Two optional cases per day, chosen after the core task. Days 5 and 10 swaps come after first check collection. All data and places are invented. Use the same reasoning target, show labelled order and units, check the result, and state what the model does not tell us. A drawing, movable objects, calculator or spoken/AAC explanation can all show the mathematics. Staff results are public.
Day 1 · name both parts
- Poster shelf: 5 triangle symbols and 3 circle symbols. Give triangle:circle, circle:triangle and each part's fraction of all symbols.
- Music cue mat: 7 beat cards and 2 rest cards. Give beat:rest and total cards, with labels.
Day 2 · order changes meaning
- Garden marker tray: 2 tall markers and 5 short markers. Give tall:short and short:tall; explain why they are not interchangeable.
- Exhibit lights: 3 square cards and 8 round cards. Give square:round and round:square with the words in order.
Day 3 · part to part versus part to all
- Map icons: 2 bridge icons and 3 path icons. Find bridge:path and bridge:all, in ratio and fraction form respectively.
- Stage marks: 4 star marks and 1 line mark. Find star:line and star fraction of all marks.
Day 4 · simplify without removing objects
- Badge box: 6 plain cards and 9 striped cards. Simplify plain:striped and check by multiplication.
- Tool tags: 14 paper tags and 21 plastic tags. Simplify paper:plastic and explain which common factor you used.
Day 5 · after-check only
- Fictional archive: 12 blue labels and 16 white labels. Simplify blue:white and find blue fraction of all.
- Gallery icons: 5 arrow icons and 15 dot icons. Simplify arrow:dot and find arrow fraction of all.
Day 6 · match units first
- Mural ribbon: compare 120 cm with 80 cm. Give the simplest first:second length ratio.
- Model path: compare 2 m with 50 cm. Convert to the same unit and simplify first:second.
Day 7 · split a total by parts
- Fictional kit cards: split 40 identical cards in ratio 3:5 between two labelled envelopes. Find each count and check.
- Stage tokens: split 36 identical tokens in ratio 1:2 between two trays. Find each count and check.
Day 8 · a drawing scale
- Sketch strip: 1 cm drawing represents 300 cm model distance. What model distance in metres does 2 cm represent?
- Small diagram: 1 cm drawing represents 50 cm model distance. What model distance in metres does 6 cm represent?
Day 9 · check a claim
- Fictional tag audit: 50 tags are split 2:3. Someone claims 25 belong to each type. Correct the counts and explain the error.
- Reverse plan: with 1 cm drawing representing 200 cm model distance, what drawing length corresponds to 12 m model distance? Check.
Day 10 · after-check only
- Paper label split: split 42 labels in ratio 2:5; find both counts and check.
- Invented plan: 1 cm represents 400 cm model distance; what model distance in metres does 3 cm represent?