Transcript Senior Maths

Senior Maths
SHAPE AND SPACE
Shape and space – 2D Shapes
 Children need to know
 Names of 2D shapes
 Definition 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 faces
 Number of edges
 Number of vertices
 Identification of shapes
 Identification 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)