Circles

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

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

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

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.