# Year 10 mathematics: ten scripted 25-minute sessions

Teach with learner-facing [data cards](STUDENT-DATA.md), [dated check cards](STUDENT-CHECKS.md), the teacher [notes and answers](MATERIALS.md), [key](ASSESSMENT.md), [scatterplot frame](../print/scatterplot-frame.svg) and [cost board](../print/cost-comparison.svg). Keep the teacher master and fresh Day 10 item out of learner copies until the check. The contexts are fictional. Six numbered phases in each lesson total **25 minutes**. A code means **partial work** on that Year 10 Australian Curriculum v9 description. Everyone attempts a brief exit; the teacher observes a rotating 2–3 focus learners and schedules later private checks where independence remains unclear. Give accessible coordinates/text whenever a visual graph is used.

## Day 1 — What a pair of numbers can show

**Codes:** `AC9M10ST03`. **Goal:** identify paired variables, units and a plausible association without claiming cause. **Prepare:** Table B and blank scatterplot frame.

1. **Launch · 2 min.** Say: “These six routes are invented. If a route is longer, is its listed travel time usually longer?” Ask which two quantities form each pair.
2. **Model · 5 min.** Plot `(2,7)` and `(4,13)` with distance in km on the horizontal axis and duration in minutes vertically. Name the ordered-pair convention and units. Make the axes start at zero on this frame.
3. **Guide · 6 min.** Pairs plot `(6,18)` and `(8,26)` then read back the coordinates. Ask why exchanging axes would change the question but not the source pairs.
4. **Complete and interpret · 7 min.** Students add `(10,31)` and `(12,35)`, then describe **positive, roughly linear** association in this invented set. A learner may describe the ordered pairs in text instead of drawing.
5. **Check a leap · 3 min.** Ask: “Can this plot guarantee a real 12 km trip takes 35 minutes?” No: the values are fictional and stops/traffic are unspecified. Discuss what the graph can and cannot support.
6. **Exit · 2 min.** Everyone labels the variables and writes “as distance increases, listed duration generally increases” with the fictional scope. Sample focus explanations.

**Access:** raised or large-grid axes, coordinate list, partner operated marking or screen-reader table. The construct is association, not eyesight or pen control.

## Day 2 — Plot the repeated cart trials

**Codes:** `AC9M10ST03`. **Goal:** construct and read a scatterplot with repeats. **Prepare:** learner [Table A](STUDENT-DATA.md), frame; note that accelerations are simulated.

1. **Set scale · 2 min.** Ask: “What must the axes include?” Force 0–4 N horizontally; acceleration 0–10 m/s² vertically, matching the printable frame.
2. **Model · 5 min.** Plot trials 1 and 2 at `x=1` with `y=1.8` and `2.1`. Say two trials may share an x-value without being the same point.
3. **Guide · 6 min.** Students plot forces 2 and 3 with a partner; partner checks each value against the table, including decimals.
4. **Complete · 7 min.** Independently add forces 4, label units and circle one pair of repeated force trials. If using digital plotting, compare with a hand or text version and keep all data local.
5. **Read · 3 min.** Ask: “At 4 N, what two simulated accelerations are listed?” **7.8 and 8.1 m/s²**. Do not read 8.1 as speed.
6. **Exit · 2 min.** Everyone states coordinates for trial 5: `(3 N, 5.9 m/s²)` and names which axis carries force.

**Access:** tactile dots, high-contrast marked axes, typed coordinate table, partner at learner direction. Record whether plotting or reading required a prompt.

## Day 3 — Describe a pattern precisely

**Codes:** `AC9M10ST03`. **Goal:** discuss direction, strength and linearity in context. **Prepare:** completed Table A plot and a four-column vocabulary strip.

1. **Notice · 2 min.** Ask for a first description, then say: “We will make it specific enough that another reader could test it.”
2. **Model · 5 min.** As net force rises from 1 to 4 N, simulated acceleration rises; points cluster near a straight upward path. Call it **strong positive and approximately linear in this constructed set**. Do not say “perfect”.
3. **Guide averages · 6 min.** At 1 N calculate `(1.8+2.1)/2=1.95`; at 2 N `(3.8+4.2)/2=4.0`. Compare with ideal `a=F/0.5`, which gives 2 and 4. Distinguish simulated readings from theoretical values.
4. **Choose and justify · 7 min.** Students either compute averages at 3 and 4 N (**6.05**, **7.95**) or explain in words how repeats vary. Then make one accurate association sentence with both units and scope.
5. **Counterclaim · 3 min.** Show “The finish on the wheels caused the trend.” Ask what is missing. No finish comparison is in Table A; association with net force does not test that claim.
6. **Exit · 2 min.** Everyone states direction, approximate form and one limitation. Teacher samples focus learners' independent wording.

