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National Curriculum: Geometry and measures - KS3

Created on 23 October 2013 by ncetm_administrator
Updated on 04 June 2014 by ncetm_administrator

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

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30 June 2014 16:30
Thank you :)
By Lam2512
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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.
By RobertWilne
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19 June 2014 11:39
Help! What does this mean?!

'interpret mathematical relationships both algebraically and geometrically'

What sort of quesion would evidence being able to do this?
By Lam2512
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