Geometry Investigation Project

Overview

In this penultimate lesson of Geometry Unlocked: Shapes and Spaces, students synthesise their learning by designing and presenting a short geometry investigation set in a real-world context. Working collaboratively, they select suitable geometric ideas, justify their decisions, and communicate their reasoning using accurate mathematical language and representations.

Learning intentions

• WALT synthesise our geometry knowledge in an investigation project.
• WALT apply geometric properties, measurements, constructions or transformations to a real-world situation.
• WALT justify mathematical decisions with diagrams, calculations and explanations.
• WALT communicate our findings clearly and respond to questions.

Success criteria

• I can identify and use relevant geometry concepts in a realistic context.
• I can create accurate diagrams, measurements, calculations or transformations.
• I can explain and justify how my geometry supports the solution.
• I can present my investigation clearly and respond to feedback or questions.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying connected mathematical ideas in a relevant, seamless context.
• Mathematics and Statistics — Additional resources for advanced learners: developing challenge, reasoning and independence through rich mathematical investigation.
• Mathematical and statistical processes: reasoning, representing, communicating and evaluating mathematical ideas.

Lesson structure (45 minutes)

1. 0–5 min · Hook and purpose. Teacher opens the investigation hook and learning intention slides with a striking image of a proposed playground, skate park or community garden made from geometric shapes, then asks, “How could we prove that this design works?” Students identify geometry they can see and briefly discuss which concepts might help investigate the design.

2. 5–10 min · Project briefing. Teacher displays the project brief and success criteria and distributes the geometry investigation project sheet. Explain that groups of three will choose or adapt a real-world context such as a floor plan, park, sports court, tiled pattern, packaging design or artwork. Their investigation must include at least three learned geometry concepts, a labelled representation, evidence such as measurements or calculations, and a conclusion supported by reasoning. Students form groups, select a context and record their initial idea.

3. 10–15 min · Model and plan. Teacher works through the worked example and planning prompts, modelling how to turn a broad idea into a testable question, such as “Which design uses the greatest area while keeping a fixed perimeter?” Emphasise accuracy, appropriate units, scale where needed, and explaining assumptions. Students complete the planning section of the geometry investigation project sheet, including their question, relevant concepts, required information and intended representation.

4. 15–30 min · Investigation workshop. Teacher circulates with the workshop checklist and reasoning prompts, conferences briefly with each group, and checks that the investigation requires reasoning rather than simply drawing a shape. Students complete their investigation on the geometry investigation project sheet, using suitable geometry such as angle relationships, properties of polygons and solids, perimeter and area, scale, symmetry, coordinates, or transformations. Groups show working, check calculations and prepare a two-minute presentation.

5. 30–39 min · Group presentations. Teacher displays the presentation instructions and audience questions and keeps time so each group presents concisely. Students present their context, investigation question, geometric evidence and conclusion; the audience records one strength and asks one purposeful question about accuracy, assumptions or the choice of method.

6. 39–45 min · Synthesis and reflection. Teacher returns to the plenary reflection prompts and leads a brief discussion: “Which geometry idea was most useful?” and “Where did a diagram or calculation change your thinking?” Students complete the reflection and self-assessment on the geometry investigation project sheet, identifying evidence of each success criterion and one improvement for the final unit lesson.

Resources

• the Lesson 17 investigation slideshow (PDF)
• the Lesson 17 geometry investigation worksheet (PDF)
• A4 paper or presentation paper
• Rulers, protractors and compasses
• Pencils, coloured pencils and erasers
• Calculators, if normally used by the class
• Grid paper or graph paper
• Projector or interactive whiteboard
• Optional geometry manipulatives and measuring tools

Assessment

• During planning, check that each group has a clear, investigable question and has selected at least three relevant geometry concepts.
• During the workshop, use questioning to assess accuracy, unit use, scale, justification and whether students can explain assumptions.
• Use presentations and the worksheet reflection as evidence of students’ ability to apply, connect and communicate geometric understanding. Note misconceptions to address in Lesson 18.

Differentiation

• Support groups with a choice of contexts, a teacher-provided question stem, a geometry vocabulary bank and partially completed diagrams. Confer first with students who need help narrowing their idea.
• Allow students to use grid paper, rulers, calculators and physical models when these help them represent spatial relationships or verify measurements.
• Provide sentence starters such as “We chose this method because…”, “Our diagram shows…”, and “This is reasonable because…”. Pair EAL learners with supportive peers and accept oral explanation alongside written evidence.
• Extend confident students by asking them to compare two possible designs, prove that their conclusion is always true, include a constraint or optimisation decision, or evaluate the limitations of their model.