Queensland General Mathematics… | Year 11 Maths · T1 W3–4 · Lessons

This continues the opening mathematics fortnight: rates, percentage changes, unit price and a small planning budget. Days 11–20 extend consumer arithmetic into salary-period conversion, piecework and commission, a category-aware budget, fully taxable GST exercises, simple interest and a repeated computation table. The exact current QCAA source is General Mathematics 2025 v1.3, Unit 1 Money, measurement, algebra and linear equations, Topic 1 Consumer arithmetic, PDF p. 17 / printed p. 15; see source/coverage crosswalk. GM-U1-T1 is only SubjectNest shorthand, not an official QCAA code. Ten 25-minute periods are 4 hours 10 minutes, so this continuation cannot complete the syllabus's 14-hour Topic 1 or 55-hour Unit 1. Schools decide sequencing and formal Unit 1–2 assessment. These public checks are teaching observations, not QCAA instruments.

Prepare: Cards A–G, five A4/text/tactile aids, calculator or paper arithmetic, optional local what-if spreadsheet. All financial inputs are invented; nobody shares personal money or labour data. Ask learners to show given / operation / units / reasonableness check / limitation. A route changes representation, not the expected mathematical reasoning or a learner identity. Record a substantive hint separately from reading, AAC or motor access. On an ordinary day the clock is 2 launch + 5 explicit model + 6 guided practice + 7 independent choice + 5 exit/response = 25 minutes. Check days use 2 + 3 + 12 + 5 + 3 = 25.

Day 11 · One annual amount, three period averages

Goal: convert Card A's gross annual model amount to correctly labelled weekly, fortnightly and monthly averages. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Display $65,520 per year; ask why $65,520 ÷ 12 and ÷52 answer different questions. Read “gross” and “model” aloud.
2–7: Model $65,520 ÷ 52 = $1,260 per model week; multiply by two for $2,520 per fortnight. Check $1,260×52=$65,520. Do not call this net take-home pay.
7–13: Learners find monthly $65,520÷12=$5,460, verify 5,460×12, and contrast average month with unequal real calendar month lengths.
13–20: Routes: move annual→52/26/12 period cards and write equations; complete the period table in large print; type or dictate three expressions with units and a reverse-multiplication check. All routes name gross-versus-net uncertainty.
20–25: Exit “Which divisor gives a fortnightly model average?” Key: 26, yielding $2,520. Move: if a learner multiplies by 26, use 26 periods × amount/period = annual amount to restore direction.

Alternative domain: A fictional theatre production salary, not a real contract. Optional/home: convert an invented $52,000 annual model; no personal payslip.

Day 12 · Paid time versus accepted pieces

Goal: compute two stipulated gross payment models without treating one as a real legal choice. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Read Card B's units: dollars per paid hour and dollars per accepted prop. Ask which count belongs to each rate.
2–7: Model hourly 5×$32=$160; piecework 20×$9=$180. Check 20×10≈200, so $180 is plausible. The $20 difference is for these stated counts only.
7–13: Learners compute 15 accepted props = $135 and compare with $160; discuss why fewer accepted props changes only the piecework side in this exercise.
13–20: Routes: pair hour and prop count tiles with their rates; annotate a two-column payment board; write/speak two unit-cancelling multiplication chains. Every route gives both totals, comparison and one unknown work condition.
20–25: Exit “Does $180 prove piecework is a better real job?” Key: no; hours, conditions, safety, legal pay entitlements and deductions are absent. Move: if a learner compares $32 with $9 alone, restore the required counts and units.

Alternative domain: Invented maker-fair badge assembly. Optional/home: compare 3 paid hours at a made-up $30/h with 12 accepted pieces at $8 each; no work undertaken.

