# Year 6 maths · three genuine practice routes per day Pick **one** route a day in your chosen response mode. Each route asks for the same day's mathematical reason through a different invented context or representation. Drawing, speaking, typing, AAC and large/tactile pieces are access choices, not fixed learner categories. D15/D20 are **later practice after the fresh check**, never a preview of its numbers. ## Day 11 · Definitions and arrays - **A · tile rectangles:** Make every distinct row-by-column rectangle for 12, recording `1×12`, `2×6`, `3×4`; then show a square for 16 and explain why it is also composite. - **B · factor-card interview:** Sort 1, 2, 12 and 16 into prime/composite/square (overlap allowed). Ask a partner to challenge one label; answer with factors, not appearance. - **C · game-board note:** A fictional board maker asks if 16 cells must be 4-by-4. Show a different rectangle and state what this proves about “square” versus “composite”. ## Day 12 · Complete factor reasoning - **A · seating diagram:** A made-up theatre has 18 seats. List each distinct complete equal-row layout, then explain why no factor pair was skipped. - **B · archive trays:** Compare 20 and 21 blank archive labels. Give all positive factor pairs for each and choose a layout with more than one row and column. - **C · prime detective:** Explain why 23 has no factor 2, 3 or 4 and why factors 5 or larger cannot start a new pair. Conclude with the exact prime definition. ## Day 13 · Square overlap - **A · square mosaic:** Draw/speak `3×3`, `5×5`, `7×7` square totals and name one additional factor for each positive square beyond 1. - **B · classification table:** Sort 1, 9, 17, 36 and 49 into square, prime and composite columns, allowing an entry in two columns; justify each non-obvious label. - **C · claim repair:** Someone says “Every square number is prime because its sides match.” Write a counterexample with two factor pairs, then explain the special case 1. ## Day 14 · Solve with factors - **A · gallery rows:** For 28, 29 and 36 fictional display cards, find a layout with both dimensions >1 where possible; tell which can form a square and why. - **B · tabletop grid:** A fictional board needs 24 cells with six across. Find the number of rows and two other complete factor layouts. Explain which condition selected your answer. - **C · quick product:** Compute `12×15` by regrouping factors into `9×20`. Show why the product stays equal and identify a factor pair in 36. ## Day 15 · **Later practice, after fresh check** - **A · new factor cards:** Classify 14 and 19 with a factor pair or complete no-small-factor argument. Do not reuse check numbers. - **B · square display:** Show why 81 is square and composite, and why 1 is square but neither prime nor composite. - **C · layout request:** A fictional maker wants 26 paper cells in equal rows with both dimensions >1. Give one possible layout and explain why 26 is not square. ## Day 16 · Same whole, first positions - **A · twelfth line:** On a blank 0–1 line with 12 equal gaps, mark `1/4`, `1/3`, `1/2` and label their twelfth names and order. - **B · recipe-card shares:** Three fictional recipe cards allocate `1/4`, `1/3`, `1/2` of the **same 12 equal-duration steps** to setup. Which is least/most time? Justify by equal steps, not different recipes. - **C · music-cycle text:** A made-up 12-beat loop has a cue after a quarter, a third and a half of **one cycle**. Name the beat positions and explain the order without needing sound. ## Day 17 · Equivalence and comparison - **A · double-name marker:** Place `2/4`, `1/2`, `6/12` at one mark; add `2/3` and `3/4`. Compare the last two with a one-twelfth gap. - **B · archive-space bars:** A fictional archive allocates `2/3` and `3/4` of identical shelf strips to two displays. Who has the greater share of **one equal strip**, and by how much? Show a 12-part model. - **C · game-state explanation:** A learner claims `2/3` is larger than `3/4` because “2 is close to 3.” Respond using equivalent fractions and one same-whole line. ## Day 18 · Beyond one - **A · extended line:** Use 0–2 with 24 equal gaps; place `5/4`, `3/2`, `6/4` and name the coincident positions. - **B · two-cycle plan:** A fictional 12-step sequence runs twice. Place cues at `5/4` and `3/2` cycles, giving step numbers from 0 and the gap between cues. - **C · art-strip proof:** Join two identical unit paper strips. Shade `5/4` on one pair and `3/2` on another equal pair. Compare their lengths, recording a common-denominator difference. ## Day 19 · Justified order - **A · exhibit caption:** Write a caption ordering `1/4`, `1/2`, `2/3` on one 0–1 line. Give twelfth names so a visitor could verify the order. - **B · error-repair dialogue:** Answer “`1/3 > 1/2` because 3 > 2” with equal-part bars, then explain when a larger denominator makes a **unit** fraction smaller. - **C · tactile sequence:** Arrange cards `2/4`, `1/2`, `3/4` over one 12-notch tactile whole. State which two coincide and which is to their right; justify by gaps. ## Day 20 · **Later practice, after fresh check** - **A · fresh ordinary line:** Compare `4/3` and `3/2` on the same 0–2 line using twelfths. Give order and gap. - **B · design shares:** In a fictional 12-panel mural, compare `1/3` and `3/4` of the same whole; show panels and justify the larger share. - **C · learner-made challenge:** Invent two fractions made from halves, thirds or quarters that lie between 0 and 2, place both on one scaled line, and provide a checked reason. Avoid reusing the held-out check pair. Original SubjectNest practice routes © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).