square kilometre hectare
The length of the boundary of a plane region. In a polygon, it is the sum of the lengths of all sides.
The amount of space inside a container. What it holds, measured in mL, L etc.
The distance from the centre of a circle to a point on its circumference.
surface area (sa)
The perimeter of a circle; the distance measured around a circle.
The total area of the outside surface of a 3-D shape.
To test the weight of objects by lifting them in the hands and comparing them.
The amount of space occupied by an object.
The highest part of a shape from the base.
The distance from one side to another; the breadth (B).
Time s min
cent. or C
Perimeter: =4xl Area: =lxl or = l2
Perimeter: =s+s+s Area: = 12 x (b x h) base
yr or y.
Rectangle Perimeter: = 2 x (l + w) Area: =lxw length
Circumference: = 2 r or x d
Area: = r2
Rules and formulas
Portions of a circle are used to show a whole divided into parts.
The edge of a 2-D shape.
These are used for classiﬁcation activities or to show possible outcomes of chance events.
Line graph A graph which has a vertical and horizontal axis and is formed by joining points with straight lines to represent data.
34 x 200 8 200 x
50 x 200
This is a stroke which is used to record items. Tallies generally use a diagonal stroke on the ﬁfth item.
34 x 200
24 x 200 50 x 200
Named after John Venn, an English logician. This diagram is used to represent the classiﬁcation of sets of items. It is possible to make a Carroll diagram from any Venn diagram.
Scatter graph Carroll diagram Named after Lewis Carroll; author, mathematician and logician. This diagram is useful when recording classiﬁcation data.
Data can be collected from a set group of people or from a ‘random sample’. A random sample is where every member of the sample has an equal chance of being chosen. For example:
2, 6, 8, 10, 12, 14, 18, 20
3, 5, 7, 11, 13, 15, 17, 19
Some common terms used in chance are: outcome A result.
probability The likelihood of a particular outcome in a chance event. For example:
The probability of throwing a ‘head’ on the toss 1 of a coin is 2 .
To calculate a chance event, we can use the following techniques:
A display of objects in some regular arrangement. An arrangement in rows and columns.
combination A subset obtained from a given set according to certain conditions. For example:
If I toss two coins, what are the chances of two heads landing face up?
HH HT TH TT (Each pairing is called a combination.) I have a
chance of two heads landing face up.
Statistics Collecting and classifying information and data from a sample for a specific purpose.
A graph which plots along a vertical and horizontal axis the relationship between two variable quantities.
Sur fac = 6 e area: x (l x h)
Describes dates arranged in the order in which they occur.
A graph which represents information regarding frequency of outcomes using bar lengths. The graph has a vertical and horizontal axis. The bars may be vertical or horizontal.
The ratio of the circumference of a circle to its diameter. It is approximately 3.14.
Number of children in each team
Is a sibling of
pi ( )
A particular side of a shape from which the height of an object can be measured.
The measurement of surfaces and regions, usually expressed in square units of measurement.
6817RE maths 2.indd 1
The amount of matter in an object.
The likelihood of an event occurring. For example:
We have a 1 in 6 chance of throwing a 6 on a die.This 1 would be written as 6 . Gold
Is used to display a number of possibilities. For example:
These are used to organise data for a particular purpose. For example:
The distance measured from end to end.
Non-standard units of measure; e.g. hand spans, counters, tiles, claps.
Information is often recorded in pictorial form. This can be done in many different ways depending on how we need the information to be presented.
Some data is best displayed in a diagram. There are many different types of diagrams.
A graph in which data is represented by pictures. One picture could represent one unit or many.
No. of pupils
Shape and space
Units of measurement
Test scores from a random group of pupils were collected. They are as follows: 11 18 13 16 16 16 19 12 15 14
Once the data is collected it can be used to calculate: range
(of a distribution)
The measurement or observation that occurs most often; the item with the highest frequency. For example:
The difference between the greatest and least values in a set of data. For example:
The greatest value is 19, the least value is 11. Therefore, the range is 19 – 11 = 8.
The test score which occurs most frequently is 16. The mode is 16.
The mean of a set of numbers is a single number used to represent the set. It is calculated by dividing the sum of the numbers by the number in the sample. For example: 11 + 18 + 13 + 16 + 16 + 16 + 19 + 12 + 15 + 14 = 150 150 ÷ 10 (pupils) = 15
The middle measurement, or score, when items are arranged in order of size. Where there is no middle score, a mean of the two central scores is taken. For example: 11, 12, 13, 14, 15, 16, 16, 16, 18, 19
The mean is 15.
The median is 15 + 16 = 15.5 2
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= 1 cm =1m = 1 km
1000 mL = 1 L 1000 L = 1 kL
Time 60 seconds = 1 minute
10 cm, 3 mm
2 m, 7 cm, 5 mm
2.075 m 3.40852 km
6 L, 430 mL
15 kL, 675 L
12 g, 325 mg
100 mm2 = 1 cm2 10 000 cm2 = 1 m2
60 minutes = 1 hour 24 hours
= 1 day
10 000 m2 100 ha
= 1 week
4 kg, 75 g
= 1 fortnight
5 t, 620 kg
= 1 ha = 1 km2
Equivalent metric and imperial units
12 months = 1 year 365 days
= 1 year
= 1 leap year
= 1 decade
= 1 century
1000 years = 1 millennium
Polygons with sides of an equal length and angles of an equal size are called regular polygons.
