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


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 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Your email address will not be published.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

Solving Inequalities using a Number Line

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values.  Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

Practical Tips for Using Mini-Whiteboards in a Mathematics Lesson

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson.  I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making.  When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback.  […]

Showing Progress during a Mathematics Lesson

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]