Area mm

square millimetre

cm

square centimetre

m2

square metre

2

2

km2 ha

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.

L kL

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.

chronological

Sport played

circumference (c)

surface area (sa)

litre

The perimeter of a circle; the distance measured around a circle.

The total area of the outside surface of a 3-D shape.

heft

volume (v)

To test the weight of objects by lifting them in the hands and comparing them.

The amount of space occupied by an object.

Mass milligram

g

gram

kg

kilogram

height (h)

width (w)

The highest part of a shape from the base.

The distance from one side to another; the breadth (B).

tonne

°F

degree Fahrenheit

K

kelvin

Time s min

second

hour

d

day

m.

month

cent. or C

Perimeter: =4xl Area: =lxl or = l2

year century

Perimeter: =s+s+s Area: = 12 x (b x h) base

minute

h

yr or y.

Triangle

Square

Rectangle Perimeter: = 2 x (l + w) Area: =lxw length

Circle

Circumference: = 2 r or x d

diameter

s diu

ra

Area: = r2

Vi

degree Celsius

height

°C

ew

Rules and formulas

Temperature

Portions of a circle are used to show a whole divided into parts.

The edge of a 2-D shape.

millilitre

Jason

Boys

46

43

49

32

Dan

Dan

Girls

40

50

35

49

Total

86

93

84

81

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.

Tally

Percentage 100

8

34 x 200 8 200 x

swimming

50

50 x 200

100

This is a stroke which is used to record items. Tallies generally use a diagonal stroke on the ﬁfth item.

netball

34

34 x 200

100

For example:

rugby

24

100

50

24 x 200 50 x 200

football

34

cricket

100

100

football

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:

Even

Not even

Square

4, 16

1, 9

Not square

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:

Roll 1

1

2

3

4

5

6

array

Roll 2

1

2

3

4

5

6

A display of objects in some regular arrangement. An arrangement in rows and columns.

Roll 3

1

2

3

4

5

6

Roll 4

1

2

3

4

5

6

Roll 5

1

2

3

4

5

6

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

1 4

chance of two heads landing face up.

Statistics Collecting and classifying information and data from a sample for a specific purpose.

rugby

A graph which plots along a vertical and horizontal axis the relationship between two variable quantities.

= 12

Venn diagram

Cube

Sur fac = 6 e area: x (l x h)

Kylie

Tree diagram

Pie chart

side (s)

Describes dates arranged in the order in which they occur.

kilolitre

mg

capacity

Jason

Kylie

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

Bar chart

pi ( )

width

Data

perimeter (p)

A particular side of a shape from which the height of an object can be measured.

sid e

Measurement

mL

t

Maths

The measurement of surfaces and regions, usually expressed in square units of measurement.

base (b)

Capacity

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

kilometre

area (a)

Arrow diagram

Is used to display a number of possibilities. For example:

Green

km

mass (weight)

These are used to organise data for a particular purpose. For example:

Red

metre

The distance measured from end to end.

Chance

Tables

Blue

m

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.

pl e

centimetre

length (l)

Diagrams

A graph in which data is represented by pictures. One picture could represent one unit or many.

m

cm

arbitrary units

Pictogram

Sa

millimetre

Graphs

No. of pupils

mm

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Mathematical terms

length

Shape and space

Length

Data

Data

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g

Units of measurement

Measurement

in

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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

mode

(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.

mean (average)

median

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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Measurement

= 1 cm =1m = 1 km

Area

1000 mL = 1 L 1000 L = 1 kL

Time 60 seconds = 1 minute

10 cm, 3 mm

10.3 cm

2 m, 7 cm, 5 mm

2.075 m 3.40852 km

6 L, 430 mL

6.43 L

15 kL, 675 L

15.675 kL

12 g, 325 mg

12.325 g

100 mm2 = 1 cm2 10 000 cm2 = 1 m2

60 minutes = 1 hour 24 hours

= 1 day

10 000 m2 100 ha

7 days

= 1 week

4 kg, 75 g

4.075 kg

14 days

= 1 fortnight

5 t, 620 kg

5.62 t

= 1 ha = 1 km2

Equivalent metric and imperial units

12 months = 1 year 365 days

= 1 year

366 days

= 1 leap year

10 years

100 years

= 1 century

1000 years = 1 millennium

Time

acute angle

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

length

tape measure balance bathroom scales

r hou

d

han

measuring spoons

capacity

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.

obtuse angle

reflex angle

An angle between 180° and 360°.

reﬂex angle

March ..............................31 days

April ................................30 days May..................................31 days

edges

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.

plane

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.

scale

tangram

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.

perpendicular

A transformation is a movement that does not change the size or shape of a ﬁgure. These movements are:

reflection (flip)

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.

ray

prisms

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.

vertices

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

pattern

classification

horizontal

straight angle An angle which is exactly 180°.

symmetry—plane

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:

translation (slide)

PR–6817 ISBN 1-84654-026-7

pm

February ...............28 or 29 days

The surface area of a three-dimensional ﬁgure.

Vi

am

right angle

Three-dimensional shapes are also called ‘solid figures’. A 3-D shape has length, width and height.

faces

The day is divided into:

An angle of exactly 90°.

3-D shapes

kitchen scales

ew

minute hand

trundle wheel

mass

right angle

An angle between 90° and 180°.

Two shapes are similar when they have the same shape but are different in size.

9!BMFCIA:TSOQUS!

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°.

acute angle

obtuse angle

Measuring tools

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.

Sa

=1g = 1 kg =1t

Volume

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.

g

~ 52 weeks = 1 year

similar

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’.

net

attribute

2-D shapes have two dimensions—width and length. They may have curved or straight sides.

28–31 days = 1 month

Mass

Moving in the opposite direction to the hands on a clock.

Angles

2-D shapes

3 km, 408 m, 52 cm

anticlockwise

Shape and space

in

10 mm 100 cm 1000 m

Measurements should be written in decimal form where possible. For example;

Capacity

Mathematical terms

pl e

Length

Decimal measures

m

Equivalent measures

Shape and space

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6817 Shape/Space/Measurement/Data Study Guide