Angles at a Point

Overview

Lesson 6 of 8 in Angles: Measure, Build, Reason. Students develop and apply the angle facts that angles at a point total 360° and angles on a straight line total 180°, using physical turns, diagrams and collaborative reasoning.

Learning intentions

• WALT recognise that a full turn is 360°.
• WALT recognise that a straight-line turn is 180°.
• WALT use addition and subtraction to find missing angles.
• WALT explain how I know my answer is reasonable.

Success criteria

• I can identify an angle at a point and an angle on a straight line.
• I can choose 360° or 180° for a missing-angle problem.
• I can subtract known angles accurately to find an unknown angle.
• I can explain my reasoning using an equation, diagram or words.

Curriculum links

• Number: use addition and subtraction strategies with whole numbers and angle measures.
• Measurement: recognise, estimate, measure and reason about angles and turns.
• Algebraic thinking: find an unknown in an equation and explain relationships.
• Mathematical communication and participation: represent thinking, justify solutions and work collaboratively.

Lesson structure (45 minutes)

1. 0–5 min – Hook: physical turns Open with the hook and turn visual. Ask students to stand beside their desks and follow instructions: quarter turn, half turn, three-quarter turn and full turn. Record the angle measure for each and ask: “How much turning brings us back to where we started?”

2. 5–13 min – Explicit teaching: two key facts Use the key angle facts and worked examples to establish that angles around one point make a full turn of 360°, while angles on a straight line make a half turn of 180°. Model a bar representation: a whole bar labelled 360° or 180°, with known angles removed. Emphasise the subtraction prompts: “What is the whole? What parts do we know? What is missing?”

3. 13–18 min – Guided examples and misconception check Work through one point diagram, such as 90° + 120° +? = 360°, and one straight-line diagram, such as 65° +? = 180°. Students show their answer on mini-whiteboards or fingers, then explain whether the diagram uses 180° or 360°. Address the common error of subtracting from 90° simply because a right angle appears in the diagram.

4. 18–30 min – Collaborative angle balance puzzle Arrange 36 students into nine groups of four. Distribute the angle balance puzzle worksheet. Each group solves missing-angle diagrams, beginning with labelled known angles and bar models. Students must agree on an equation and annotate each answer with “180°” or “360°”. Assign roles: reader, diagram marker, calculator/checker and explainer. Circulate and prompt: “What is the whole turn?” and “Can you prove the answer balances?”

5. 30–38 min – Build and reason: compound angles Return to the collaborative puzzle instructions and compound-angle examples. Groups choose one completed diagram and physically model it with students facing different directions or by rotating a paper arrow. They explain how smaller adjacent angles combine to make 180° or 360°. Invite groups to compare two different subtraction strategies.

6. 38–43 min – Share and challenge Select two groups to present different diagrams. The class checks each solution by adding all parts back together. If ready, ask students to create a new diagram with at least three known angles and one unknown, then swap with another group to solve.

7. 43–45 min – Exit reflection Use the final retrieval and reflection prompt. Students complete the final question on the worksheet: “Three angles at a point are 85°, 140° and?. Find the missing angle and explain why you subtract from 360°.” Collect responses for next-lesson grouping.

Resources

• the Angles at a Point teaching deck
• the angle balance puzzle worksheet
• Mini-whiteboards, markers and erasers
• A large arrow or pointer for modelling turns
• Display board or projector
• Pencils, rulers and coloured pens
• Desks arranged for nine groups of four

Assessment

• Listen for correct identification of the whole: 180° for a straight line and 360° for a point.
• Check group equations and annotations on the worksheet, focusing on whether students subtract known parts from the correct total.
• Use the exit response to identify students needing further support with angle vocabulary, subtraction or interpreting diagrams.

Differentiation

• Support: provide partially completed bar models, highlight the straight line or central point, and offer subtraction frames such as “360° − ___° − ___° = ___°”.
• Support: pair students strategically and allow them to model turns with a physical arrow before calculating. Read instructions aloud and use consistent visual symbols for 180° and 360°.
• Extension: ask students to create puzzles with more than one unknown, or compound angles where a known angle must first be split into smaller parts.
• EAL/SEN: pre-teach and display point, straight line, full turn, whole, known and unknown; accept oral explanations, labelled diagrams or equations as evidence.