National Curriculum: Geometry and measures - Key Stage 3

Pupils should be taught to:

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 (including cylinders)

calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

draw and measure line segments and angles in geometric figures, including interpreting scale drawings

derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

understand and use the relationship between parallel lines and alternate and corresponding angles

derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

interpret mathematical relationships both algebraically and geometrically

30 June 2014 15:26 Pupils need to be able to use symbols to describe geometric properties: for example, a question could say that a cone has equal radius and height and volume 1 litre, and then ask what the radius is; or a question could say that in a certain isosceles triangle, one angle is three times the size of another angle, and then ask for the size of each angle. These sorts of questions require pupils to take a geometric statement and "algebratise" it, prior to solving a problem. The reverse could also be required: for example, a question could ask for a comment with a reason about a triangle with lengths 3x, 4x and 5x, where x is any (real) number, and the expected answer would be that the triangle must be right angled because (3x)^2 + (4x)^2 always equals (5x)^2. I hope this is helpful. Robert Wilne, Director for Secondary.

Thank you :)