# Essential Mathematics learner cards · fictional ratio settings

These cases were written for the **Queensland Essential Mathematics Applied (Essential) pathway**. They do not imply that every Year 11 student takes this subject. All objects, places and quantities below are invented. No learner needs to disclose a household situation, disability, income or community affiliation. A ratio's order matters: say what the first and second numbers count. Show `given → matching units → operation → check → limited conclusion`. Use [A4/text/tactile aids](print/TEXT-ALTERNATIVES.md) or the optional [offline ratio lab](ratio-lab.html). The [public checks](STUDENT-CHECKS.md) contain new cases.

## Card A · community maker table

An imaginary maker table displays **3 round wooden tokens** and **2 square paper tokens**. The ratio of **round : square** is `3:2`; the ratio of **square : round** is `2:3`. There are **5 tokens altogether**. Say what each ratio number means, then find the fraction of all tokens that are round and the fraction that are square. No actual community stock is being counted.

## Card B · theatre cue cards

A fictional theatre tray holds **4 amber cue cards** and **6 blue cue cards**. Write amber:blue, simplify it with a common factor, and reverse the order for blue:amber. The simplified ratio describes the same composition in smaller whole-number parts; it does **not** mean four physical cards have vanished.

## Card C · library display badges

A made-up library display uses **8 story badges** and **12 information badges**. Find story:information in simplest whole-number form. Then find the fraction of **all 20 badges** that are story and the fraction that are information. Explain why story:information and story:all are different comparisons. These are invented display materials, not reader categories.

## Card D · lengths need a common unit

A fictional workshop plan shows one ribbon strip **150 cm** long and another **1 m** long. Find the first strip : second strip ratio in simplest whole-number form. Convert 1 m to 100 cm **before** simplifying. The ratio compares lengths, not money or people.

## Card E · share a fixed number of prop labels

A made-up stage team has **35 identical prop labels** to place in two printed bundles, **large : small = 2:3**. Find the number of labels in each bundle. The labels can be handled as five equal groups; this is a mathematical allocation, not advice about accessibility or real production needs. Check the total and ratio afterward.

## Card F · simple drawing scale

On an invented mural sketch, **1 cm on paper represents 200 cm on a model wall**. With both quantities in centimetres, the drawing:wall scale is `1:200`. A **4 cm** line on the sketch represents how many centimetres and metres on the model wall? A **3 cm** line represents how many metres? This is a paper exercise, not an actual site plan or construction measurement.

## Card G · three claims to audit

A fictional set has **12 green tags and 18 orange tags**. Decide whether each claim is true, show one reason and correct any false claim:

1. “Green:orange simplifies to `2:3`.”
2. “The fraction of **all tags** that are green is `2/3`.”
3. “If the same composition is made with **40 tags**, there will be 16 green and 24 orange.”

No real attendance or identity group is being represented by these colours. Use labels or textures if colour is not useful.

## More imagined settings

Swap tokens for poster icons, stage marks, library labels, garden-bed markers, paper model tiles, game pieces, repair-kit cards or map symbols. Keep equal units when comparing quantities. Home practice may use drawings or invented numbers only; no shopping, survey, personal data or field measurement is required.