Area and Arc Length of Sectors

Finding the area and arc length of sectors following on Perimeter and Area where students first learn about circles.  Throughout this unit on sectors students develop their algebra skills by deriving and changing the subject of the arc length and area formulae.  This unit takes place in Term 3 of Year 11 for foundation students.


Area and Arc Length of Sectors
Revision Lessons

Prerequisite Knowledge

  • Know and apply formulae to calculate: area of triangles, parallelograms and trapezia;
  • Know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes;

Success Criteria

  • Calculate arc lengths, angles and areas of sectors of circles
  • Understand and use standard mathematical formulae; rearrange formulae to change the subject
  • Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments

Key Concepts

  • A sector is a fraction of 360° of the entire circle.
  • Students need to have a secure understanding of using the balance method when rearranging formulae. Recap inverse operations, e.g., x^2=>√x.
  • When generating formulae it is important to associate mathematical operations and their algebraic notation with key words.

Common Misconceptions

  • Arc length and area of a sector are often rounded incorrectly. Encourage students to evaluate as a multiple of pi and calculate the decimal at the end.
  • Students often have difficult generating formulae from real life contexts. Encourage them to carefully break down the written descriptions to identify key words.

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Your email address will not be published.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 […]