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 or the optional offline ratio lab. The public checks 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:
- “Green:orange simplifies to
2:3.” - “The fraction of all tags that are green is
2/3.” - “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.