Keep this file separate from learner cards and fresh checks. 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.
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