# Year 11 General Mathematics learner cards · invented adult contexts

All prices, payments, products, roles, budgets and rates below are **fictional teaching assumptions**, except the explicitly cited general GST rule. They do not state a wage award, tax eligibility, benefit, investment return, contract, price quote or advice. You need not disclose personal or family finances. State `given → method → units → check → limited conclusion`. A missing fee is **unknown**, not $0. The [teacher plan](LESSONS.md) gives when to use a card; the [A4 and text aids](print/TEXT-ALTERNATIVES.md) support paper, tactile and enlarged routes.

## Card A · an annual salary expressed in different periods

A fictional adult print-studio role has a stated **gross annual model amount of $65,520**. For this classroom model use **52 equal weeks**, **26 equal fortnights**, and **12 equal months**. These are conversion assumptions, not a real payslip calendar or a net take-home guarantee. No taxes, deductions, leave changes or award conditions are supplied. Find the gross weekly, fortnightly and monthly average and label each period.

## Card B · one fictional piecework session

An imaginary prop-finishing brief offers either a stipulated **$32 per paid hour for 5 paid hours**, or **$9 for each accepted finished prop**. The example has **20 accepted props**. Calculate both gross totals. Then test 15 props and identify the minimum whole number of accepted props whose stated piecework total **exceeds** the hourly total. Work conditions, fairness, safety, actual hours needed and legal entitlements are unknown. This is a mathematical comparison, not advice on a job.

## Card C · an invented base-plus-commission rule

For a single fictional adult shift, model gross pay as **$180 base plus 4.5% of eligible sales**. Use invented eligible sales of **$800**, **$1,200** and **$1,600** in three separate scenarios. The percentage base is eligible sales, not the total pay. No returns, caps, deductions, minimum pay rules or time worked are supplied. Compare the three model totals; do not decide whether any real role is preferable.

## Card D · a planning-only weekly budget

Use Card A's fictional **$1,260 weekly gross amount as a stipulated available model income** for arithmetic only. In a real budget, gross is not necessarily spendable income; actual deductions and timing would need verification. The model lists:

| Type | Fictional weekly item | Amount |
| --- | --- | ---: |
| Fixed | Housing | $520 |
| Fixed | Transport pass | $120 |
| Fixed | Connectivity | $40 |
| Variable essential | Food plan | $220 |
| Discretionary | Leisure | $65 |
| Discretionary | Creative materials | $45 |

Calculate fixed, variable-essential and discretionary subtotals, total planned spending and the **unassigned model balance**. Check `planned + unassigned = 1,260`. An unassigned balance is not a recommendation to spend or save any particular amount. Never use a classmate's actual household figures.

## Card E · GST on stipulated fully taxable supplies

These are invented **fully taxable** design supplies for arithmetic. The current general Australian GST rate for taxable supplies is **10%**, as verified from the [Australian Taxation Office](https://www.ato.gov.au/law/view/document?LocID=%22GST%2FGSTR20016%2FNAT%2FATO%2FftF7%22&PiT=20221123000001). Actual supplies may be GST-free, input taxed or mixed; this card does not decide classification or tax obligations.

1. A fictional workshop print costs **$84 excluding GST**. Find 10% of that base and the GST-inclusive total.
2. A different fictional design item is labelled **$121 including GST**. For a fully taxable item, find the exclusive base and GST component. Explain why taking 10% *off* $121 does not reverse adding 10% to the earlier base.

## Card F · a simple-interest model

A fictional study of simple interest states principal **P=$2,400**, annual rate **i=3.5%=0.035**, time **n=2 years**, and **no compounding, fees or tax**. Use `I=Pin` for interest and `A=P+I` for final model amount. What changes if the time is **one year**, holding the other invented assumptions fixed? No real deposit, loan, return, product or recommendation is represented.

## Card G · repeated budget what-ifs

Treat all columns as separate fictional weeks with the same **stipulated model income $1,260** and no personal information. Formula: `unassigned = income − fixed − variable essential − discretionary`.

| Week | Income | Fixed | Variable essential | Discretionary |
| --- | ---: | ---: | ---: | ---: |
| A | $1,260 | $680 | $220 | $110 |
| B | $1,260 | $680 | $250 | $125 |
| C | $1,260 | $700 | $230 | $85 |

Calculate each unassigned balance, check by addition and ask whether a model target of **at least $200 unassigned** is met. This is a numerical constraint, not a real household target. The optional [offline what-if spreadsheet](print/budget-what-if.xlsx) repeats the visible formula; this table is equivalent for the arithmetic. Enter no personal information.

## Beyond today's main case

Optional fictional transfer settings include an adult arts studio, sports-equipment planning, community garden supply, transport itinerary, theatre props, digital media commission and maker workshop. Keep the same rate/base/period rule and state which unlisted conditions remain unknown. No purchase, sign-up or data gathering is required at home. The [fresh checks](STUDENT-CHECKS.md) are separate public files; save first responses before reading feedback.