Circles, Cylinders and Circular Shapes

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

Prerequisite Knowledge

  • 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.

Key Concepts

  • 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.

Working Mathematically

  • 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.

Subject Content

  • 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

Circles, Cylinders and Circular Shapes  Resources

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