Day 13 · Whole-number threshold in piecework

Goal: find and justify the first whole item count that exceeds a fixed stated total. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Retrieve Card B's $160 hourly total and $9 per accepted prop. Ask “How many accepted props first give more than $160?”
2–7: Model 9n > 160; n > 160/9≈17.78, so the first whole count is 18, giving $162. This is a mathematical boundary, not a productivity target.
7–13: Learners check 17 props = $153 and 18 = $162. Contrast “at least $160” with “strictly more than $160”; the threshold happens to be 18 for both here, so ask why the words still matter.
13–20: Routes: build a $9-per-piece number line using tokens; fill 15–20 rows in the payment board; solve the inequality and verify adjacent whole counts. All routes show the two boundary values and the unknown real work time.
20–25: Exit “Why not round 17.78 to 17?” Key: 17 gives only $153. Move: make learner test both adjacent whole counts before selecting a conclusion.

Alternative domain: Fictional photo-editing deliverables. Optional/home: find the first whole count at $7 each exceeding a fictional $50 target; no real gig advice.

Day 14 · Commission is a percentage of a named base

Goal: calculate Card C base-plus-commission scenarios and interpret percentage base. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Point to “4.5% of eligible sales”. Ask whether 4.5% is taken from $180 base, $1,200 sales or total pay.
2–7: Model 0.045×$1,200=$54 commission; 180+54=$234 gross model shift total. Estimate 5% of $1,200 is $60, so $54 is credible.
7–13: Learners compute $800 sales → $36 commission/$216 total and $1,600 → $72/$252; compare how an extra $400 eligible sales adds $18 in this fixed rule.
13–20: Routes: move a base-pay block plus 4.5%-of-sales strips; complete the commission table; write a formula T(s)=180+0.045s and explain it orally/AAC. All routes label base, sales, commission and unknown real conditions.
20–25: Exit “Why is $180 + 4.5 = $184.50 wrong?” Key: 4.5 is a percent, not a dollar commission. Move: estimate 5% of $1,200 first, then calculate exactly.

Alternative domain: Imaginary adult gallery sales desk. Optional/home: calculate 3% of invented $600 eligible sales with a fictional $200 base; no actual sales.

Day 15 · Fresh public Check A

Goal: independently transfer period conversion and commission-base reasoning to new fictional data. 25 = 2 + 3 + 12 + 5 + 3.

0–2: Explain this public prompt is fresh relative to lessons, not a secure exam or QCAA assessment. Adapt locally if previously seen.
2–5: Give exact prompt, large text, calculator, tactile period cards, AAC/sign or exact-word scribe without demonstrating its new numbers.
5–17: Learners answer independently; retain first work before feedback. Note access, interpretive cue and calculation separately.
17–22: After collection, reflect on period / percent base / unit / missing condition. Routes: period-card reconstruction; table annotation; spoken/typed explanation. This is feedback, not replacement first evidence.
22–25: Use the public teacher key to select one next move. Move: if a prompt was known, recheck later with fresh locally chosen numbers.

Alternative domain: Fictional sports-facility adult role after the check. Optional/home: explain why pay for one shift and one month cannot be compared without the time basis.

Day 16 · A budget keeps essentials visible

Goal: classify Card D's fixed, variable-essential and discretionary costs before finding an unassigned model balance. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Say Card A's $1,260 gross weekly figure is stipulated as available in this exercise only; a real budget must verify deductions. No private family budget is requested.
2–7: Model fixed 520+120+40=$680; food is variable essential, not discretionary. Model 680+220+65+45=$1,010 planned.
7–13: Learners calculate discretionary 65+45=$110, unassigned 1,260−1,010=$250 and reverse check 1,010+250=1,260.
13–20: Routes: move labelled cost counters on the budget mat; fill subtotal boxes in large print; enter or dictate income − fixed − variable essential − discretionary. All routes preserve food's category and say what a real budget still needs.
20–25: Exit “Is $250 proven available in a real household?” Key: no; gross/net and unlisted costs remain unknown. Move: if food is called discretionary, ask whether the classification matches the stated essential role before recomputing.

Alternative domain: Imaginary community workshop operating plan. Optional/home: sort a made-up $900 income and three invented costs; no personal money disclosure.

