# Year 7 mathematics: ten daily 25-minute lessons

Use the [teacher examples](MATERIALS.md) and the [rational benchmark strip](../print/rational-benchmarks.svg). Six numbered steps total **25 minutes per lesson**. Keep the written calculation, representation, context and checking method separate in the [assessment record](ASSESSMENT.md). Everyone attempts each brief exit; note a rotating 2–3 focus learners, then use later quiet checks if independent reasoning was obscured. Calculator use is for a **post-solution check** when noted, not a substitute for modelling. Codes mark partial Year 7 ACARA v9 work.

## Day 1 — Three names for the same amount

**Codes:** `AC9M7N04`. **Goal:** connect a familiar fraction, decimal and percentage as equivalent rational quantities. **Prepare:** 100-square sketch or folded strip, `1/2`, `0.5`, `50%` cards.

1. **Launch · 3 min.** Say: “A battery icon at half, a race at 0.5 of its route, and 50% of a playlist may point to the same share. What does ‘same’ mean here?” These are invented contexts; compare the proportion, not units.
2. **Model · 4 min.** Shade 50 of 100 equal cells. Say: “50/100 simplifies to 1/2; 50 hundredths is 0.50 or 0.5; per hundred is 50%.” Put all three labels at the halfway mark on 0–1.
3. **Guide · 6 min.** Shade 25/100, rename `1/4 = 0.25 = 25%`; then 75/100, rename `3/4 = 0.75 = 75%`. Ask why 0.25 and 25% are related but not written with the same symbol.
4. **Choose and justify · 7 min.** Pairs match nine shuffled cards for the three quantities. One explains using equal parts or hundredths; the other checks with the strip, then they swap. For a challenge, locate 10%=0.1=1/10.
5. **Use a domain · 3 min.** “A fictional phone download is at 75%. Is it three quarters complete?” Yes, under the usual 0–100% indicator. Ask what the whole is (the download).
6. **Exit · 2 min.** Everyone gives two other forms of `1/4`. Listen to focus learners' explanation of the whole. If a child says 0.4, return to 25 of 100 cells.

**Access:** tactile 4-part strip, readable high-contrast labels, spoken or AAC matching; offer the same representations in text for screen readers.

## Day 2 — A number line is a test of order

**Codes:** `AC9M7N04`. **Goal:** order rational values by common representation and position. **Prepare:** 0–1 strip, `3/8`, `0.4`, `1/2` cards.

1. **Start · 2 min.** Ask: “Is 3/8 before or after 0.4 on a 0–1 line? A guess is fine; we will check.”
2. **Model · 5 min.** Divide a strip into eighths. `3/8 = 0.375` by 3 ÷ 8 or 375/1000. Mark it just left of 0.4. Explain that each tick represents equal numerical distance, not equal printed space between arbitrary labels.
3. **Guide comparison · 6 min.** Convert `1/2 = 0.5`; order `0.375 < 0.4 < 0.5`. Use 0.4 = 2/5 as a second representation. Check that 0.4 is 4 tenths, not 4 hundredths.
4. **Pairs place and defend · 7 min.** Add `1/4`, `3/4` and `0.62`. Pairs place cards approximately on the labelled strip and defend two neighbour relationships numerically. They may use a conversion or benchmark argument; line position without reason is incomplete.
5. **Error talk · 3 min.** Show a fictional placement of 0.62 to the left of 0.5. Ask: “Which benchmark tells us that cannot be right?” 0.62 is greater than 0.50.
6. **Exit · 2 min.** Everyone orders `0.25`, `3/8`, `0.5` → `0.25 < 0.375 < 0.5`. Sample focus reasoning; revisit thousandths if 0.375 is misread.

**Access:** large desk/floor line, tactile marked endpoints and quarters, worded comparison read aloud, AAC `before/after` choices. Record which conversion support was supplied.

