather another sample before inferring a gap.

## Worked answer bank · 30 core learner cards

| Day | A | B | C |
| ---: | --- | --- | --- |
| 11 | `52×18=52×(20−2)=1,040−104=936`; `50×20=1,000` is a high rough anchor. | `73×14=730+292=1,022`; `70×15=1,050` is nearby, so 100 is implausible. | `208×5=1,040`; `200×5=1,000`, with another `8×5=40`. |
| 12 | `235×7=1,400+210+35=1,645`; more than `200×7=1,400`. | `602×4=2,400+0+8=2,408`; zero tens retained. | `481×6=2,400+480+6=2,886`; near `480×6=2,880`. |
| 13 | `215×14=2,150+860=3,010`; ten sets contribute 2,150. | `76×32=2,280+152=2,432`; `75×32=2,400` is nearby. | `142×26=2,840+852=3,692`; twenty strips contribute 2,840. |
| 14 | `396×9=400×9−4×9=3,600−36=3,564`. | `125×24=2,500+500=3,000`; also `125×8×3=1,000×3`. | `318×19=318×20−318=6,360−318=6,042`; near `300×20=6,000`, not 60,000. |
| 15, **after check** | `106×13=1,060+318=1,378`. | `72×28=72×30−72×2=2,160−144=2,016`; also 1,440+576. | `309×6=1,800+0+54=1,854`. |
| 16 | `12×$34=$408`; under $420 by **$12**. | `19×$27=$513`; under $530 by **$17**. | `11×$42=$462`; under $480 by **$18**. |
| 17 | `215×9=1,935`; inverse `1,935÷9=215`, near `200×9=1,800`. | `324×7=2,268`; inverse `2,268÷7=324`, near `320×7=2,240`. | `507×6=3,042`; inverse `3,042÷6=507`, near `500×6=3,000`. |
| 18 | `18×39=702`; unknown **39**, substitute or use `18×(40−1)=720−18`. | `32×26=832`; unknown **32**, `832÷26=32`. | `45×28=1,260`; unknown **28**, `45×(20+8)=900+360`. |
| 19 | `30×24=720` and `45×16=720`; **Plan 1** fits at most 32 bundles. | `40×21=840` and `30×28=840`; **Plan 2** fits at most 35 envelopes. | `36×26=936` and `24×39=936`; **Plan 1** fits at least 30 stations. |
| 20, **after check** | `57×19=57×20−57=1,083`; near 1,140. | `24×35=720+120=840`; also `12×70=840` by halving/doubling. | `108×11=1,080+108=1,188`; inverse `1,188÷11=108`, near 1,100. |

**Feedback that changes the next lesson:** If a child loses a zero in `×20`, physically put 20 counters in two rows of ten and write `number×(2×10)`. If a result is one-tenth size, first compare it with a lower bound such as `128×20` before repeating the algorithm. If the exact product is right but an estimate is missing, model rounding before the calculation with a fresh pair. If a constraint is ignored, make a two-column table: **arithmetic total** and **stated limit**. A different correct strategy should be accepted and discussed, not converted into the teacher's method by default.

## Optional extension answers · 20 routes

| Day | A | B |
| ---: | --- | --- |
| 11 | `39×21=819`; `39×20=780 < 819 < 40×21=840`. | `62×15=930`, near `60×15=900`; 93 misses a factor of ten. |
| 12 | `504×3=1,512`; `54×3=162`; a zero in 504 separates hundreds from ones. | `706×4=2,800+0+24=2,824`. |
| 13 | `84×20=1,680`, not 168; `84×7=588`; total `2,268`. | `46×32=1,380+92=1,472`; `(40+6)×32=1,280+192=1,472`. |
| 14 | `214×19=4,280−214=4,066`; near 4,000. | `25×48=1,200`; `25×4×12=100×12`, or 1,250−50. |
| 15 | Wrong partial `132×4` is **528**, not 428; total **1,848**, not 1,748. | Example `119×20=2,380`, near 2,400; other justified two-digit multipliers may fit. |
| 16 | `14×$29=$406`; $14 remains from $420. | `$456÷12=$38` each; the source gives no real vendor price. |
| 17 | `306×8=2,448`; `2,448÷8=306`, `2,448÷306=8`; near 2,400. | `390×7=2,730`; thus `2,730÷7=390` is correct but `390×7=2,370` is false. Correct the stated product to 2,730. |
| 18 | `?=50`, since `50×18=900`; 5×18 is only 90. | `?=42`, since `24×42=1,008` (960+48). |
| 19 | Both totals **600**. “At most 15 bundles” favours 12×50; “at least 18 groups” favours 20×30. These are *invented possible* criteria, not given. | Both totals **420**. No pack prices were supplied, so cheaper is unknown. |
| 20 | Open design: independently check the child's chosen factors, both partial products and the deliberate error against exact arithmetic. | Open design: verify both products really match and the declared limit selects the child's named plan; a deliberately unresolved tie is valid only if stated. |

