Test and Improve Proposals

Overview

In this ninth lesson of Design a Sustainable Community, students evaluate their community proposals against mathematical, environmental, social and financial criteria. They use calculations, a decision matrix and feedback from a short conference to test assumptions, identify trade-offs and recommend specific improvements before final presentation.

Learning intentions

• WALT evaluate a proposal using stated sustainability and feasibility criteria.
• WALT use calculations to compare trade-offs such as cost per user, water use and available area.
• WALT test assumptions and communicate evidence-based judgements.
• WALT recommend practical improvements to a design.

Success criteria

• I can apply each criterion consistently using evidence from the proposal.
• I can support judgements with accurate calculations and appropriate units.
• I can explain at least one trade-off and test whether an assumption is reasonable.
• I can recommend specific improvements and explain how they improve the outcome.

Curriculum links

• Measurement — mathematical modelling involving ratios, rates and financial contexts.
• Number — modelling practical problems involving rational numbers, percentages and financial decisions.
• Algebra — modelling applied problems involving linear relationships, including financial contexts.
• Algebra — representing, solving and verifying linear equations and inequalities where they arise in a model.

Lesson structure (90 minutes)

1. 0–8 min · Hook and retrieval. Open with the sustainability dilemma hook showing two community proposals and ask, “Which is better: the cheapest, the greenest or the fairest?” Students individually rank the proposals, then justify their choice using one calculation or piece of evidence from the previous lesson.

2. 8–20 min · Model the evaluation process. Use the evaluation criteria and worked example to introduce the four criteria: mathematical feasibility, environmental impact, social benefit and financial sustainability. Teacher models one decision-matrix row using a sample proposal, including a calculation such as total cost ÷ expected users, and demonstrates how to record an assumption, evidence, judgement and possible limitation. Students identify where the model may be unrealistic and suggest a question to test.

3. 20–30 min · Prepare the workshop. Distribute the proposal evaluation workshop and explain the scoring scale and evidence requirements. Students review their own proposal data, highlight missing information and select three assumptions to test, such as expected users, water consumption, construction area or running cost. Teacher checks that units, time periods and quantities are comparable before students begin.

4. 30–57 min · Evaluation workshop. Students work in three pairs, with each pair evaluating one proposal or reviewing their own team’s proposal using the matrix. They calculate relevant measures, such as cost per user, litres of water per user per day, percentage of site area used and estimated annual cost. Students record a score and written evidence for every criterion, then identify one benefit, one weakness and one trade-off. Teacher conferences with each pair for approximately eight minutes, using prompts: “What evidence supports this score?”, “What assumption affects the result?” and “Would the result change if this value increased?”

5. 57–70 min · Compare and challenge. Display the comparison and what-if prompts. Pairs exchange worksheets and act as critical reviewers, checking one calculation, questioning one assumption and proposing one alternative weighting. Students complete a brief “what if?” calculation, such as a 10% increase in construction cost, 20% increase in users or reduction in available land, and explain whether the recommendation changes.

6. 70–83 min · Feedback conference and improvement plan. Each pair presents its provisional recommendation in a two-minute conference: decision, strongest evidence, key trade-off and recommended improvement. Peers and teacher give one evidence-based commendation and one question. Students revise their worksheet, changing at least one design feature or explaining why no change is needed.

7. 83–90 min · Plenary and exit check. Use the reflection and exit questions to revisit the hook. Students complete the final section of the proposal evaluation workshop, answering: “Which criterion most influenced your decision?”, “Show one calculation that supports it” and “What would you investigate next before construction?” Collect responses to identify readiness for the final lesson.

Resources

• the sustainability evaluation slide deck
• the proposal evaluation workshop
• Student community proposals and design data from previous lessons
• Calculators or spreadsheet software
• Graph paper, rulers and coloured pens
• Sustainability checklist displayed on the board
• Timer and conference prompt cards
• Whiteboard or shared digital workspace

Assessment

• During modelling, question students about units, assumptions, scale and whether their calculations represent the situation appropriately.
• Collect workshop sheets to assess accurate calculations, consistent criterion scores, interpretation of trade-offs and quality of recommendations.
• Use the exit responses to identify students needing support with modelling, percentages, rates or communicating evidence before the final presentation.

Differentiation

• Support students with a simplified decision matrix containing the four criteria, sentence starters (“The proposal scores… because…”) and a worked cost-per-user example. Provide criterion cards and allow calculator or spreadsheet use.
• Teacher gives targeted mentoring to one pair at a time, reading questions aloud, checking units and breaking multi-step calculations into labelled stages. Pair students strategically and provide additional processing time where required.
• For EAL learners, display visuals and accessible definitions for criterion, assumption, trade-off, feasible and evidence. Accept oral explanations before students record a concise written judgement.
• Extension students create a weighted decision model, assign and justify percentage weights, conduct two “what-if” scenarios and defend how changing the weighting alters—or does not alter—the final recommendation.

Extension

• Create a weighted model in a spreadsheet and compare its outcome with the unweighted matrix.
• Test two further scenarios, such as reduced rainfall or increased population, and explain which design is most resilient.
• Prepare a short evidence-based defence for the final lesson, including one limitation of the model.