## Day 3 — Convert for a reason, not by a trick

**Codes:** `AC9M7N04`. **Goal:** explain `3/5 = 0.6 = 60%` using equal parts. **Prepare:** 10-column strip or 100-grid.

1. **Question · 3 min.** Say: “A game save meter shows three of five equal segments. What percentage is full?” Ask what one segment represents.
2. **Model · 4 min.** Multiply numerator and denominator by 20: `3/5 = 60/100`; then `60/100 = 0.60 = 60%`. Show six of ten columns shaded, so the representation can be checked visually.
3. **Guided practice · 6 min.** Convert `7/10` to 0.7 and 70%. Convert `1/8` to 0.125 and 12.5% using 125 thousandths or a calculation, then ask whether 1/8 is smaller than 1/4. Note that not every fraction has a terminating decimal.
4. **Meaningful choice · 7 min.** Pairs choose a fuel gauge, art-project progress or sports possession **fictional example** and write three matching representations for either 3/5 or 7/10. Partner identifies the whole and explains a check. Extension: 2/3 is about 66.7%, not exactly 67%.
5. **Find a false match · 3 min.** Display `3/5 = 0.35 = 35%`. Ask students to show why 3 of 5 is more than one half, while 35% is less than one half. Repair the label.
6. **Exit · 2 min.** Everyone completes `7/10 = ___ = ___%` → 0.7, 70%. Focus learners justify via tenths/hundredths.

**Access:** manipulable ten strips, screen-reader text `three fifths`, quiet calculation route. Do not demand a particular digital tool for conversion.

## Day 4 — Rounding means naming the accuracy

**Codes:** `AC9M7N05`. **Goal:** round decimals to a stated place and explain whether a context supports that precision. **Prepare:** place-value line and examples.

1. **Open · 2 min.** Show `3.468 m`. Ask: “If the measuring tape is reported to hundredths of a metre, what should we write?”
2. **Model · 5 min.** Mark hundredths in 3.468; the thousandths digit 8 rounds 6 hundredths up to 7. Write **3.47 m**. Say the unrounded measurement would require an instrument that genuinely supports thousandths; our number is a practice example, not a measurement we took.
3. **Guided changes · 6 min.** Round `18.374` to one decimal → **18.4**. Round `0.946` to two decimals → **0.95**. Ask which place is kept and which next digit decides.
4. **Context decisions · 7 min.** Pairs get invented values: a relay time 14.387 s reported to hundredths → **14.39 s**, and a jar mass 2.136 kg to tenths → **2.1 kg**. Discuss why showing three decimal places from a rough estimate would imply false precision.
5. **Estimate check · 3 min.** Ask whether 3.468 is closer to 3.46 or 3.47. It is 0.008 from 3.46 and 0.002 from 3.47, so the rounded result is sensible. Mark both hundredths on a line.
6. **Exit · 2 min.** Everyone rounds `12.684` to one decimal → **12.7** and names the hundredths digit 8 as the reason. Focus learners must state the requested place.

**Access:** enlarged place labels, tactile digit cards, spoken value plus accessible text. A learner may type the explanation; handwriting is not the rounding evidence.

## Day 5 — Equivalent forms and sensible precision

**Codes:** `AC9M7N04`, `AC9M7N05`. **Goal:** sample Week 1 knowledge and choose next teaching. **Prepare:** [Check A](ASSESSMENT.md), benchmark strip, quiet station.

1. **Purpose · 2 min.** Say: “Show how you know, then check if your answer makes sense on a 0–1 line.”
2. **Warm-up · 5 min.** Together rename `1/2`, `0.5`, `50%` and round `4.238` to a tenth (4.2). This is rehearsal, not scored evidence.
3. **Equivalence task · 6 min.** Everyone writes `2/5 = 0.4 = 40%` and places it relative to 0.25 and 0.5. Observe planned focus learners privately while others check a partner's reason.
4. **Precision task · 7 min.** Round `12.684` to tenths (12.7), then choose larger of `0.65` and `3/4` (0.75). Require a numeric reason; a correct guess alone leaves the strategy unobserved.
5. **Feedback · 3 min.** Name the precise work: “You made 2/5 into 4/10. Now let's connect four tenths to forty percent.” Let the learner repair one step, recording the prompt.
6. **Close · 2 min.** Child names one helpful representation. Teacher selects the next model from [the key](ASSESSMENT.md), marking individual evidence `independent / prompted / not yet observed`.