## Day 15 · Fresh Check A key

Estimate `200×15≈3,000` is a sensible benchmark; so is `210×14=2,940`. Exact `213×14 = 213×10 + 213×4 = 2,130+852 = 2,982`. The proposed `29,820` is **ten times too large**; even `213×20=4,260` is well below it. Accept another valid efficient method with its value/place shown. Do not require one particular estimate, but ask whether its rounding direction makes sense. A pupil who says 2,982 without method may know it; ask for a partial product or reverse check on a new item before claiming strategy security.

| Construct | 2 · independent and explained | 1 · partial or prompted | 0 · not yet observed after usable access |
| --- | --- | --- | --- |
| Benchmark | Nearby benchmark with reason and scale | Nearby value but weak reason, or correct after prompt | No defensible size sense yet |
| Partial products/exact | `2,130+852=2,982` or valid equivalent, places intact | Method mostly right with arithmetic/place slip, repairs after prompt | Group value or operation not established |
| Plausibility | Rejects 29,820 using benchmark, bound or factor of ten | Rejects but gives vague reason | Accepts tenfold total without a check |

**Next move:** If ten pages become 213 instead of 2,130, teach `×10` with place cards then retest using a different 3-digit×two-digit example. If a learner's method is good but adding 2,130+852 slips, give a short addition check separately; do not erase multiplication understanding. If access/time prevented response, repeat with a new source after adapting the access route; mark this item not yet observed.

## Day 20 · Fresh Check B key

One useful estimate is `180×24≈4,320`, intentionally **above** exact because 180 exceeds 178; another is `180×25=4,500`, a looser upper anchor. Exact `178×24 = 178×20 + 178×4 = 3,560+712 = 4,272`. Inverse `4,272÷24=178` or two-way check `24×(180−2)=4,320−48=4,272`. The plan fits the **4,500-label** count limit with **228 spaces** left. Price, actual shelf safety and existence of labels are unknown; “cheapest” has no evidence.

| Construct | 2 · independent and explained | 1 · partial or prompted | 0 · not yet observed after usable access |
| --- | --- | --- | --- |
| Estimate | Useful rounded product and correct direction/scale | Reasonable rounded value with incomplete explanation | No reliable benchmark yet |
| Product | Exact 4,272 with inspectable tens/ones or equivalent | Valid structure, one arithmetic slip repaired with prompt | Group/place structure not evident |
| Independent check | Inverse or different route gives 178/4,272 and is explained | Copies a fact or checks after cue | No check yet |
| Interpretation | `4,272≤4,500`, 228 spare; refuses unsupported price claim | Correct fit with weak evidence limit | Constraint or price boundary misunderstood |

**Next move:** If 178×20 becomes 356, compare it to 178×2×10 and use the partial-products mat. If the result is exact but the recommendation ignores the 4,500 limit, highlight only the constraint sentence and ask the child to compare. If a child asserts “cheap,” give two invented price cards with different values and show why price data is required; never ask about family purchases. If inverse division is inaccessible, let the learner verify with 24×(180−2) and revisit division in a later separate lesson.

## Decision after these two weeks

These checks sample **one fortnight** of multiplication and estimation. They do not prove all of AC9M5N06/08/09 or the Year 5 achievement standard. Collate classwork, alternate representations and later transfer with the school's local assessment rules. A 0 is an invitation to find out *why evidence is missing*, not a diagnosis. Keep named work outside the public repository.

**Original resource rights:** © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit, link and indicate changes. This is a teacher copy.