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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. Circles, cylinders and circular shapes typically takes 6 one hour lessons.

- 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.

February 16, 2018

Back in May 2017 maths teachers around the country eagerly awaited the first exam for the new GCSE Mathematics syllabus. Proving geometrical relationships using algebra featured at grade 9. In Paper 1 of Edexcel’s test paper the last question of the higher tier looked like this. Edexcel wrote about student’s performance on this question in […]

February 10, 2018

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 […]

January 28, 2018

Higher GCSE maths students are required to plot and interpret histograms with unequal class widths. Drawing histograms with unequal class widths are very common in GCSE maths papers. Histograms versus bar charts Histograms look like bar charts but have important differences. Histograms use a continuous horizontal scale which means the bars touch so the difference […]