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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