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Circles, cylinders and circular shapes follows on from area of 2D shapes and surface area of 3D cuboids and prisms which students study in Term 2 of Year 8.

In this unit students learn how to calculate the circumference and area of circles both as decimals and in terms of π. Learning progresses from 2D circles to finding the total surface area and volume of cylinders.

- Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, 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 of radius is radii.
- The diameter is the distance across the circle through the centre.
- π 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 = πD 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 = πr
^{2}where r is the radius.

- A = πr
- 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.

June 8, 2018

To introduce teaching reciprocals of numbers and terms I begin the lesson explaining that everything has an opposite. The opposite of shutting a door is to open it. The opposite of saying hello is to say goodbye. Numbers have opposites too we call them reciprocals. Teaching Reciprocals of Numbers and Terms To start the lesson […]

May 11, 2018

When I teach how to find the surface area of cylinders I like to add a constant level of challenge and enjoyment to the lesson. Rather than repetitively calculating the surface area of a cylinder I introduce more complex cylindrical shapes. How to find the Surface Area of Cylinders To find the surface area of […]

April 15, 2018

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching […]