Model Model Design

Overview

In this fifth lesson of the eight-lesson unit, students launch a culminating design project: a themed three-dimensional model built from mathematical nets. They apply similarity, scale factors, nets, shared faces, and surface-area estimation to plan a feasible model before construction begins.

Learning intentions

Students will:

• design a themed composite 3-D model using mathematical nets;
• identify the component solids, their nets, and shared faces;
• include at least two similar 2-D shapes and state a scale factor;
• estimate the model’s external surface area using appropriate measurements;
• communicate a clear plan for approval.

Success criteria

• I can sketch a themed composite model and identify its component solids.
• I can show at least two similar 2-D shapes and label corresponding parts.
• I can state a realistic scale factor and explain how it applies.
• I can estimate external surface area and submit a complete Checkpoint 1 plan.

Curriculum links

• Shape and space — analyse and construct 2-D shapes and 3-D objects using nets.
• Shape and space — investigate similarity and use scale factors to describe corresponding measurements.
• Shape and space — determine and estimate surface area of composite 3-D objects, accounting for shared faces.
• Mathematical processes — problem solving, reasoning, communicating, connecting, and representing mathematical ideas.

Lesson structure (30 minutes)

1. 0–4 min · Project hook. Teacher opens the project launch slides with a visual comparison of a flat net and its assembled solid, then asks, “How can a collection of flat shapes become one model with a measurable outside surface?” Students discuss the question with a partner and identify what information a builder would need before starting.

2. 4–9 min · Success criteria and model. Teacher displays the project requirements and briefly models a simple composite object, such as a rectangular-prism building with a triangular-prism roof; teacher identifies the solids, circles the shared faces, marks two corresponding 2-D shapes, and demonstrates a scale factor of 2. Students annotate the example and suggest which faces should not be counted in external surface area.

3. 9–13 min · Planning instructions. Teacher distributes the net-planning and Checkpoint 1 worksheet and explains that students may work individually or with one partner. Students choose a theme, list possible solids, and confirm that their design will include at least two similar 2-D shapes, a composite object, visible nets, labelled dimensions, a scale factor, and an estimated surface area.

4. 13–23 min · Design studio. Teacher circulates, conferences with students, and uses the prompts in the project planning slides: “Which faces are shared?”, “What makes these shapes similar?”, and “What will your scale factor change?” Students sketch a front or perspective view, identify each solid, draw or attach the required nets on the worksheet, mark corresponding lengths, label shared faces, state the scale factor, and calculate or estimate the external surface area.

5. 23–27 min · Peer design check. Teacher asks students to exchange plans with a nearby pair and display the peer-check questions on the peer review slides. Students check whether the design is buildable, the solids and shared faces are identified, the similarity claim is supported, and the surface-area estimate excludes internal shared faces. Partners provide one strength and one specific revision suggestion.

6. 27–30 min · Checkpoint submission. Teacher reviews the approval checklist and collects Checkpoint 1, allowing students to mark “revise and resubmit” if a required feature is missing. Students submit the completed planning sheet or place it in the designated collection area, then write one action they will take before the next lesson.

Resources

• the project launch and planning slide deck
• the net-planning and Checkpoint 1 worksheet
• Pencils, erasers, rulers, and coloured pencils
• Grid paper or geometry notebooks
• Sample 2-D shape and 3-D solid diagrams
• Optional cardboard, paper, or recycled packaging for visualising construction
• Project approval checklist
• Document camera or interactive display

Assessment

• During modelling and conferencing, check whether students correctly identify solids, corresponding parts, scale factor, and shared faces.
• Review peer feedback for mathematical accuracy, feasibility, and recognition that shared internal faces are excluded from external surface area.
• Use Checkpoint 1 as an exit assessment: approve, approve with revisions, or return for clarification. A complete response includes a labelled sketch, component solids, nets, two similar shapes, scale factor, shared faces, and a surface-area estimate.

Differentiation

• Provide a choice board of familiar themes and a partially completed example showing a rectangular prism and triangular prism for students who need a starting point.
• Offer sentence starters: “These shapes are similar because…”, “The scale factor is…”, and “I excluded this face because…”.
• Permit students to sketch with templates, use grid paper, or explain their design orally while a partner or teacher records labels; pre-teach terms such as net, corresponding, composite, shared face, and surface area for EAL learners.
• Extend confident students by requiring two different scale factors in one design, comparing how the scale factor affects area, or justifying why their surface-area estimate is reasonable.