# Teacher key, formative interpretation and transfer

**Teacher copy.** Keep this separate from [learner cards](student-cards.md) and [checks](student-checks.md). The checks are public formative material and are **not secure tests**. Give a new item after feedback. Record first response, mode, mathematical prompt and later revision separately. A read-aloud or adult-operated counter under the learner's direction is access support; a model that shows the answer is a concept prompt.

## Card totals and the move each asks for

| Day | A | B | C and intended follow-up |
| --- | ---: | ---: | --- |
| 11 | 52 | 54 | 55; remove two ones → 53 |
| 12 | 58; one more → 59 | 59; one more → 60 | 60 = six tens or five tens + ten ones |
| 13 | 62 | 64, which is two more than A | 65 = six tens + five ones = five tens + fifteen ones (extension) |
| 14 | 67 | 69; one more → 70 | 70 = seven tens or six tens + ten ones |
| 15 | 53 | 61 | 68; order 53 < 61 < 68 |
| 16 | 72 | 74, two more than A | 75; remove two ones → 73 |
| 17 | 77 | 79; one more → 80 | 80 = eight tens or seven tens + ten ones |
| 18 | 82 | 84, two more than A | 85; 83 or 84 is between A and C |
| 19 | 87 | 89; one more → 90 | 90 = nine tens or eight tens + ten ones |
| 20 | 56 | 78 | 86; full-tens order A < B < C |

## Check keys and a precise next lesson

| Check | Evidence to look for | If absent, teach and recheck with a **new** item |
| --- | --- | --- |
| 1.1 | 57 = five tens + seven ones, numeral digits tied to columns. | Rebuild 50, add six loose ones for 56 and connect to 50 + 6. |
| 1.2 | 63 = six tens + three ones, placed after 62/before 64. | Pair one verified strip with 10 cells, count six tens as 10…60, then add one for 61. |
| 1.3 | 58 < 60 < 69, with tens comparison across the boundary. | Contrast 59/61 concretely, then order fresh 57, 60, 67. |
| 1.4 | Five tens + ten ones = six tens + zero ones = 60; quantity unchanged. | Physically exchange in 29+1, then recheck with 79+1. |
| 2.1 | 76 = seven tens + six ones; 7 is the tens digit and 6 the ones. | Align a model of 74 and then contrast with 47. |
| 2.2 | 83 = eight tens + three ones; count the eight full tens first. | Touch-count one strip to verify ten, then solve seven strips + two ones = 72. |
| 2.3 | 81 < 89 < 90; both 81 and 89 have eight tens, and 90 has nine. | Compare 82/88, then use 78, 80, 87 as a fresh order. |
| 2.4 | Eight tens + ten ones = nine tens + zero ones = 90; equal amount. | Rebuild with large strips and trade, then recheck a new 69+1 model. |

**Do not convert the eight-item pattern into an achievement-standard verdict.** A correct numeral copied from a card is different from a child-constructed quantity. A child who is confident to 50 but needs more time at the 60 exchange should use the same mature context with a smaller amount, then return to the progression. A child secure to 90 needs Week 5 onward to reach at least 120 and demonstrate number lines, charts and alternative partitions.

## Two larger optional assignments

**A. Design a countable exhibit, 25–35 minutes:** The learner chooses a fictional library shelf, game map, craft kit or another interest. They create 6–9 groups of ten drawn or physical objects plus 0–9 loose ones; label the numeral and `tens + ones` equation; give a visitor a different representation to check it. A peer or adult deliberately makes one plausible error (digit reversal, incomplete strip, or failure to exchange). The learner explains and revises. Collect the original, visitor's check and revised model. No real personal item collection or purchase is required.

**B. A route across a new ten, 20–30 minutes:** Make a 56→60, 76→80 or 86→90 paper movement story. Show every single step, trade ten loose marks into a strip at the boundary, and narrate what stayed equal. A child can build, direct, record audio locally under school policy, or create a tactile strip. No identified recording needs to leave the school.

| Dimension | Ready evidence | Next teaching when developing |
| --- | --- | --- |
| Count structure | Every group is verified as ten; loose pieces are counted once. | Audit one strip and rebuild a new total together. |
| Numeral connection | Tens and ones match the two digit places. | Align columns, contrast a reversal and try a new number. |
| Ordering/exchange | Comparison uses total, and an exchange preserves quantity. | Pair full tens or physically trade ten ones, then transfer. |
| Explanation | Child uses a model, number position or precise words rather than a guess. | Give a sentence/pointing frame, then fade it on a new example. |

Use **ready / developing / not yet observed** by dimension, noting access and prompts. Do not compare children by speed or response mode. Translate only with a qualified reviewer for the named variety; a numeral may travel across languages while an English word problem's classroom meaning does not automatically do so.

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