Model & Decide

Lesson 1: Learn & Prepare

Driving Question: How can Mathematics help us design a site that is more resilient to wildfire?

Students begin by connecting the Year 8 Science strand to Mathematics. Science has explored cause, spread, risk and response; Maths now asks practical questions such as how big, how far, how much and what percentage. The strand follows the process Model -> Calculate -> Adapt -> Optimise.

Students learn and practise:

• scale using 1 cm = 5 m
• area and perimeter for site features and boundaries
• percentages, including the requirement that at least 35% of the site remains protected wildlife habitat
• budget calculations using a starting budget of £150,000
• how mathematical constraints affect real design choices
• how to justify decisions using calculations rather than appearance alone

Students then complete a short pair design problem before receiving the full Rebuild Dunwich project brief. The main fictional site is 100 m × 70 m, giving a total area of 7,000 m² and a 20 cm × 14 cm scaled plan on A3.

Students produce: Initial Planning Calculations + Design Preparation

Lesson 2: Design

Driving Question: How can different mathematical constraints be combined into one workable site design?

Students work in pairs to create the first version of their Rebuild Dunwich Wildfire Resilient Design Challenge. They use one blank A3 sheet to design a fictional visitor and conservation site inspired by what they learned from Dunwich Heath.

The plan uses a scale of 1 cm = 5 m. Students must fit the required features onto the 100 m × 70 m site while keeping the Mathematics visible and accurate.

The first design must satisfy these constraints:

• Visitor Centre with a minimum area of 500 m²
• Protected Wildlife Habitat covering at least 35% of the 7,000 m² site
• an Emergency Access Route to the Visitor Centre
• an Evacuation Route to a Safe Assembly Area
• a Safe Assembly Area with a minimum area of 400 m²
• at least one Water Access Point
• strategically placed Managed Fuel Breaks
• a clear key, scale and labelled dimensions

Students also use the projected cost table to control spending. Costs include water access points, emergency access road length, fuel break length, vegetation management, emergency information points and additional evacuation exits. The total must remain within the starting £150,000 budget.

Students produce: First Version A3 Wildfire Resilient Site Plan with Scale, Area, Percentage and Budget Evidence

Lesson 3: Develop & Adapt

Driving Question: How should a mathematical design change when new planning information appears?

• Students continue developing the A3 design, add dimensions to the most important features and show the required calculations. Halfway through the period, new planning information is revealed.
• A protected nesting area has been discovered:
• the area measures 20 m × 15 m
• it must remain untouched
• no buildings can be placed on it
• no roads can cross it
• it can count towards the protected wildlife habitat requirement

Students must adapt the design they already created rather than starting again. They record the adaptation using Change -> Reason -> Effect: what they moved or resized, what new evidence forced the change, and how the revised plan still meets the mathematical requirements.

Students produce: Updated A3 Design + Adaptation Evidence

Lesson 4: Finalise & Optimise

Driving Question: How can we prove that a final design still works when the budget changes?

• The final lesson introduces a new financial constraint. The available budget is reduced by 10%, from £150,000 to £135,000. Students must recalculate their total cost and adapt the design if it no longer fits the new budget.
• Students may need to remove, resize or replace features, but a cheaper design is not automatically better. The final site must still protect people, support wildlife, reduce wildfire risk and meet the mathematical brief.
• The final A3 must show:
• the scale written clearly and the site plan completed
• all mandatory features
• at least four area calculations
• at least two length or perimeter calculations
• proof that the habitat percentage requirement is met
• the final budget total and remaining money
• the protected nesting area update
• the 10% budget update and at least three design justifications

Students then submit the A3 design for MSC judging. The marking gives most weight to mathematical accuracy, scale, area, perimeter, budgets and percentages, with additional marks for design quality, response to updates, scientific reasoning and clarity.

Students produce: Final A3 Wildfire Resilient Design + Budget Evidence + Reflection

Each pair contributes a score /100 to the MSC Maths Championship. Tutor group scores are calculated from pair averages, and faculty scores are calculated from tutor group averages so that every pair contributes fairly.

Each period produces evidence of learning, giving students a clear record of how their design develops:

• L1: Initial Planning Calculations + Design Preparation
• L2: First Version A3 Wildfire Resilient Site Plan
• L3: Updated A3 Design + Adaptation Evidence
• L4: Final A3 Design + Budget Evidence + Reflection
• Across the strand, students practise applying scale, area, perimeter, percentages and budgets within one practical design while responding mathematically to changing constraints.
• Across the strand, students practise:
• using scale accurately to represent real dimensions
• calculating area and perimeter for practical design features
• using percentages to protect a required proportion of habitat
• working within a changing budget
• combining several mathematical constraints at once
• adapting a model when new information appears
• justifying practical decisions using visible mathematical evidence
• checking and optimising a final solution before submission