# Mathematics materials, source limits and teacher calculations

The [0–1 benchmark sheet](../print/rational-benchmarks.pdf) and [plain-text/tactile version](../print/TEXT-ALTERNATIVES.md#rational-benchmarks) show quarter positions with matching decimal and percentage names. Make an additional ten-part or hundred-square model when teaching tenths and percentages beyond the quarter benchmarks. Add folded strips for eighths/sixths as needed; make every whole the same length when comparing. A calculator can verify an already represented result on Days 7 or 9. Students can work on paper without a device. Keep an accessible large-format strip and a text version available.

**Original practice contexts (all fictional):**

- A download meter is 75% complete: `3/4 = 0.75 = 75%` of *that download*.
- A fictional relay time is 14.387 seconds; to hundredths it is 14.39 seconds. No real timing or instrument precision is implied.
- A fictional receipt has $12.75 and $8.60 items: total $21.35. From $25.00, the remaining amount is $3.65.
- A fictional community event has $120.00 available; transport $38.40 and materials $46.75 leave $34.85. These are not quotes, prices or recommended spending.
- A fictional project has $100.00; costs of $26.80 and $35.75 leave $37.45.

**Number conventions:** a percent is per hundred **of a named whole**. `0.5 = 50%`, whereas `0.05 = 5%`. `3/8 = 0.375` and `3/5 = 0.6`; use equivalent fractions or division and check placement. For fractions, match unit pieces before adding/subtracting. For decimal money, align whole dollars and cents. For rounding, state the requested place and check whether the rounded value is near the original; do not imply more precision than the stated context supports.

**Access and extension:** use the same mathematical target with a tactile bar, raised number line, large print, spoken equations, keyboard/AAC or scribed strategy. Record prompts. A student ready to extend can compare 2/3 with 0.67 and discuss approximate versus exact; a learner needing foundation can establish tenths and quarters with physical strips before an unseen mixed-format check. Neither route is a permanent group label.

**Rights:** Original examples/arrangement © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit, link and indicate changes.