SHAPE AND SPACE

Senior Maths

Shape and space – 2D Shapes

Children need to know Names of 2D shapesDefinition of a polygon: a 2D shape bordered

by straight lines which has the same number of sides as it has angles

Examples of polygons: triangle, quadrilateral,pentagon, hexagon,heptagon,octagon,nonagon,decagon

Properties, number of sides, number of congruent sides, number and types of angle, sum of angles (divide into triangles)

The Joy of Triangles!

•3 types of triangle: equilateral, isoceles and scalene, type dependent on number of congruent sides and angles!•3 equal sides, 2 equal angles = equilateral•2 equal sides, 2 equal angles = isoceles•0 equal sides, 0 equal angles = scalene•Right angled triangle a special case, can be scalene or isoceles but never equilateral•Angles in a triangle always add up to 180•To find the missing angle in a triangle, add the 2 given angles and subtract from 180•Children should be able to construct a triangle given the length of 2 sides and one angle.•Children should be able to calculate the sum of the angles in any polygon by dividing it into triangles.•Discuss practical use of triangles e.g. in roof struts.

Other 2D shapes

Children will need to know names and properties of polygons from 4 – 10 sides

Will need to know: number and types of angles, number of sides, number of parallel sides, number of equal sides.

Lines and angles

Definitions of lines: vertical, horizontal, diagonal (oblique) parallel and perpendicular – last 2 terms present difficulty.

Vertical Horizontal Diagonal Parallel Perpendicular

Types of angles

Measuring and constructing angles

This is a BIG problem for a lot of kids!Introducing …the protractor!

The Protractor

A major cause of confusion is which line of figures to use.

We explain it as follows: The line of figures you use depends on (a) whether you measure from the right or the left or (b) whether you’re measuring an obtuse or acute angle.

Here’s a useful link: http://www.mathplayground.com/measuringangles.html

3D Shapes

With 3D shapes, the major issues are:Number of facesNumber of edgesNumber of verticesIdentification of shapesIdentification and construction of nets

Example

Look at the net below. What 3D shape does it represent?

Example (2)

Identify this shape:How many faces has it?How many edges has it?How many vertices has it?Will it stack neatly with other shapes of the

same type?

Rotations

This is an area which causes frequent problems. It requires a specialised skill – spatial ability.

Here’s an example: Rotate this shape 90 clockwise.

(a) (b)