# Year 7 maths · three daily practice routes

Pick **one** A/B/C route for the day. Modes are choices for access and agency, not fixed “learning styles”. The D15/D20 routes are **later practice**, after a first fresh-check response. All contexts are invented and need no purchase or personal information.

## Day 11 · Fraction operations

- **A · mosaic strip:** On one same-size strip, show `1/2+3/8=7/8`; explain why the denominator stays eighths after renaming.
- **B · timing card:** A fictional 1-hour animation uses `5/6` of the hour; `1/3` is removed from that planned time. Find the remainder as a fraction of the same hour, with an equivalent-name step.
- **C · wrong-rule reply:** A peer writes `1/2+3/8=4/10`. Repair the unit error with eighths, then give a numerical check that your result is below one.

## Day 12 · Decimal places

- **A · design lengths:** Add 4.75 m and2.60 m, then find the remainder from10.00 m, with a rounded estimate and inverse.
- **B · storage readout:** Fictional file segments use3.45 GB and1.80 GB of an 8.00 GB allowance. Find used and remaining; check by adding back.
- **C · path error audit:** A fictitious map notes 6.35 km then2.70 km. Critique the claimed total8.105 km; give the correct total and place-value reason.

## Day 13 · Fraction of a fraction

- **A · rectangle overlay:** Show `3/4×2/3=1/2` in a 3-by-4 grid; name six of twelve overlapping cells.
- **B · signal window:** A made-up 20-minute signal period is active for `3/4`; `2/5` of the active part uses one pattern. Find the part of the whole period (`3/10`) and minutes (`6`), with an area or equivalent-fraction reason.
- **C · counterexample card:** Someone claims `2/5×3/4=6/9`. Show the correct `3/10` with a 5-by-4 array and explain which denominator was changed wrongly.

## Day 14 · Grouping and percentage

- **A · equal markers:** A fictional 2.4-unit track has 0.6-unit intervals. Count intervals, not markers; verify by multiplication.
- **B · quarter-unit strips:** Divide1.5 units into pieces of0.25 unit. Give the piece count and an inverse equation.
- **C · panels:** On a fictional48-panel display, find12.5% by using one eighth; explain why the answer is a number of panels, not 12.5 panels.

## Day 15 · **Later practice, after fresh check**

- **A · new fraction pair:** Solve `3/5+1/10` with tenths and a below-one check.
- **B · new decimal group:** Find `4.8÷0.8` and verify by multiplication.
- **C · new percent whole:** Find20% of70 equal game tokens, naming70 as the whole.

## Day 16 · Prime leaves

- **A · two trees:** Start60 as6×10 and3×20; show both end at `2²×3×5` and multiply back.
- **B · tile packs:** Factor84 into prime packs using4×21, then write the product in exponent notation.
- **C · stop-rule critique:** A proposed “prime factorisation” of60 is `4×3×5`. Explain which factor is not prime and finish it correctly.

## Day 17 · Exponent meaning

- **A · compare trees:** Break72 as8×9 and12×6. Give identical prime-leaf counts and exponent notation.
- **B · spoken/card product:** Build `2³×3²` with three 2 cards and two 3 cards, then evaluate. Explain why `2³≠2×3`.
- **C · alternate number:** Factor54 into primes and exponent notation, then check by multiplication.

## Day 18 · Shared factors

- **A · original collections:** Factor90 and150, circle one shared2,3,5 in each, and show `90/150=3/5`.
- **B · leaf-card explanation:** Explain why two copies of a prime cannot be cancelled if one product contains only one. Use the 90/150 leaves and give the correct simplest fraction.
- **C · false simplification:** A peer divides90 by10 but150 by30 to claim `90/150=9/5`. Explain why both parts must use the **same** divisor, then divide both by30 and check the result.

## Day 19 · Squares and roots

- **A · square grid:** Explain 12×12=144 and why `√144=12`; factorise12 and square its prime product to check144.
- **B · second square:** Show `100=2²×5²=10²`, then state `√100` with a multiplication check.
- **C · false-root reply:** A peer says `√81=3` because `81=3⁴`. Repair the claim using `9²=81` and explain what `√` asks.

## Day 20 · **Later practice, after fresh check**

- **A · new factorisation:** Factor120 into primes and exponent notation, then multiply back.
- **B · new square:** Show169 is a perfect square and give its positive root with a product check.
- **C · exponent editor:** Correct `2³×5²=150`; evaluate the left side and either repair the value or write a true prime product for150.

Original SubjectNest routes © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).