Day 17 · The GST base changes with the price label

Goal: calculate included and excluded GST in explicitly fully taxable fictional supply examples. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Read Card E's condition fully taxable and the ATO-source note. The 10% rate is verified for a taxable supply; a real item's treatment needs its own check.
2–7: Model $84 excluding GST: $84×0.10=$8.40; inclusive $92.40. Check 84×1.10=92.40.
7–13: For $121 including GST, model reversal 121÷1.10=$110 exclusive, GST $11; check 110+11=121. Explain why $121−10%×121 uses the wrong base.
13–20: Routes: move base/tax/total blocks with labelled denominators; complete the price-base ladder; write/spoken calculation with factor 1.10 and reverse addition. Each route states the fully-taxable assumption and no real classification claim.
20–25: Exit “Is 10% of $121 the included GST?” Key: no; for this fully taxable example it is $11, one eleventh of inclusive price. Move: reconstruct base×1.10=total with $110 before a shortcut.

Alternative domain: Fictional adult poster-print supply. Optional/home: under an explicitly fully taxable invented example, find inclusive $55 from exclusive $50; no shopping task.

Day 18 · Simple interest is not compounding

Goal: apply I=Pin with a yearly rate and labelled time, then test a changed term. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Name P, annual i and years n in Card F. Say these are fictional assumptions, not a real account or return.
2–7: Model I=2400×0.035×2=$168; final amount $2,568. Check 3.5% of 2400 is $84 for one year, so two simple-interest years give $168.
7–13: Learners recompute one year: interest $84/final $2,484. Explain why multiplying the first year's new amount by 3.5% would be compounding, which is not this stated model.
13–20: Routes: two equal $84 annual strips attached to original P only; fill the interest timeline; use symbolic P×i×n then verbalise units and no-compounding limit. All routes compare one and two years.
20–25: Exit “Which amount is the base in year 2 of this simple model?” Key: original $2,400. Move: if learner compounds, draw both $84 strips from the same P.

Alternative domain: Fictional invoice late-charge maths without a real contract. Optional/home: find I for invented P=$1,000, i=2%, n=2 years; no financial recommendation.

Day 19 · Repeated computations must keep the same formula

Goal: audit three Card G budget what-ifs with one visible formula and check a numerical constraint. 25 = 2 + 5 + 6 + 7 + 5.

0–2: Ask which inputs change by fictional week and which formula stays fixed. No one provides personal data.
2–7: Model Week A 1260−680−220−110=$250 unassigned; reverse check 680+220+110+250=1260.
7–13: Learners calculate Week B $205 and Week C $245, then check each against the invented at least $200 constraint. Show where a spreadsheet could repeat =income-fixed-essential-discretionary; a paper table is equivalent for arithmetic.
13–20: Routes: budget counters and a $200 boundary strip; budget map for each week; optional local what-if spreadsheet or typed/paper table with the same formula and a manual spot check. Every route reports all three values, one reverse check and an assumption limit. Actual spreadsheet use is documented separately.
20–25: Exit “If Week B food rises $10 alone, what happens?” Key: unassigned falls from $205 to $195, failing the stated model threshold. Move: if a student edits multiple cells, freeze unchanged inputs and subtract the one new $10.

Alternative domain: Invented stage-prop materials plan. Optional/home: change just one made-up cost by $5 and predict the balance; no family budget.

Day 20 · Fresh public Check B

Goal: transfer GST-base and simple-interest reasoning to new independent values. 25 = 2 + 3 + 12 + 5 + 3.

0–2: Explain the new case is public practice and its tax and interest assumptions are stipulated; it is not a QCAA exam or real advice.
2–5: Offer exact reading, large text, calculator, tactile factor cards, AAC/sign or exact-word scribe without giving the method for these new values.
5–17: Learners show first independent reasoning; collect before content feedback.
17–22: After collection, revisit exclusive or inclusive base? / annual rate and years? / model or reality? Routes: price blocks; annotated equation table; spoken/typed two-case audit. Preserve first evidence and record any hint.
22–25: Use the public worked key to choose a specific next practice. Move: create a new local parallel check when prior access made the first response ambiguous.

Alternative domain: Fictional sports-poster supply and a completely invented interest table after assessment. Optional/home: explain the difference between a percentage on a base and an included total.