**Access:** four vocabulary cards, text readout of pairs, calculator only after a shown average method if an access plan calls for it.

## Day 4 — A headline can select the wrong comparison

**Codes:** `AC9M10ST01`, `AC9M10ST03`. **Goal:** audit a numerical claim against the original dataset and identify a biased selection. **Prepare:** fictional [media post](../english/STUDENT-READING.md) and learner Table A.

1. **Read · 2 min.** Display the source's actual “Silver finish makes cart four times faster!” and ask what comparison the headline invites.
2. **Model · 5 min.** Locate **8.1** from a 4 N trial and **1.8** from a 1 N trial. Their ratio is 4.5, not exactly four; force also changed. The readings are acceleration, not speed. Say that unmatched conditions and the absent finish variable cannot isolate a wheel-finish effect.
3. **Guide · 6 min.** Pairs list what would need to be comparable to test finish: mass, net force, track/method and repeat procedure. The supplied table has **no finish variable**.
4. **Repair · 7 min.** Students write a scoped alternative caption: “In eight fictional simulated trials of a 0.50 kg cart, acceleration increased as net force increased.” Add “approximately” if describing a linear trend. No finish conclusion.
5. **Ethics · 3 min.** Ask why choosing only high/low values could matter if readers used it to decide on equipment. Require exact source and uncertainty, not a shaming judgement of the fictional writer.
6. **Exit · 2 min.** Everyone names one numerical fact and one unsupported inference in the headline.

**Access:** read both headline and table aloud, allow highlighting or text notes, AAC claim/evidence/limit cards.

## Day 5 — Check A: scatterplot and claim

**Codes:** `AC9M10ST01`, `AC9M10ST03`. **Goal:** sample independent representation and critique. **Prepare:** learner [Check A](STUDENT-CHECKS.md), teacher [key](ASSESSMENT.md); Table B values on a clean sheet.

1. **Orient · 2 min.** Say: “A valid conclusion names the data it comes from and what remains unknown.”
2. **Rehearse · 5 min.** Together place one **different** example pair `(3,9)` on a fresh axis and recall units. This pair is practice only, not part of either dataset.
3. **Independent plot · 6 min.** Learners plot four supplied Table B pairs `(2,7),(4,13),(8,26),(12,35)` or provide a precise text-coordinate description.
4. **Independent reading · 7 min.** They describe direction/form and repair “Every real 12 km trip takes exactly 35 minutes.” Teacher collects before feedback.
5. **Feedback · 3 min.** Respond to actual work: “Your coordinates are sound; add the minutes unit,” or “Your claim reaches beyond the fictional set; name its scope.” Do not turn the check into a class ranking.
6. **Close · 2 min.** Everyone records one graph choice that helped; teacher schedules an unseen transfer item for an uncertain learner.

**Access:** exact adult reading of the prompt, large/tactile axes or text list, quiet response. Note any cue supplied.

## Day 6 — Turn a plan into an equation

**Codes:** `AC9M10A04`. **Goal:** formulate two linear cost models and say what their terms mean. **Prepare:** fictional [device-hire brief](MATERIALS.md) and cost board.

1. **Context · 2 min.** “This is an invented adult household choice. We compare simplified totals; no one will disclose personal finances or make a purchase.”
2. **Model · 5 min.** Let `m` be complete months. `A(m)=240+80m`: $240 setup at m=0, then $80 per month. Write the parallel `B(m)=480+50m` with units.
3. **Guide values · 6 min.** Calculate at m=4: A **$560**, B **$680**. Ask why multiplying setup by four would be wrong.
4. **Represent · 7 min.** Learners fill a small table for m=0,4,8,10. Use the cost board or text table. Check A/B at 8 both $880 but with different cost structures.
5. **Assumptions · 3 min.** Name one omitted real condition: actual contract, device quality, repair outcome or exit terms. Fixed monthly increase makes these **linear** within the model; real total cost might not be.
6. **Exit · 2 min.** Everyone explains the 50 and 480 in `B(m)` and gives B(4) = $680.

**Access:** money counters, large text, typed formula, speech/AAC explanation. Do not require a home-budget story from the learner.

## Day 7 — Solve and read the crossing point

**Codes:** `AC9M10A02`, `AC9M10A04`. **Goal:** solve a pair of linear equations and interpret the graphical intersection. **Prepare:** cost models and axes 0–12 months, $0–$1,300.

