Area and Arc Length of Sectors

Scheme of work: GCSE Higher: Year 10: Term 6: Area and Arc Length of Sectors

Prerequisite Knowledge

  • Know and apply formulae to calculate: the 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=>root x.
  • When generating formulae it is important to associate mathematical operations and their algebraic notation with key words.

Common Misconceptions

  • The 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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