Circles

Scheme of work: GCSE Foundation: Year 10: Term 3: Circles

Prerequisite Knowledge

  • know and apply formulae to calculate:
    • rectangles
    • rectilinear composite shapes
    • area of triangles
    • parallelograms
    • trapezia
  • calculate the perimeters of 2D shapes, including composite shapes;
  • round numbers to a given decimal place and significant figure

Success Criteria

  • identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
  • 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;
  • calculate arc lengths, angles and areas of sectors of circles

Key Concepts

  • To understand the relationship between circumference and diameter of a circle students should measure the circumference of several circles using a piece of string and compare this to its diameter. 
  • To understand the formula for the area of a circle, students should explore how the sectors of a circle can be arranged to make a parallelogram and later a rectangle.
  • The area of a semi-circle is half the area of a circle.
  • A sector is a fraction of a circle.  The fraction is determined by the angle, theta of the sector over 360°.
  • Students should be able to derive the formulae for the area and arc length of a sector.
  • Students need to be equally confident leaving answers in terms of pi as they are with decimals

Common Misconceptions

  • Students often confuse the area and circumference formulae
  • Students often confuse the different names for the parts of a circle.
  • Students often make rounding errors when approximating solutions.  Encourage students to work in terms of pi until the final stage of the question.

Circles and Circular Shapes Resources

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