Angles Beyond Straight

Overview

This is lesson 5 of 8 in Angles: Measure, Build, Reason. Students extend their understanding beyond a straight angle by classifying, measuring and constructing reflex angles up to 360°, using benchmarks, turn diagrams and a two-step protractor strategy.

Learning intentions

• WALT identify and describe angles greater than 180° and less than 360°.
• WALT measure and construct reflex angles using a full turn or two-step strategy.
• WALT connect angle measures with quarter-turn, half-turn and full-turn descriptions.
• WALT explain and justify our thinking when solving a rotating-robot problem.

Success criteria

• I can identify a reflex angle and explain why it is greater than 180° but less than 360°.
• I can measure a reflex angle accurately by finding the smaller angle and subtracting it from 360°.
• I can construct a reflex angle and label its measure.
• I can describe a turn in more than one way and explain how I know my answer is correct.

Curriculum links

• Number and algebra: use whole-number measures and subtraction within 360 to solve practical problems.
• Measurement and geometry: identify, compare, measure and construct angles, including angles related to quarter, half and full turns.
• Mathematical practices: represent ideas with diagrams and equipment, reason about relationships, and communicate mathematical thinking.
• Key competencies: thinking; using language, symbols and texts; managing self; participating and contributing.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook: “Which way did the robot turn?” Open with the turning robot hook. Show a robot facing north, turning clockwise past west and stopping at a direction such as south-east. Ask: “Has it turned more or less than a half-turn?” Students silently estimate, then share with a partner. Emphasise that the larger path around the outside is a reflex turn.

2. 5–13 minutes – Teach and model reflex angles Use the reflex angle teaching slides to establish the classifications: straight angle = 180°, reflex angle is greater than 180° and less than 360°, and a full turn = 360°. Model a reflex angle of 240° using a circular turn diagram. Then model the two-step strategy: measure the smaller angle inside the arms, then calculate 360° − smaller angle. For example, a smaller angle of 120° gives a reflex angle of 240°. Discuss why the correct protractor scale and starting point matter.

3. 13–18 minutes – Guided measurement check Display the benchmark examples from the benchmark and measurement slides. Students hold up or point to whether each turn is a quarter-turn, half-turn, more than a half-turn or a full turn. Work through two examples together, using 90°, 180° and 360° as reference points. Ask students to explain how they know an answer is reasonable before calculating.

4. 18–32 minutes – Turning robot investigation Organise 36 students into groups of four, with roles of reader, turn modeller, recorder and checker. Distribute the turning robot investigation worksheet. Students solve a sequence of robot turns, recording both the turn description and angle measure. They should draw arrows or turn diagrams, identify the smaller angle where useful, and calculate the reflex angle. Include challenges such as: “The robot turns 110° the short way. How far is the long way?” and “Give two descriptions for a 270° turn.” Circulate and prompt: “What is the full turn?” and “Which angle are you measuring?”

5. 32–39 minutes – Construct and compare Students use protractors to construct two specified reflex angles on the worksheet, such as 220° and 315°. They may construct the smaller angle first and complete the turn, or use a full-turn protractor if available. Partners check each other’s baseline, vertex, scale and final measure. Invite groups to compare different representations of the same angle, such as 270°, three quarter-turns and 360° − 90°.

6. 39–45 minutes – Share, assess and consolidate Return to the discussion and plenary slides. Select two groups to explain different strategies for one robot problem. Students complete the final reflection on the worksheet: “A reflex angle is…” and “My checking strategy is…”. Collect the worksheet or photograph selected responses for assessment. Reinforce that a reflex angle is measured around the larger part of a turn, not the smaller interior angle.

Resources

• the complete angles presentation covering the hook, modelling, instructions, discussion prompts and plenary
• the turning robot investigation worksheet
• Protractors, ideally one per student or pair
• Pencils, rulers and coloured pens
• Mini whiteboards or scrap paper
• A large floor or board turn diagram
• Optional full-turn protractor or circular angle model
• Classroom clock or spinner image for turn comparisons

Assessment

• Observe whether students distinguish the smaller angle from the reflex angle and use 360° subtraction accurately.
• Check worksheet diagrams, calculations, constructed angles and explanations for correct use of benchmarks and protractor scales.
• Use the final reflection to identify students needing further practice with classification, subtraction or protractor placement.

Differentiation

• Support: provide a turn diagram marked at 90°, 180°, 270° and 360°; begin with multiples of 90°; allow students to physically rotate an arrow or use a circular model.
• Support: pair students strategically and provide the sentence frame, “The full turn is 360°. The smaller angle is __°, so the reflex angle is 360° − __° = __°.”
• EAL/SEN: pre-teach and display turn, clockwise, anticlockwise, smaller angle, reflex angle; use colour-coded arms and give one instruction at a time.
• Extension: ask students to find three equivalent descriptions for one reflex angle, create a robot route with a total of 720° over two turns, or explain why two different-looking diagrams represent the same angle.