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


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.

 

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