Maths · three genuine… | Year 6 Maths · T1 W3–4 · Daily Choices

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.