Title Chapter06-Patterns and Rules Variable (Mathematics) Formula Atomic Nucleus Algebra Physics & Mathematics 3.6 MB 30
```                            Student text
Imprint page
Preface
How to use this book
How to use the CD-ROM
Acknowledgements
Syllabus reference grid
1 The history of numbers
Different number systems
The Hindu–Arabic number system
Place value
Expanded notation
The four operations
Arithmagons
Dividing by a two-digit number
Order of operations
The symbols of mathematics
Topic overview
Chapter review
2 Angles
Naming angles
Comparing angle size
The protractor
Drawing angles
Angle geometry
Naming lines
Angles and parallel lines
Finding parallel lines
Topic overview
Chapter review
3 Exploring numbers
Special number patterns
Tests for divisibility
Factors
Prime and composite numbers
Prime factors
Index notation
Squares, cubes and roots
Topic overview
Chapter review
Mixed revision 1
4 Solids
Naming solids
Convex and non-convex solids
Polyhedra
Prisms and pyramids
Cylinders, cones and spheres
Classifying solids
Euler’s rule
Edges of a solid
The Platonic solids
Drawing and building solids
Different views of solids
Topic overview
Chapter review
5 Integers
Number lines
Numbers above and below zero
Directed numbers
Ordering directed numbers
Adding and subtracting integers
Multiplying integers
Dividing integers
The four operations with integers
Reading a map grid
The number plane
The number plane with negative numbers
Topic overview
Chapter review
6 Patterns and rules
Number rules from geometric patterns
Using pattern rules
The language of algebra
Tables of values
Finding the rule
Finding harder rules
Finding rules for geometric patterns
Algebraic abbreviations
Substitution
Substitution with negative numbers
Topic overview
Chapter review
Mixed revision 2
7 Decimals
Place value
Understanding the point
Ordering decimals
Decimals are special fractions
Adding and subtracting decimals
Multiplying and dividing by powers of 10
Multiplying decimals
Calculating change
Dividing decimals
Decimals at work
Converting common fractions to decimals
Recurring decimals
Rounding decimals
More decimals at work
Topic overview
Chapter review
8 Length and area
The history of measurement
The metric system
Converting units of length
The accuracy of measuring instruments
Estimating and measuring length
Perimeter
Area
Converting units of area
Area of squares, rectangles and triangles
Areas of composite shapes
Measuring large areas
Topic overview
Chapter review
9 Geometric figures
Polygons
Classifying triangles
Naming geometric figures
Constructing triangles
Constructing perpendicular and parallel lines
Topic overview
Chapter review
Mixed revision 3
10 Fractions
Highest common factor and lowest common multiple
Naming fractions
Equivalent fractions
Ordering fractions
Adding and subtracting fractions
Adding and subtracting mixed numerals
Fractions of quantities
Multiplying fractions
Dividing fractions
Topic overview
Chapter review
11 Volume, mass and time
Volume
Volume of a rectangular prism
Capacity and liquid measure
Mass
Timelines
Converting units of time
Time calculations
World standard times
Timetables
Topic overview
Chapter review
12 Algebra
Algebraic expressions
Algebraic abbreviations
From words to algebraic expressions
Like terms
Multiplying algebraic terms
Expanding an expression
Expanding and simplifying
Algebraic substitution
Topic overview
Chapter review
13 Interpreting graphs and tables
Picture graphs
Column graphs and divided bar graphs
Sector graphs
Line graphs
Travel graphs and conversion graphs
Step graphs
Topic overview
Chapter review
Mixed revision 4
General revision
Index
Glossary
A
B
C
D
E
F
G H
I J
K L
M
N
O
P
Q
R
S
T
U V
W X Y Z
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 11
Chapter 12
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 13
Help
Licence agreement
```
##### Document Text Contents
Page 1

PR_skilltest plus_L

Patterns and algebra

Patterns
and rules

6

Mathematicians and scientists try to find patterns in their investigations
and then make rules to describe the patterns. You did a similar thing
with Euler’s rule in Chapter 4.

This chapter introduces you to the language of mathematics called

algebra

. It is used to write the rules which describe mathematical and
scientific relationships.

Page 2

PR_worksheet plus_L

■ build a geometric pattern, complete a table of values and describe the
pattern in words and as a formula

■ use the rule to calculate the corresponding value for a larger number
■ translate between words and algebraic symbols
■ understand and use variables, algebraic abbreviations and formulas
■ determine a formula to describe the pattern in a table of values
■ substitute into algebraic expressions
■ generate a number pattern from an algebraic expression.

■ algebra A mathematical language for describing relationships using
letters to stand for numbers.

■ formula A general mathematical rule written using letters and symbols.
■ variable A letter of the alphabet used to stand for a number.
■ pronumeral Another name for a variable.
■ substitute To replace a letter (variable) with a number.
■ evaluate To find the value of an algebraic expression after substituting.

Evan the taxi driver charges different fares for different journeys. For a 5 km
trip, he charges \$6.80. For a 10 km trip, it’s \$10.30. For a 14 km trip. it’s
\$13.10. How much will Evan charge for a 20 km trip? Can you find a
mathematical rule?

