Constructions and Scale Drawing

In constructions and scale drawings students learn how to construct triangles and elevation drawings to scale.  As learning progresses they explore how to bisect lines and angles as in introduction to Constructing Loci at GCSE.  Later, students solve problems involving bearings using scale drawings.  This topic takes place in Term 5 of Year 8.


Constructions and Scale Drawing Lessons
Prerequisite Knowledge
  • 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
  • You use different methods to draw triangles depending on what information you are given.
    • Side, Side, Side is constructed using a pair of compasses and ruler
    • Angle, Side, Angle is constructed using a protractor and ruler.
    • Side, Angle, Side is constructed using pair of compasses, protractor and ruler.
  • The perpendicular bisector of a line is a line that divides the first line into two
    equal lengths and is at right angles to it.
  • The angle of elevation is the angle between the horizontal line of sight and the object.  The angle of depression is the angle between the line looking straight ahead and the line looking down at the object.
  • A bearing is a compass direction.  A three figured bearing is a clockwise angle measured from North.  North lines are parallel.
  • The bisector of an angle is the line or line segment that divides the angle into two equal parts.
Working mathematically

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.
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

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Literacy in Mathematics – Creating Problem Solvers

Last year my school had a OFSTED trial inspection. Whilst the maths team recieved favourable feedback the inspectors noted a need for a focus on whole school literacy. Because of this I was asked to demonstrate how we develop student’s literacy in mathematics. Literacy in Mathematics By developing student’s literacy in mathematics we aim to […]

Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]