Mathematics: relationships for creating · Lesson 08 / 08

Mission: a square of possibilities

Now you are responsible for a decision you can explain. Choose one of four scenarios, predict the totals and try the workshop. More than one answer can be right: it depends on the conditions you choose.

Let's discover together

1
A uses 12 fixed tokens and 2 per lantern. The stated reduction applies ONLY to A’s 2 × n part: total A = 12 + (2 × n) × (100 − reduction) ÷ 100. B remains 4 × n.
2
Before calculating, predict both totals. Small gathering: 3 lanterns, no reduction, limit of 13 tokens. Team effort: 6 lanterns, no reduction, limit of 24. Festival: 8 lanterns, a 25% reduction in A’s materials, limit of 26. Tight limit: 8 lanterns, no reduction, limit of 20. At the festival, A’s materials go from 16 to 12; preparation stays at 12.
3
Choose the lower total that fits the limit. If both totals are equal and fit, choose a tie. If neither fits, choose neither. The requested difference is always the larger total minus the smaller, even when neither fits.
4
Calculate, read the bars and table, and review your prediction. Change scenarios to test a different conclusion. Download the report or confirm copying it to the editor before leaving; the final ZIP is a starter kit, not an automatic copy of your trial.

✦

YOUR MISSION

Combine percentages, tables, charts and a limit in a reproducible comparison.

Now it's your turn

Discovery workshop

Workshop of choices

Fictional tokens; both plans deliver the same number of lanterns. Reduction only on A’s materials. Choose a scenario and make your predictions.

01Scenario to investigate02Your prediction: total A, in tokens03Your prediction: total B, in tokens04Lowest total that fits the limit05Difference between totals, in tokens

A square of possibilities

Choose the scenario above and make a prediction before calculating. The rules use fictional tokens; no real resources are spent.

Choose a scenario and predict the totals. Calculating does not complete the lesson; check your answers in the activity.

Bars with a zero origin and a shared scale from 0 to 60 tokens. Exact values are also in the table.

Variation by quantity — same reduction in A

The table uses the materials and preparation rules; values alone do not indicate whether they fit the limit. Fractions of a token are allowed in this model.

Variation by quantity — same reduction in A
Lanterns	Plan A	Plan B

Trials stay on this page and disappear on reload. Download the report or confirm copying it to the editor, which has a local draft. Sending to GitHub still requires your confirmation.

A has the lowest total that fits this limit.B has the lowest total that fits this limit.not recordedTie: both totals are equal and fit the limit.Available limitCalculate and compareBars with a zero origin and a shared scale from 0 to 60 tokens. Exact values are also in the table.Replace the editor’s current text with the report? First download any text you want to keep.Report copied to the editor. Check the draft status; nothing has been sent to GitHub yet.Origin at 27: notice the cropped scaleDifference between totalsDownload my reportA’s fixed preparationTrials calculated on this pageThe report keeps up to four scenarios, with the latest calculation for each. Predictions are recorded when you calculate; later edits require another calculation.Sign in and unlock this activity to copy to the editor. You can download the workshop report.A’s materials after reductionNeither fits the limit. Revise the conditions before choosing.Choose the scenario above and make a prediction before calculating. The rules use fictional tokens; no real resources are spent.Offline workshop: it does not connect your account, award XP or automatically save trials. Use the report button before closing.Plan APlan BMy prediction at calculation timeLanternsExtract the entire ZIP into one folder and open index.html in a browser. No installation, server or internet is required. Choose a scenario, make a prediction and calculate; the table provides a text alternative to the chart. workshop.js contains the model and interface; style.css defines presentation; workbook.md is your workbook. The starter kit does not include your Rullst Academy answers. Save the report separately and see PUBLISH.md for optional publishing. Try: why is there a tie at 6 lanterns without a reduction? What changes when only A’s materials receive a 25% reduction? Time, transport and quality are outside the model.Choose a scenario and predict the totals. Calculating does not complete the lesson; check your answers in the activity.Reduction only on A’s materials## My explanation - My prediction and what I revised: - Two conditions with different conclusions: - Unit and percentage base: - Something this model does not include: - My next test: Do not use personal data. Written justification is not automatically graded.Rules: A = 12 + (2 × n) × (100 − reduction) ÷ 100; B = 4 × n. Fictional tokens, the same lantern quantity, reduction only on A’s materials.Clear workshop trialsBoth drawings represent A = 28 and B = 32 tokens. Only the scale changed. The difference is still 4 tokens.Trials stay on this page and disappear on reload. Download the report or confirm copying it to the editor, which has a local draft. Sending to GitHub still requires your confirmation.The scenario changed. Calculate again; the previous result does not apply to the new conditions.Variation by quantity — same reduction in AThe table uses the materials and preparation rules; values alone do not indicate whether they fit the limit. Fractions of a token are allowed in this model.A square of possibilitiesCopy report to the editortokensZero origin

Build your answers and check when you are ready.

A moment to understand

What makes your conclusion reliable within this model?

Record conditions, units and calculations; test another situation and recognise limits.Choose a plan and claim it will always be best.Keep only the colour of the winning bar.

I need a hint

Your result applies to stated conditions. Another quantity or limit may change the decision.

Loading your journey…

How can I tell what I learned?

Use the objectives and challenge below for reflection or a conversation with someone who can help. This is guided self-assessment: it sends no answers, awards no XP and does not automatically verify independence.

In Foundations, change an example, predict results, check a normal case and an error case, and explain your choices. If you need help, identify what to practice again.

Your transfer challenge

Record your prediction, calculation and what changed in your thinking. Compare at least two scenarios. Write one limitation and a next question; your written justification is not automatically graded.

Keep evidence: prediction, attempt, result, an original change and what you still cannot explain. Seek feedback when possible; if studying alone, return later without copying and compare attempts.

Try again another time

After a break, explain the idea without opening the solution and try a different example. Compare with your first attempt: what can you do independently, and where do you need a hint? You may write, speak or draw; choose a way to check the same idea. Record help received, including AI, and revisit the part you need. There is no universal deadline or extra XP for this record.

Completions and XP record Rullst Academy assessments. An introductory track can help everyday life and prepare further study; alone it does not prove complete mastery or professional readiness. Level indicates depth, not age.

Take it with you

At your own pace

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Student guide

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Your path, step by step

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