Angles, Directions, Nets

Overview

In this first lesson of the two-part “PAT Geometry Reasoning” unit, students revisit angle classification, enlargement, compass directions and cube nets. They apply visual reasoning and explain strategies while working through PAT-style questions 13, 35, 37 and 40.

Learning intentions

• We are learning to identify obtuse angles greater than 90° and less than 180°.
• We are learning to recognise that enlarging a shape does not change its angle sizes.
• We are learning to locate positions using compass directions, including south-east.
• We are learning to visualise and test which nets fold into a cube.
• We are learning to explain our reasoning clearly, rather than relying on a guess.

Success criteria

• I can justify why an angle is obtuse using its relationship to 90° and 180°.
• I can explain why corresponding angles remain the same when a shape is enlarged.
• I can locate a position south-east of a reference point and describe my method.
• I can test whether a net will fold into a cube by tracking faces, edges and vertices.
• I can show working or explain the clue that helped me answer each PAT-style question.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying challenge questions alongside relevant mathematics content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, visualisation and justification through non-routine problems.
• Mathematical and statistical practices in the refreshed curriculum: representing, reasoning, communicating and checking mathematical ideas.

Lesson structure (60 minutes)

1. 0–7 min · Hook and diagnostic. Open with the hook and learning intention slides showing an enlarged triangle, a compass grid and several possible cube nets. Ask: “What changes, and what stays the same?” Students make a quick individual prediction, then compare with a partner. Collect a few explanations without confirming every answer.

2. 7–17 min · Angle reasoning. Use the angle comparison and worked-example slides to review right, acute, obtuse and straight angles, focusing on “greater than 90° but less than 180°”. Model estimating first, then checking with a known right angle or protractor if needed. Students classify displayed angles and explain one classification using precise language. Ask: “Could an obtuse angle ever be larger than a straight angle? Why not?”

3. 17–29 min · Enlargement and direction. Display the enlarged-shape example and compass grid from the enlargement and south-east slides. Demonstrate that enlarging changes lengths and overall appearance but preserves corresponding angle sizes. Then model moving from a reference point to the south-east: first move south, then east, or use the diagonal direction if the diagram indicates it. Students complete the paired prompts on the geometry reasoning practice sheet and compare methods with a partner.

4. 29–43 min · Cube-net investigation. Introduce the cube-net problem using the cube-net visualisation slides. Students work in groups of three: one predicts, one traces the folding sequence, and one records the reasoning. They test possible nets on the worksheet by marking the face that would become the base and tracking which faces meet. Groups must identify at least one net that works and explain why another does not. Encourage students to physically fold a spare paper copy only after making a prediction.

5. 43–54 min · PAT-style application. Students complete PAT-style questions 13, 35, 37 and 40 independently on the geometry reasoning practice sheet. Set a quiet first attempt, then allow students to compare answers in pairs. Require each student to circle the visual clue or calculation that supports an answer and write a short explanation for one selected question. Confer with students who are choosing answers without recording reasoning.

6. 54–60 min · Plenary and exit check. Return to the discussion and plenary slides and revisit the opening predictions. Students complete the final reflection box on the geometry reasoning practice sheet: “One idea I can now explain is…” and “One question I still need to check is…”. Invite two students to share different strategies, then collect sheets to identify needs for lesson 2.

Resources

• the Angles, Directions, and Nets slide deck
• the geometry reasoning practice sheet
• Thirty pencils and erasers
• Spare paper copies of simple cube nets
• Rulers and a small number of protractors
• Mini whiteboards or scrap paper
• Visualiser or interactive whiteboard
• Coloured pencils for tracking cube faces
• One copy of the PAT-style question set per student

Assessment

• Listen for accurate use of “obtuse”, “greater than 90°”, “less than 180°”, “enlarged” and “south-east” during partner explanations.
• Check group reasoning during the cube-net investigation: students should track faces and explain why a net will or will not close into a cube.
• Use the worksheet and reflection response to identify misconceptions for lesson 2, especially confusing enlargement with a change in angle size or interpreting south-east inconsistently.

Differentiation

• Provide a right-angle corner template, a labelled compass rose and sentence starters such as “The angle is obtuse because…” and “The position is south-east because…”.
• Pair students strategically and assign clear group roles during the cube-net task; allow students to trace or lightly annotate faces before explaining.
• For students needing extension, ask them to create a different valid cube net or prove why two nets that look similar behave differently when folded.
• Support EAL learners with visual models, gesture and a small word bank; offer enlarged diagrams, reduced visual clutter and additional processing time for students with learning or visual needs.