Constructions and Loci

Students learn how to construct angle and line bisectors using a pair of compasses.  Later, students apply this knowledge to solve problems involving loci about a point and line.  This unit takes place in   Year 9 Term 6.  


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

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

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.

Mr Mathematics Blog

Trigonometric Identities Sin, Cos and Tan

How to introduce the sin, cos and tan trigonometric identities.

Calculating a Reverse Percentage

How to teach calculating the original amount after a percentage change.

Comparing Datasets using the Mean and Range

The importance of the range when comparing comparing datasets.