Foundation GCSE Scheme of Work Circles

Students learn how to calculate the area and circumference of circles.  Later, as learning progresses they find the composite area and perimeter of circular shapes, including sectors.

Circles and Circular Shapes Lessons

Revision & Problem-Solving Lessons

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.

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