**Access:** verbal or tactile line, AAC/written equivalence, separate quiet interview later if the partner's answer concealed independence.

## Day 6 — Fraction operations keep the whole in view

**Codes:** `AC9M7N06`. **Goal:** add/subtract positive fractions using equivalent denominators and check magnitude. **Prepare:** eighth strips and fraction cards.

1. **Launch · 2 min.** Ask: “If half a page and a quarter page are filled, should the answer be less or more than one half?”
2. **Model · 5 min.** Turn `1/2` into `2/4`, then `2/4 + 1/4 = 3/4`. Mark both shares on the same whole strip. Explain why adding denominators to get 2/6 would change unit size and be wrong.
3. **Guided subtraction · 6 min.** Change `3/4` to `6/8`; `6/8 − 1/8 = 5/8`. Ask which whole is represented and whether 5/8 is between 1/2 and 3/4.
4. **Partner choices · 7 min.** Choose `2/3 + 1/6 = 5/6` or `5/6 − 1/3 = 1/2`. One partner builds equivalent parts, another checks with the strip or inverse. Swap. Offer like-denominator practice before unlike cases if prerequisite knowledge is insecure.
5. **Domain link · 3 min.** “A fictional mural uses 1/2 of a board for sketches and 1/4 for titles. What fraction is used?” **3/4**, and **1/4** remains if the areas do not overlap.
6. **Exit · 2 min.** Everyone solves `3/4 − 1/8 = 5/8` with one clear conversion. Focus learners explain denominator choice.

**Access:** same-size physical fraction strips, raised partitions, written or spoken symbols; a partner may move pieces at the learner's direction.

## Day 7 — Decimal arithmetic in a money context

**Codes:** `AC9M7N06`, `AC9M7N05`. **Goal:** add and subtract decimals while respecting place value and checking an estimate. **Prepare:** fictional receipt card in [materials](MATERIALS.md).

1. **Estimate · 2 min.** “$12.75 and $8.60 should total around $13 + $9 = $22. What exact total?”
2. **Model · 5 min.** Align decimal points and cents: `12.75 + 8.60 = 21.35`. Say: “Five cents plus zero cents remains five; seven tenths plus six tenths makes thirteen tenths, so we exchange one unit.” Confirm total is close to $22.
3. **Guided balance · 6 min.** If a person had $25.00, subtract $21.35 → **$3.65**. Check `21.35 + 3.65 = 25.00`. Explain cents are hundredths of a dollar, not free-floating digits.
4. **Pair practice · 7 min.** Solve `$42.30 − $17.85 = $24.45` with a place-value sketch or written method, then verify by addition. A ready pair creates a different fictional receipt and checks it. A calculator may confirm after a shown method.
5. **Context check · 3 min.** Ask whether `$21.35` or `$213.50` makes sense for two items near $13 and $9. Use estimate as an error alarm, not a replacement for exact work.
6. **Exit · 2 min.** Everyone gives `$25.00 − $21.35 = $3.65` and one inverse check. Sample focus explanation.

**Access:** accessible monospaced decimal columns, tactile decimal marker, adult read-aloud of prices, AAC digits. Never require real spending or disclosure of family money.

## Day 8 — A percentage is a part of a named whole

**Codes:** `AC9M7N06`, `AC9M7N09`. **Goal:** calculate simple percentages of a quantity using efficient decomposition and interpret the unit. **Prepare:** 100-grid/benchmark strip.

