# Year 6 maths · fresh learner checks, Days 15 and 20

Open each new packet **only on its named day**, before the later-practice routes. These are original invented situations, not real school, gallery or household data. You can read, listen to a neutral read-aloud, use a screen reader or tactile line, point, sign/AAC, speak, type, dictate or write. Show a reason, not just a label. The adult records the route used separately from any mathematical hint.

## Day 15 · Unseen number properties

Use **positive whole-number factors**. A prime number is greater than 1 with exactly two positive factors; a composite is greater than 1 with more than two; a square is a whole-number side multiplied by itself. Explain with a factor pair, a checked list or an array.

1. **Twenty-seven:** Give every distinct positive factor pair of **27**. Classify 27 as prime or composite, and say whether it is square.
2. **Thirty-seven:** Is **37** prime or composite? Show a systematic small-factor check that makes your conclusion more than a guess.
3. **Sixty-four:** A fictional designer has **64** identical paper squares. Can they make a square array? Give its side lengths. Is 64 also composite? Give a different factor pair.
4. **Choose a layout:** A fictional maker may use **31** or **33** paper cells. They need equal whole-number rows and columns with **both dimensions greater than 1**. Which total works? Give an exact layout and explain why the other does not.

## Day 20 · Unseen same-whole fraction line

Use the [blank 0–1/0–2 line](print/fraction-lines.pdf) or a teacher-provided same-scale tactile line. On the 0–2 line there are **12 equal gaps in each unit**; 0, 1 and 2 are ticks 0, 12 and 24. Do not place an answer until you have fixed the whole.

1. **One equal whole:** A fictional exhibit has a **24-tile** panel. Its three planning cards show `1/3`, `1/2` and `3/4` of that **same panel**. How many tiles does each fraction name? Place or order the three fractions on a 0–1 line, explaining the order.
2. **Beyond one:** On the same 0–2 line, compare **`5/3`** and **`7/4`**. Give each an equivalent twelfth name, mark the ticks counted from 0, then state which is larger and by what fraction of one unit.
3. **Check the whole:** Plan A uses `1/3` of a **24-tile** panel. Plan B uses `1/2` of a **12-tile** panel. Someone says “B must use more tiles because a half is bigger than a third.” Is that conclusion correct **for these two differently sized panels**? Calculate each number of tiles and repair the explanation. Do not use this example to claim that `1/3 > 1/2` when the wholes are equal.

These first responses show a next teaching step, not a permanent judgement. Original SubjectNest check texts © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).