1. **Predict · 2 min.** “Plan A starts cheaper but rises faster. Could the totals meet?” Ask for a reasoned guess.
2. **Model algebra · 5 min.** Set `240+80m=480+50m`. Subtract `50m` and $240: `30m=240`, so **m=8**. Substitute: both **$880**.
3. **Graph check · 6 min.** Plot each plan at m=0 and m=8; straight lines meet at `(8 months, $880)`. Discuss that the intersection means equal modelled cost, not equal service quality.
4. **Independent comparison · 7 min.** Compare m=6: A $720, B $780, so A cheaper by $60. Compare m=10: A $1,040, B $980, so B cheaper by $60. Ask why ordering reverses.
5. **Error check · 3 min.** Show `30m=240 → m=30/240`. Repair the inverse operation and substitute to test 8.
6. **Exit · 2 min.** Everyone states the crossing coordinate **with both units** and one model limit.

**Access:** tactile crossing lines or paired value table; demonstrate equality by substitution without demanding visual graph reading.

## Day 8 — A budget makes an inequality

**Codes:** `AC9M10A02`, `AC9M10A04`. **Goal:** solve and interpret linear inequalities for whole-month commitments. **Prepare:** $1,000 practice cap, cost models.

1. **Ask · 2 min.** “If the fictional cap is $1,000, does a solution of 9.5 months mean 9.5 payments are possible?” No: the model uses complete months.
2. **Model A · 5 min.** `240+80m ≤ 1000` → `80m ≤ 760` → `m ≤ 9.5`; with whole months 0–12, **maximum 9**. Check A(9)=$960 and A(10)=$1,040.
3. **Guide B · 6 min.** `480+50m ≤ 1000` → `50m ≤ 520` → `m ≤ 10.4`; maximum **10**. Check B(10)=$980 and B(11)=$1,030.
4. **Apply · 7 min.** A fictional planner needs 10 complete months. Students decide which plan fits the *stated cap*: B only, within this model. They must say what the calculation does not judge.
5. **Challenge · 3 min.** Ask whether A at m=9 and B at m=10 is a fair price-only comparison for the same service duration. No; compare the same horizon.
6. **Exit · 2 min.** Everyone writes A's maximum whole months and the pair of values that check the boundary.

**Access:** number-line inequality and table route; calculator as check after symbolic steps; oral explanation of whole-month boundary accepted.

## Day 9 — Change a model when a condition changes

**Codes:** `AC9M10A04`, `AC9M10A02`. **Goal:** evaluate a model's assumptions and test a change without silently moving the goalposts. **Prepare:** cost board, brief.

1. **Set problem · 2 min.** “Suppose the household now needs only four months. Is B still the price-only choice?”
2. **Recall · 5 min.** Calculate A(4)=$560 and B(4)=$680. Explain why A is cheaper for four months while B is cheaper at ten.
3. **Model review · 6 min.** The two formulas increase by fixed amounts each month, so a **linear** model fits the invented price rules. A percentage fee each month would require a different growth model; none is stated here.
4. **Modify · 7 min.** Give an invented variation: B's setup is reduced by $60 to $420 while monthly cost stays $50. Write `B_new(m)=420+50m`; solve equality with A: `240+80m=420+50m` → `m=6`, total $720. Compare with original crossing at 8.
5. **Evaluate · 3 min.** Ask whether the reduced setup proves B has better value. No: the exercise omits service and rights; price is only one criterion.
6. **Exit · 2 min.** Everyone states one changed assumption, new crossing and one real-world question to verify.

**Access:** value table before algebra, paired line model, typed or dictated reasoning. Mark which representation revealed the change.

## Day 10 — Check B: independent model and audit

**Codes:** `AC9M10A02`, `AC9M10A04`, `AC9M10ST01`. **Goal:** independently formulate, solve and qualify a new fictional comparison. **Prepare:** learner [Check B](STUDENT-CHECKS.md) and teacher [key](ASSESSMENT.md); give the new X/Y data only on Day 10.

1. **Orient · 2 min.** “Use a model and substitution check. A correct number without a sensible interpretation is unfinished.”
2. **Read · 5 min.** Supply X $180 setup+$90/month and Y $420 setup+$60/month, whole months 0–12; $1,000 cap at ten months. Adult may read the exact prompt without explaining strategy.
3. **Solve · 6 min.** Students write both equations and find the crossing. Teacher does not announce the answer.
4. **Apply · 7 min.** Students calculate both at ten months, decide whether either fits $1,000, and name one missing condition before a real decision. Collect work before class correction.
5. **Self-check · 3 min.** Learners substitute the crossing into both models and label units; they may repair an error, showing the revision.
6. **Close · 2 min.** Everyone submits a written, tactile, spoken/AAC or typed solution. Teacher uses the keyed next moves and marks independent/prompted/not yet observed.

**Access:** accessible text brief, large table, quiet space, tool use documented. Later individual recheck if a scaffold hid algebraic reasoning.

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