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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**

- 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

- 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 = πr
^{2}; - 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.

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