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# National Curriculum: Geometry and measures - KS3 - Articles

Created on 24 October 2013 by ncetm_administrator
Updated on 04 June 2014 by ncetm_administrator

# Activities

## Cuboid Challenge

In this activity pupils investigate the volume of a box, without a lid, made from a square sheet of paper. It extends into maximum volumes and investigating the relationships between the size of the paper, the size of the corner cut and the maximum volume.

This activity enables pupils 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)

## Pick’s Theorem

This activity invites pupils to find a relationship between the perimeter, area, the number of dots on the perimeter and inside shapes drawn on square dotty paper. The shapes are generated by joining points with straight lines.

This activity enables the pupils to:

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

## Triangle Tantaliser

This activity invites pupils to draw all the possible distinct triangles on a 4 × 4 dotty grid. In doing so they use and apply concepts of rotation, reflection, translation and congruence.

This activity enables the pupils to:

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

## Property Chart

While doing this activity pupils draw and work collaboratively to identify quadrilaterals with two given properties.

This activity enables the pupils to:

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

## Combining transformations

Pupils investigate the outcome of repeating and combining transformations and inverse transformations, including reflections, rotations and transformations both geometrically and algebraically.

This activity enables the pupils to:

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

## Who is the fairest of them all?

This activity requires pupils to draw enlargements with scale factors k and 1/k with different centres of enlargement and to investigate the single transformation that maps from one enlargement to the other.

This activity enables the pupils to:

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

## Weekly problem 3 - 2012

This activity requires learners to apply Pythagoras’ Theorem to decide which pieces of hardboard can be passed through a window frame.

This activity enables the pupils to:

• use Pythagoras’ Theorem … to solve problems involving right-angled triangles

## 3-D shapes –Short Problems

These short activities support pupils to develop their skills to solve problems in 3-D.

This activity enables the pupils to:

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

## Bull’s Eye and Algebra from geometry

These two linked activities enable the pupils to:

• interpret mathematical relationships both algebraically and geometrically

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