Constructions and Scale Drawings

Students learn how to construct triangles to scale using a pair of compasses and protractor.  As learning progresses they construct angle and line bisectors using a pair of compasses.  Finally, students apply this knowledge to solve problems involving loci about a point and line.  This unit takes place in  Year 10 Term 2.


Constructions and Scale Drawings Lessons
Revision Lessons


Prerequisite Knowledge

  • identify and construct a radius, diameter, circumference, area, chord, tangent and arc.
  • measure and begin to record lengths and heights
  • identify acute and obtuse angles and compare and order angles up to two right angles by size

Success Criteria

  • use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description
  • 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);
  • use these to construct given figures and solve loci problems;
  • know that the perpendicular distance from a point to a line is the shortest distance to the line


Key Concepts

  • It is important for students to sketch the diagram before attempting their construction. The sketch should be drawn freehand and contain all the necessary information.
  • Bisectors are used to half an angle as well as a length of a line segment.
  • Constructing a 60° angle using a pair of compasses is an essential skills throughout this topic as it goes on to equilateral triangles and reflex angles.

Common Misconceptions

  • Students often have difficulty constructing smooth arcs using a pair of compasses. Encourage them to try different techniques such as rotating the paper rather than the compasses.
  • It is important to leave in construction lines as these form the working out.

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Your email address will not be published.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

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 […]

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]