In this chapter you will:

Wordbank

Think!

PATTERNS AND RULES 167

CHAPTER 6

Page 15

PR_worksheet plus_L

180 NEW CENTURY MATHS 7

1 Find the rule used for each of the following tables, then complete the last two columns
of each table:

2 Find the rule used for each of the following tables, then complete the last two columns
of each table:

a f 1 2 3 4 5 6 7 8

h 1 4 7 10 13 16

b m 1 2 3 4 5 6 7 8

p 2 7 12 17 22 27

c m 0 1 2 3 4 5 6 7

b 3 6 9 12 15 18

d h 3 4 5 6 7 8 9 10

k 8 10 12 14 16 18

e r 0 1 2 3 4 5 6 7

s 1 4 7 10 13 16

f a 2 3 4 5 6 7 8 9

b 2 4 6 8 10 12

a m 0 1 2 3 4 5 6 7

n 5 8 11 14 17 20

b c 1 2 3 4 5 6 7 8

d 11 21 31 41 51 61

c w 1 2 3 4 5 6 7 8

x 4 9 14 19 24 29

d y 3 4 5 6 7 8 9 10

z 0 2 4 6 8 10

e a 1 2 3 4 5 6 7 8

m 5 9 13 17 21 25

Exercise 6-06
Example 5

Page 16

PR_worksheet plus_R

PATTERNS AND RULES 181 CHAPTER 6

Finding rules for geometric patterns

3 For practice, use the link to take you to an Excel file that has more of these exercises.

f z 4 5 6 7 8 9 10 11

t 1 3 5 7 9 11

g d 0 1 2 3 4 5 6 7

a 4 7 10 13 16 19

h g 3 1 5 2 10 6 7 4

h 4 0 8 2 18 10

i j 8 3 10 1 7 2 5 4

k 22 7 28 1 19 4

j w 5 1 3 6 4 2 8 10

t 49 9 29 59 39 19

6-04

Tables and
rules

Worksheet
6-04

Patterns and
rules

Example 6

arm length 1 arm length 2 arm length 3

a Copy and complete this table about the pattern above.

b In words, write the rule for your completed table.
c Write the rule as a formula.
d How many tiles would be needed for an arm length of

i 50? ii 100?

Solution

Arm length, a 1 2 3 4 5 7 9

Number of tiles, t

a Arm length, a 1 2 3 4 5 7 9

Number of tiles, t 3 5 7 9 11 15 19

Page 29

RV_skillbuilder plus_L

194 NEW CENTURY MATHS 7

Chapter 6 Review Topic test
Chapter 6

1 Bridges.
Here are the first three bridge shapes. Copy and complete the results table below.

2 Copy and complete each of these tables:
a n = 5m

b q = p − 7

c d = 3c − 4

3 Find the rule used for each of these tables:

Each new paddock pattern is made by adding fence sections.

a Make a results table to show the pattern for the number of paddocks and the number
of fence sections.

Lanes on bridge 1 2 3 4 5 7 9 50 100

Number of tiles 5 6 16

m 1 3 12 0 7 4 2 11

n

p 10 7 11 15 20 18 14 30

q

c 2 12 5 3 7 20 9 6

d

a x 12 4 8 7 2 9 b a 3 1 4 6 11 5

y 10 2 6 5 0 7 b 21 7 28 42 77 35

c m 16 8 40 56 36 28 d r 7 2 0 9 4 6

n 4 2 10 14 9 7 t 11 6 4 13 8 10

e g 1 2 3 4 5 6 f p 7 8 9 10 11 12

k 5 8 11 14 17 20 q 4 6 8 10 12 14

Ex 6-01

1-lane bridge 2-lane bridge 3-lane bridge

Ex 6-04

Ex 6-05

Ex 6-01

Page 30

PR_worksheet plus_R

PATTERNS AND RULES 195 CHAPTER 6

b In words, write the rule linking the number of paddocks with the number of fence
sections needed to make them.

c Write the rule as a formula.
d Calculate the number of fence sections required to make 100 paddocks.

5 Terrace houses.
A pattern of terrace houses made of sticks is shown:

a Make a table and find the rule connecting the number of houses in the terrace and
the number of sticks.

b Calculate the number of sticks needed to make a terrace of 21 houses.

6 a Here are the first four diagrams of a pattern. Draw the next one.

b Copy and complete the results table:

c Write the rule for the pattern, in words.
d Write the rule as a formula.
e How many triangles would there be if there were:

i 14 dots? ii 50 dots?

7 Copy and complete each of the following tables:
a f = g + 5 b B = 3A − 2

c B = 5A + 10 d y = 200 − 5x

e j = + 3

f q = 4p − 7

Number of dots 2 4 6 8 10

Number of triangles 0 4

g 1 3 5 7 120 A 5 6 7 10 30

f B

A 1 2 3 78 89 x 1 5 10 12 20

B y

k 2 −2 6 −4 −8 12 −10 −20

j

p 3 −1 −3 6 0 −2 1 −5

q

Ex 6-07

1-house
terrace

2-house
terrace

3-house
terrace

4-house
terrace

Ex 6-07

Ex 6-09

k
2
---