Compass Directions Geometry

Overview

In this lesson, students use compass points and three-figure bearings to describe and follow routes on geometric maps. They build on prior work with angles, direction, coordinates and scale drawings, applying mathematical language accurately to communicate spatial relationships.

Learning intentions

• WALT identify the cardinal and intercardinal compass points.
• WALT interpret and write three-figure compass bearings.
• WALT use bearings to describe and construct routes on a map.
• WALT explain how a bearing gives a precise direction.

Success criteria

• I can label the eight main compass points.
• I can measure a clockwise angle from north and write it as a three-figure bearing.
• I can follow a route and give clear directions using bearings.
• I can check whether a map route and its bearings match.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers alignment: applying relevant mathematical ideas seamlessly to a new geometric mapping context.
• Mathematics and Statistics — additional resources for advanced learners: reasoning, explanation and challenge through non-routine spatial problems.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Display the opening map and ask, “Could two people interpret ‘travel right’ differently?” using the opening map and mystery route. Students silently predict how they would describe a route, then compare answers with a partner. Invite two or three responses and identify the need for a common direction system.

2. 5–13 min · Teach compass points. Use the compass points teaching slides to establish north, east, south and west, followed by north-east, south-east, south-west and north-west. Model how to orient a map with north at the top and how each direction relates to a quarter, half or three-quarter turn. Students label a quick compass rose on their worksheet and explain one direction to a partner.

3. 13–22 min · Introduce bearings. Teach that a bearing is measured clockwise from north and written with three digits, such as 000° or 360° for north, 090° for east, 180° for south and 270° for west. Model using a protractor: place its centre at the starting point, align 0° with north, measure clockwise and record the bearing. Use the bearings worked examples for a north-east direction and a non-cardinal direction. Students practise two examples on the compass and bearings practice worksheet, showing construction lines and checking their three-digit notation.

4. 22–34 min · Paired route investigation. Distribute the map route investigation worksheet to pairs. Students use a ruler and protractor to follow the mapped route, record each bearing and distance where shown, then use the bearings to reconstruct a short route from a given starting point. Circulate and ask: “Where is your north reference?” “Are you measuring clockwise?” and “How do you know your answer is reasonable?” Pause midway to address common errors, including measuring from east or writing 90° rather than 090°.

5. 34–41 min · Reasoning challenge and share. Show the challenge route in the route comparison and discussion slides. Pairs decide whether two sets of directions could lead to the same destination, justifying their answer with angles, bearings and a labelled sketch. Select contrasting solutions for a brief discussion; emphasise that a precise mathematical explanation is more useful than an answer alone.

6. 41–45 min · Exit check and reflection. Display the plenary questions. Students complete the final questions on the exit check section: label a compass point, write the bearing for east, and describe one step needed to measure a bearing accurately. Students self-assess against the success criteria using “secure”, “developing” or “not yet”.

Resources

• Lesson 12 compass directions and bearings slideshow PDF
• Lesson 12 compass directions and bearings worksheet PDF
• Protractors, one per student
• Rulers, pencils and erasers
• Visualiser or interactive display
• Board and markers
• A4 paper for quick compass-rose sketches
• Optional enlarged map copies for students who need them

Assessment

• During modelling, check that students orient the protractor with 0° at north and measure clockwise.
• During paired work, inspect compass roses, three-figure notation and route constructions; question students about their reference direction rather than correcting immediately.
• Use the exit check to identify students who confuse compass points, clockwise measurement or three-digit bearings. Revisit the relevant idea before the next lesson.

Differentiation

• Support students with an enlarged compass rose, a north arrow on every map and the sentence frame: “From ___, travel ___° clockwise from north for ___ units.”
• Pair students strategically and provide a protractor demonstration under the visualiser; allow students to trace the north line before measuring.
• For EAL learners, display direction words with symbols and gestures, and repeatedly connect “clockwise from north” to the same visual model.
• Extend confident students by asking them to design a route with at least four legs, including one reverse or near-opposite direction, then exchange it with another pair to solve and verify.