# Teacher key, diagnostic next moves and response record

Keep this page separate from [learner cards](student-cards.md) and [checks](student-checks.md). Accept equivalent explanations through objects, selection, sign, AAC, pointing or learner-directed adult movement. Record the mathematical prompt separately from reading, motor or communication access. A chart answer without a quantity explanation is evidence about locating, not automatically about grouping.

## Thirty card totals and intended changes

| Day | Card A | Card B | Card C and action |
| ---: | --- | --- | --- |
| 21 | 91 | 94; B > A by 3 | 95, remove 2 loose ones → 93 |
| 22 | 97 | 99, add 1 → 100 | ten tens = one hundred = 100; before is 99 |
| 23 | 101 | 104, B > A by 3 | 105 = ten tens + five ones; 103 or 104 is between 102 and 105 |
| 24 | 107 | 109, add 1 → 110 | 110 = 11 tens = hundred + ten; reopen ten and remove two ones → 108 |
| 25 | 93 | 100 | 106; order 93 < 100 < 106 |
| 26 | 111 | 114, B > A by 3 | 115, remove two singles → 113 |
| 27 | 117 | 119, add 1 → 120 | 120 = twelve tens = hundred + two tens; one less is 119 |
| 28 | 96 | 112; 96 < 107 < 112 | 119; between 112 and 119: 113–118 |
| 29 | 104 = ten strips + four singles | 118 = eleven strips + eight singles | 120 = hundred + two strips; endpoint 120 |
| 30 | 97 | 109 | 115; order 97 < 109 < 115 |

For each strip, verify **10** actual marks. A hundred square or bundle **replaces** ten strips; it is not added to them. At 99 + 1, ten loose ones trade to a tenth ten and ten tens trade to a hundred. At 109 + 1, loose ones trade to a ten while the hundred remains. At 119 + 1, the second ten-strip appears while the hundred remains. All trades preserve amount. `AC9M1N02` is restricted to partitions of one- and two-digit numbers; three-digit examples here support `AC9M1N01`, not a false expansion of `N02`.

## Check 1 exact key and next teaching

1. **96** = nine tens + six ones; chart cell 96. Other equal models such as eight tens + sixteen ones can show flexible partition if the learner explains them; do not require that extra form for this item.
2. **103** = one hundred, zero separate tens, three loose ones. The middle 0 means *no separate tens in this bundled representation*, not that 103 has no groups of ten at all.
3. **99 < 104 < 108.** One valid reason: 99 has no full hundred; 104 and 108 each have a hundred, and 108 has four more loose ones than 104.
4. **100** before and after both trades; 9 tens + 10 ones = 10 tens + 0 ones = 1 hundred + 0 tens + 0 ones. The quantity does not change.

If the child sees 903 for nine tens/three ones, use a labelled mat and contrast 93 with 903 without requiring 903 mastery. If 99 + 1 gives 910 or 901, count and exchange all ten loose ones, then ten full strips, and recheck with a different bridge such as 89 + 1. If order follows written digit size, compare actual bundles and chart positions. If access prevented a response, change the format and record **not observed** rather than incorrect.

## Check 2 exact key and next teaching

1. **118** = 100 + 10 + 8 = **11 full ten-strips + eight singles**. The square and ten replacement strips must not both be counted. Keep the first model to see whether the learner independently names its quantity.
2. **106 < 119 < 120**. 119 is one one-step before 120; 106 is six after 100 and less than 110. A one-step line or chart must have consecutive marks; accepting a different scale requires the learner to label its intervals consistently.
3. **120** = 100 + 20 + 0 loose ones = **12 full tens**. One hundred + one ten + ten ones before exchange is also 120.
4. **Disagree** on a one-mark-per-whole-number line. 113 is **ten** one-steps after 103. The values 104, 105, 106, 107, 108, 109, 110, 111 and 112 lie *between* the two endpoints; 113 is the tenth next mark. A model has the same hundred and three singles plus **one more full ten**.

If 118 becomes 1018, point to the H/T/O mat, count each full unit and recheck a new value with one hundred, one ten and fewer than ten singles. If the square and its ten strips are both counted, physically replace instead of append. If a line comparison is reversed, label 100 and 110 and count equal-sized steps; ask for a new location. If the child gives an answer without a reason, ask for a new unseen card and one quantity explanation; do not silently promote the guess to understanding.

**Private formative record:** learner code/date ___; task/context ___; first amount/numeral/line placement ___; quantity explanation ___; access mode ___; adult mathematical hint ___; revised answer after teaching ___; chosen next lesson ___; new recheck date ___. Keep the record in the school's approved system. A first-pass answer is never a fixed learner label or whole-year grade.

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