Question: How should 24 trial cards be laid out so each is checked? Kit: 24 paper squares/counters, array mat. 35 = 3 + 7 + 12 + 8 + 5.
- 0–3: State the design need: label every prototype, keep the whole count visible and make checking orderly. This is planning, not evidence that one layout is scientifically fair.
- 3–10: Model
24 = 4 × 6 = 3 × 8 = 2 × 12: all make equal rectangular rows. Compare23, which is prime, and25 = 5 × 5, a square number. Twenty-four is composite, not square. - 10–22: Children arrange 24 tokens in two different arrays, record factor pairs and explain which arrangement leaves room for a label beside each. The choice of row count must be justified by a criterion, not presented as mathematically “best”.
- 22–30: Give a hypothetical 24-prototype retest: two fold designs, 12 each. Can
4 × 6place equal numbers of each in two labelled halves? Yes, 12/12. Discuss why equal quantity alone does not hold surface, paper size or check time constant. Routes: move large paper squares; write factors with a calculator/check grid; direct an adult or peer to form a tactile 4-by-6 array and explain it by speech/sign/AAC. - 30–35: “Is 25 prime because its factor pair is 5 by 5?” Key: no; 25 is composite and square. Response move: show 1×25 and 5×5; if 24 called square, ask for equal row and column length.
Another domain: Use fictional seed-label cards, event menu cards or exhibition captions as the 24 objects. Home: draw arrays for 24 on scrap paper; no physical kit needed.