1 metre = 3.3 yards 1 kilometre = 0.6 miles 1 kilogram = 2.2 lb 1 litre = 1.75 pints
Polygons with three sides are called ‘triangles’.
Various tools are used to measure in different situations. For example: ruler
tape measure balance bathroom scales
measuring cups measuring jugs graduated cylinders
Months of the year
January ...........................31 days
Parts of a 3-D shape include:
before noon (ante meridiem) and after noon (post meridiem). The duration of time can also be measured. In some sporting activities, times are measured to one-hundredth of a second using a stopwatch.
Other shapes include circles, semicircles and ellipses.
An angle between 180° and 360°.
March ..............................31 days
April ................................30 days May..................................31 days
The intersections of two faces of a three-dimensional ﬁgure.
June .................................30 days July ..................................31 days
August ............................31 days September .....................30 days October ..........................31 days
November ......................30 days
December ......................31 days
There are different types of 3-D shapes:
A characteristic of an object. A way to classify objects; e.g. round, red, thick.
A repeated sequence; e.g.
Arrangement into classes (sets or groups) accordng to attributes.
clockwise Moving in the same direction as the hands on a clock.
congruent Two ﬁgures are congruent if they are the same size and shape.
model A representation of an object preserving the signiﬁcant features.
line Made up of an inﬁnite set of points extending in both directions.
symmetry—rotational A two- or three-dimensional shape or object is rotated about a point and remains the same shape.
The ratio of measurements of a model or diagram to corresponding measurements of an enlarged or reduced version.
section A ﬂat surface made by cutting through a solid in any direction.
A Chinese puzzle made of a square cut into seven pieces. All seven pieces can be rearranged to make shapes and pictures.
tessellation A repeating pattern of congruent shapes that completely cover an area leaving no gaps or overlaps.
Transformation parallel lines Two or more straight lines in the same plane which will never meet. They are always the same distance apart.
A transformation is a movement that does not change the size or shape of a ﬁgure. These movements are:
Two lines which form right angles.
line segment A line with two end points.
oblique line A line at an angle, (slanting/sloping).
plane A ﬂat surface which has no boundaries.
Made up of an inﬁnite set of points emanating from a point and going in one direction.
The two ends of a prism are the same size and shape; they are congruent.
rotation (turn) (about a point – x)
vertical A line which is perpendicular to the horizon.
The intersections of two or more edges of a three-dimensional ﬁgure.
A line or plane divides a two- or threedimensional shape or object so that the two parts are mirror images of one another.
A surface which is ﬂat and has no boundaries.
Lines Describes a line or plane parallel to the horizon.
straight angle An angle which is exactly 180°.
pyramids A pyramid is made up of a base shape such as a triangle, square, hexagon or decagon. The opposite end of the shape forms a point called an ‘apex’.
Coordinates A point on a grid can be referenced using an ‘ordered pair’ of numbers. These are called the coordinates of the point. The horizontal axis is always read or written before the vertical axis. For example:
PR–6817 ISBN 1-84654-026-7
February ...............28 or 29 days
The surface area of a three-dimensional ﬁgure.
Three-dimensional shapes are also called ‘solid figures’. A 3-D shape has length, width and height.
The day is divided into:
An angle of exactly 90°.
An angle between 90° and 180°.
Two shapes are similar when they have the same shape but are different in size.
Analogue time midnight 1.00 am 2.00 am 3.00 am 4.00 am 5.00 am 6.00 am 7.00 am 8.00 am 9.00 am 10.00 am 11.00 am midday 1.00 pm 2.00 pm 3.00 pm 4.00 pm 5.00 pm 6.00 pm 7.00 pm 8.00 pm 9.00 pm 10.00 pm 11.00 pm
An analogue clock shows the time by continuously moving two hands, an hour hand and a minute hand. It may also have a second hand.
An angle less than 90°.
Time can be a moment, hour, day or year as shown on a clock or calendar. Time can be shown in digital form, analogue or 24-hour time.
Quadrilaterals with both pairs of opposite sides parallel, and equal angles, are called ‘parallelograms’.
A ﬂat pattern that can be folded to make a three-dimensional model.
1000 mm3 = 1 cm3 3 1 000 000 cm = 1 m3
6817RE maths 2.indd 2
A degree (°) is a unit of angular measure. There are 360° in one complete rotation. A protractor is a tool used to measure the size of an angle.
=1g = 1 kg =1t
24-hour time 0000 0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300
Shapes with straight sides are called ‘polygons’. Polygons have three or more sides and angles.
~ 52 weeks = 1 year
No part of this publication may be reproduced in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage and retrieval system, without written permission from the publisher.
1000 mg 1000 g 1000 kg
An angle ( ) is formed when two lines meet. Angles are measured in degrees.
Polygons with four sides are called ‘quadrilaterals’.
2-D shapes have two dimensions—width and length. They may have curved or straight sides.
28–31 days = 1 month
Moving in the opposite direction to the hands on a clock.
3 km, 408 m, 52 cm
Shape and space
10 mm 100 cm 1000 m
Measurements should be written in decimal form where possible. For example;
Shape and space
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