Maths · fresh learner checks, Days 15 and 20Year 6 Maths · T1 W3–4 · Learner checks

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 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.