1. **Question · 2 min.** “A fictional 80-minute playlist is 25% complete. How many minutes have played?” Ask what 100% represents.
2. **Model · 5 min.** `25% = 1/4`; one quarter of 80 is **20 minutes**. Show 4 equal bars of 20 and check 4 × 20 = 80.
3. **Guided second path · 6 min.** Find 15% of 60: 10% is 6, 5% is 3, total **9**. Say 15% means 15 per 100 of the whole, even though we calculate with useful parts.
4. **Choice practice · 7 min.** Pairs choose 20% of 45 (9) for a fictional poster space, or 12.5% of 48 (6) for a fictional game progress bar. They state the whole, unit, method and reasonableness check. The context does not alter the arithmetic.
5. **Spot a mismatch · 3 min.** Display `25% of 80 = 25`. Ask why copying the percent number ignores the whole. Rebuild one quarter.
6. **Exit · 2 min.** Everyone finds 30% of 50 → **15**, via 10% × 3 or 3/10. Focus learners explain the unit.

**Access:** tactile segmented bar, enlarged text, calculator after a model if individual plan allows; avoid speed-only judgement.

## Day 9 — A model for a constrained decision

**Codes:** `AC9M7N06`, `AC9M7N09`, `AC9M7N05`. **Goal:** formulate and check a practical rational-number calculation. **Prepare:** fictional $120 event brief; no real purchase or club funds.

1. **Read · 2 min.** “A fictional community event has $120 for two listed costs: $38.40 transport and $46.75 materials. How much remains?” Ask what quantities are known and unknown.
2. **Estimate · 5 min.** Approximate `$120 − $40 − $47 ≈ $33`; label estimate. Say exact remainder should be near this, not negative or above $120.
3. **Model · 6 min.** Add costs: `$38.40 + $46.75 = $85.15`; subtract `$120.00 − $85.15 = $34.85`. Check `$85.15 + $34.85 = $120.00`. State **$34.85 remains** and that a budget does not tell us whether the event is worthwhile.
4. **Partner alternative · 7 min.** Pairs use a different valid strategy, e.g. subtract transport first: `$120 − $38.40 = $81.60`; then `$81.60 − $46.75 = $34.85`. Ask which steps are easy to explain to a committee reader. A calculator can verify after the two methods are visible.
5. **Interpret · 3 min.** Ask: “Can we add another $40 item?” No, not within $34.85 remaining. Ask what else a real organiser would need to know; do not invent tax or prices.
6. **Exit · 2 min.** Everyone gives remainder with unit and one check. Focus learners explain why the rounded estimate differs from the exact answer.

**Access:** read-aloud brief, line-by-line text, screen-reader-friendly amounts, paper tokens if helpful. No student or family financial data.

## Day 10 — Show a representation, a calculation and a check

**Codes:** `AC9M7N04`, `AC9M7N05`, `AC9M7N06`, `AC9M7N09`. **Goal:** sample fortnight learning and set a specific next step. **Prepare:** [Check B](ASSESSMENT.md), number strip and private station.

1. **Set purpose · 2 min.** Say: “You may change your answer if your model shows a better one. Tell me what convinced you.”
2. **Review · 5 min.** Together match 1/2, 0.5 and 50%, then estimate `$20 + $35`. These are familiar rehearsal values, not check answers.
3. **Equivalent and precision prompts · 6 min.** All show `3/5 = 0.6 = 60%`, mark it on 0–1, and round `7.486` to hundredths → **7.49**. Focus learners explain why 0.6 is to the right of one half.
4. **New money problem · 7 min.** Read: “A fictional project has $100.00. It spends $26.80 and $35.75. What remains?” Learners model, estimate and solve **$37.45**; check with the costs. Keep their work before class correction. This is arithmetic in an invented context, not a decision about actual funds.
5. **Feedback · 3 min.** Use the actual error: “Your bar shows 3/5 correctly; let's connect six tenths to sixty hundredths.” Or “Your subtraction model is sound; let's align the cents.” Record prompt level.
6. **Close · 2 min.** Learner chooses a representation worth keeping. Teacher records separate equivalence, rounding, modelling and calculation evidence, with a next teaching move from the key.

**Feasible assessment:** one teacher cannot interview a whole class individually in 25 minutes. Use 3–4 minute quiet conversations on Days 8–10 and later where needed; mark unseen independent work as not yet observed.

**Rights:** Original lessons and fictional contexts © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit, link and indicate changes. ACARA codes retain [separate terms](https://www.australiancurriculum.edu.au/copyright-and-terms-of-use).