Key Stage 3 — Constructions and Scale Drawing — scheme of work

Home → Curriculum Hub → Maths Lessons → Schemes of Work → Key Stage 3 → Constructions and Scale Drawing

Key Stage 3: Constructions and Scale Drawing Scheme of Work

This Key Stage 3 Constructions and Scale Drawing scheme of work is designed for Year 8 work on constructing triangles using compasses and protractors, bisecting angles and lines, perpendicular bisectors, angles of elevation and depression, and scale drawings of bearings.

Use this page to sequence the lessons below, keep construction technique vocabulary precise, and connect ruler-and-compass methods to the geometric reasoning students will meet in congruence and loci work.

Last updated: May 2026

For more schemes and topic routes across KS3, GCSE and A-Level, browse the Mr Mathematics Curriculum Hub.

How to use this scheme

Read the prerequisite and key-concept cards first so angle measurement, acute/obtuse/reflex classification and basic geometric notation are secure. Teach the lessons in the order listed unless your timetable requires otherwise — keep triangle constructions before bisectors, and introduce angles of elevation and bearings after students can construct and interpret scale drawings confidently.

Mr Mathematics membership

Presentations, worksheets, question generators and video tutorials for the lessons in this unit are available to members. Explore Mr Mathematics membership if you need full access to the library and schemes of work.

If you are comparing options for a department, the membership page sets out exactly what is included so you can align this unit with your wider KS3 geometry and measures plan.

Prerequisite knowledge

Students should be secure with the following before this unit.

  • Know angles are measured in degrees; estimate and compare acute, obtuse and reflex angles.
  • Draw given angles, and measure them in degrees (°).
  • Identify: angles at a point and one whole turn total 360°; angles at a point on a straight line total 180°; other multiples of 90°.
  • Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

Key concepts

Ideas to keep explicit while students work with constructions and scale drawing.

  • Different methods are used to construct triangles depending on the information given: SSS uses compasses and a ruler; ASA uses a protractor and ruler; SAS uses compasses, a protractor and a ruler.
  • The perpendicular bisector of a line segment divides it into two equal lengths and meets it at right angles.
  • The angle of elevation is the angle between the horizontal line of sight and an object above it. The angle of depression is the angle between the horizontal and the line looking down to an object.
  • A bearing is a compass direction given as a three-figure clockwise angle measured from North. North lines are parallel.
  • The bisector of an angle is the line or line segment that divides it into two equal parts.

Subject content (Geometry and measures)

  • Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
  • Derive and use the standard ruler and compass constructions: perpendicular bisector of a line segment; constructing a perpendicular to a given line from/at a given point; bisecting a given angle. Recognise and use the perpendicular distance from a point to a line as the shortest distance to the line.
  • Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles.
  • Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles.
  • Identify and construct congruent triangles.

Working mathematically

How this unit supports fluency, reasoning and problem solving in Key Stage 3.

  • Develop fluency
    • Use language and properties precisely to analyse 2-D and 3-D shapes.
  • Reason mathematically
    • Begin to reason deductively in geometry using geometrical constructions.
  • Solve problems
    • Begin to model situations mathematically and express the results using a range of formal mathematical representations.
    • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Common misconceptions

Typical slips to address during teaching and marking.

  • Confusing SSS, SAS and ASA — using a protractor when compasses are needed, or vice versa, leading to inaccurate constructions.
  • Drawing the perpendicular bisector without keeping the compass width constant for both arcs, so the bisector does not pass through the true midpoint.
  • Treating angles of elevation and depression as the same direction, or measuring from the vertical rather than the horizontal.
  • Writing bearings without three figures — for example writing 45° instead of 045°.
  • Measuring a bearing anticlockwise from North rather than clockwise, or forgetting that North lines on a diagram are parallel and must be drawn at each point.

Frequently asked questions

How do I use this scheme page in practice?

Use it to sequence teaching, align vocabulary and spot likely errors before they become habits. Then use the lessons below as the delivery route for the unit.

What should students already know before this unit?

They need confident angle measurement and classification, knowledge of angle facts on a straight line and at a point, and basic geometric notation so new work focuses on construction technique, bisectors and scale rather than revisiting measurement fundamentals.

Where are the lesson presentations and worksheets?

Each lesson listed below has its own page with downloadable resources and, where available, online tasks. Access depends on your membership level.

Can I change the order of the lessons?

Yes if your timetable requires it — keep triangle constructions and bisectors before scale drawing applications, and introduce bearings after students can construct and read angles of elevation and depression confidently.

Where can I find revision resources for this topic?

Additional revision lessons, exam-style questions and topic-based practice are available on the GCSE Maths Revision Hub. This is useful for consolidating learning after teaching the unit or for Year 11 exam preparation.

Lessons in this Constructions and Scale Drawing scheme of work

  • Constructing Triangles using Compasses and Protractors
  • Bisecting an Angle
  • Perpendicular Bisectors and Equidistant Paths
  • Angles of Elevation and Depression
  • Scale Drawings of Bearings

Mr Mathematics Blog

Developing Mathematical Thinking Beyond Procedural Fluency

A research-backed case exploring why over-reliance on automated math homework platforms and repetitive worksheets lowers student expectations, and how departments can build genuine mathematical thinking.

Converting Between Fractions, Decimals and Percentages

How to teach converting between fractions, decimals and percentages.

From Key Skills to Deep Connections: Problem Solving in Secondary Maths

Four problem solving lessons to develop student’s mathematical reasoning and communication skills.