Senior Maths SHAPE AND SPACE Shape and space

Senior Maths SHAPE AND SPACE

Shape and space – 2 D Shapes �Children need to know �Names of 2 D shapes �Definition of a polygon: a 2 D 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 2 D 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

3 D Shapes With 3 D shapes, the major issues are: �Number of faces �Number of edges �Number of vertices �Identification of shapes �Identification and construction of nets

Example �Look at the net below. What 3 D 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)