Transforming World Challenge

Overview

This is lesson 9 of 10 in Shape Shifters: Transformations. In groups, students design a visual scene, logo or floor pattern featuring a 3D object with a net, transformations and a tessellation. They annotate their mathematical thinking and explain which properties remain unchanged.

Learning intentions

• WALT design a visual pattern using translations, reflections, rotations and/or enlargements.
• WALT show how a 2D net forms a 3D object.
• WALT create or include a tessellation using repeating shapes.
• WALT explain properties that transformations preserve, including side lengths, angles and parallel lines.
• WALT communicate mathematical ideas clearly using diagrams, labels and mathematical language.

Success criteria

• I can include a recognisable 3D object and show or label its net.
• I can use at least two transformations accurately and annotate what happened.
• I can create a tessellating section with no gaps or overlaps.
• I can identify properties that stayed the same and justify my answer.

Curriculum links

• Geometry: describing, visualising and constructing 2D shapes and 3D objects.
• Geometry: recognising and describing transformations, including translations, reflections, rotations and enlargements.
• Geometry: identifying symmetry, congruence, angle relationships, parallel lines and tessellations.
• Mathematical processes and competencies: communicating, representing, reasoning, and participating and contributing collaboratively.

Lesson structure (60 minutes)

1. 0–5 minutes – Hook and challenge briefing Open with the challenge hook and examples. Show a striking before-and-after image of a simple shape transformed into a logo or floor pattern. Ask: “What has changed, and what must have stayed the same?” Introduce the design brief and success criteria.

2. 5–12 minutes – Revisit key ideas Use the transformation recap slides to review translation, reflection, rotation, enlargement, nets and tessellation. Model a small example: rotate a triangle, copy it to make a repeating pattern, and identify unchanged side lengths, angle sizes and parallel lines. Clarify that an enlargement changes lengths but preserves angle size and shape.

3. 12–17 minutes – Plan the design Place students in groups of four or five and assign roles: designer, construction checker, transformation annotator and presenter. Distribute the Transforming World design planner. Groups choose a visual scene, logo or floor pattern, select a 3D object, and sketch where the net, transformations and tessellation will appear.

4. 17–42 minutes – Group design challenge Groups create their design on paper or card. They may use the 3D shape nets cut-outs to explore how a net folds into a solid, then draw or attach the net beside the finished object. Require at least two transformations, arrows or mirror lines, labels, and a tessellating section. Circulate with the prompt: “How do you know this is a reflection/rotation/translation?” and check that annotations identify preserved and changed properties.

5. 42–51 minutes – Mathematical gallery walk Display group designs around the room. Students circulate in pairs and leave one specific comment or question on the worksheet: one accurate mathematical feature and one suggestion for clearer evidence. Encourage students to check whether transformations are labelled and whether the tessellation has gaps or overlaps.

6. 51–57 minutes – Group presentations Invite three or four groups to present, selecting a range of designs. Each group explains its 3D object and net, demonstrates one transformation, and justifies at least two invariants. Use the presentation prompts and discussion slides to structure responses: “What stayed the same?”, “What changed?”, and “How can you prove it?”

7. 57–60 minutes – Reflection and next steps Return to the reflection and self-assessment section. Students complete: “One transformation we used was…”, “A property that stayed unchanged was… because…”, and “Our next improvement would be…”. Collect planners and designs to inform the final lesson.

Resources

• the complete lesson slide deck
• the Transforming World design planner
• the 3D shape nets cut-outs
• A3 paper or large design sheets
• Coloured pencils, markers, rulers and protractors
• Scissors and glue
• Sticky notes for gallery feedback
• Sample 2D shapes and 3D objects
• Group role cards or a displayed list of roles

Assessment

• Observe group planning and construction, listening for accurate use of transformation and shape-property language.
• Check each design for a suitable 3D object and net, at least two labelled transformations, and an accurate tessellation.
• Use the planner and reflection to assess whether students can identify preserved properties and justify their claims.

Differentiation

• Support students with a choice of simple designs, partially completed planning templates, pre-drawn grids, traced shapes and a reduced requirement of two clearly labelled transformations.
• Provide transformation word prompts and sentence frames: “The shape was ___ because ___”; “The ___ stayed the same because ___”.
• Allow students with fine-motor or writing needs to use larger paper, digital drawing tools, cut-out nets, oral explanations or a peer scribe.
• Extend confident students by requiring a combined transformation, such as a rotation followed by a translation, and a mathematical justification of at least three invariants. Ask them to explain why enlargement preserves angles but not side lengths.