Circles, Cylinders and Circular Shapes

Scheme of work: Key Stage 3: Year 8: Term 4: Circles, Cylinders and Circular Shapes

Derive and apply formulae to calculate and solve problems involving: the perimeter and area of triangles, parallelograms, trapezia, the volume of cuboids (including cubes) and other prisms.
Calculate and solve problems involving: perimeters of 2-D shapes and composite shapes.

The radius is the distance from the centre to any point on the circumference. The plural radius is radii.
The diameter is the distance across the circle through the centre.
Ï€ is a Greek letter used to represent the value of the circumference of a circle divided by its diameter.
The circumference is the distance about the edge of a circle. The circumference of a circle can be calculated as:
- C = ÏπD where D is the diameter, or,
- C = 2πr
- Where r is the radius.
The area of a circle can be calculated using the formula
- A = πr², where r is the radius.
A cylinder is a circular prism.

Develop fluency
- Use language and properties precisely to analyse numbers, algebraic expressions, 2-D
  and 3-D shapes, probability and statistics.
- Use algebra to generalise the structure of arithmetic, including to formulate
  mathematical relationships
- Substitute values in expressions, rearrange and simplify expressions, and solve
  equations
Reason mathematically
- Make and test conjectures about patterns and relationships; look for proofs or counterexamples.
- Begin to reason deductively in geometry, number and algebra, including using geometrical constructions
Solve problems
- Begin to model situations mathematically and express the results using a range of
  formal mathematical representations
- Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine
  problems.

Shape
- Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
- Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
- Derive and apply formulae to calculate and solve problems involving: perimeter and area of circles and cylinders