1
WORK PROGRAM
Chapter 4 Algebra
Strands: Patterns and algebra; Number
Substrands and outcomes:
Algebraic techniques
PAS4.1 Uses letters to represent numbers and translates between words and algebraic symbols
Algebraic techniques
PAS4.3 Uses the algebraic symbol system simplify, expand and factorise simple algebraic expressions
Algebraic techniques
PAS5.1.1 Applies the index laws to simplify algebraic expressions
Fractions, decimals and percentages NS4.3 Operates with fractions, decimals, percentages, ratios and rates
Section
Are you ready? (page 134)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles
SkillSHEETs,
WorkSHEETs, Interactive
games, Test yourself,
Topic tests
(CD–ROM)
SkillSHEETs (page 134)
4.1: Alternate expressions
used to describe the
four operations
4.2: Completing a formula
for a table of values
4.3: Writing a formula for
a table of values
4.7: Combining like terms
4.8: Simplifying fractions
4.9: Highest common
factor
4.10: Operations with
fractions
Technology applications
(CD–ROM)
Learning outcomes
PAS4.1
 using letters to
represent numbers and
developing the notion
that a letter is used to
represent a variable
 translating between
words and algebraic
symbols
PAS4.3
 recognising like terms
and adding and
subtracting like terms
to simplify algebraic
expressions
NS4.3
 finding highest
2
Using pronumerals
(page 135)
WE 1a-f
Ex 4A Using pronumerals
(page 137)
Substitution (page 142)
WE 2a-b, 3
Maths Quest challenge:
Q1-4 (page 139)
Investigation: Patterns and
rules (page 140)
SkillSHEET 4.1:
Alternative expressions
used to describe the
four operations
(page 137)
SkillSHEET 4.2:
Completing a formula
for a table of values
(page 141)
SkillSHEET 4.3: Writing a
formula for a table of
values (page 141)
SkillSHEET 4.4: Order of
operations II
Mathcad: Substitution
(page 144)
common factors
 reducing a fraction to
its lowest equivalent
form
 adding fractions using
written methods
 multiplying and
dividing fractions
PAS4.1
 using letters to
represent numbers and
developing the notion
that a letter is used to
represent a variable
 translating between
words and algebraic
symbols and between
algebraic symbols and
words
 linking algebra with
generalised arithmetic
(Reflecting)
PAS4.3
 distinguishing between
algebraic expressions
where letters are used
as variables, and
equations, where
letters are used as
unknowns
PAS4.3
 substituting into
3
Ex 4B Substitution
(page 144)
(page 144)
Game time 001 (page 145)
Excel: Substitution
(page 144)
Excel: Substitution game
(page 144)
Working with grouping
symbols (page 145)
WE 4a-b
Ex 4C Working with
grouping symbols
(page 145)
SkillSHEET 4.5: Order of
operations with
grouping symbols
(page 146)
Mathcad: Substitution
(grouping symbols)
(page 146)
SkillSHEET 4.6:
Mathcad: Substitution
Substituting positive and
Investigation: ‘Rules of
algebraic expressions
 replacing written
statements describing
patterns with equations
written in algebraic
symbols
 translating from
everyday language to
algebraic language and
from algebraic
language to everyday
language
PAS4.3
 recognising the role of
grouping symbols and
the different meanings
of expressions
 substituting into
algebraic expressions
 replacing written
statements describing
patterns with equations
written in algebraic
symbols
 translating from
everyday language to
algebraic language and
from algebraic
language to everyday
language
PAS4.3
4
negative numbers
(page 147)
WE 5a-c
Ex 4D Substituting
positive and negative
numbers (page 149)
Simplifying expressions
(page 151)
WE 6a-c
Ex 4E Simplifying
expressions (page 152)
thumb’ (page 149)
Code puzzle (page 150)
10 Quick Questions 1
(page 151)
Multiplying pronumerals
(page 153)
WE 7a-b
Ex 4F Multiplying
pronumerals (page 154)
Investigation: Sonar
measurements
(page 155)
Dividing pronumerals
(page 155)
WE 8a-b, 9
Ex 4G Dividing
pronumerals (page 156)
Expanding expressions
with grouping symbols
(page 159)
WE 10a-b
10 Quick Questions 2
(page 157)
History of mathematics:
The Rhind Papyrus
(page 158)
Operations with
directed numbers
(page 149)
WorkSHEET 4.1
(page 149)
SkillSHEET 4.7:
Combining like terms
(page 152)
(positive/negative)
(page 149)
Mathcad: Simplifying
expressions (page 152)
SkillSHEET 4.8:
Simplifying fractions
(page 156)
WorkSHEET 4.2
(page 157)
Mathcad: Expanding
grouping symbols
(page 160)
Excel: Expanding

recognising the role of
grouping symbols and
the different meanings
of expressions
 substituting into
algebraic expressions
PAS4.3
 recognising like terms
and adding and
subtracting like terms
to simplify algebraic
expressions
PAS4.3
 simplifying algebraic
expressions that
involve multiplication
and division
 generating a variety of
equivalent expressions
that represent a
particular situation or
problem (Applying
strategies)
PAS4.3
 simplifying algebraic
expressions that
involve multiplication
and division
PAS4.3
 recognising the role of
grouping symbols and
the different meanings
5
Ex 4H Expanding
expressions with
grouping symbols
(page 160)
Expanding and collecting
like terms (page 160)
WE 11a-d
Ex 4I Expanding and
collecting like terms
(page 161)
Factorising (page 163)
WE 12, 13, 14, 15
Ex 4J Factorising
(page 165)
History of mathematics:
John Coates (page 162)
Game time 002 (page 161)
SkillSHEET 4.9: Highest
common factor
(page 165)
WorkSHEET 4.3
(page 166)
grouping symbols
(page 160)
GC program – Casio:
Expanding grouping
symbols (page 160)
GC program – TI:
Expanding grouping
symbols (page 160)
GC program – Casio:
Expanding (page 161)
GC program – TI:
Expanding (page 161)
Mathcad: Factorising
(page 165)
Excel: Finding the HCF
(page 165)

of expressions
expanding algebraic
expressions by
removing grouping
symbols (the
distributive property)
PAS4.3
 recognising like terms
and adding and
subtracting like terms
to simplify algebraic
expressions
 recognising the role of
grouping symbols and
the different meanings
of expressions
 expanding algebraic
expressions by
removing grouping
symbols (the
distributive property)
PAS4.3
 factorising a single
term
 factorising algebraic
expressions by finding
a common factor
NS4.3
 finding highest
common factors
6
Algebraic fractions
(page 166)
WE 16a-b, 17a-b, 18a-b,
19a-b
Ex 4K Algebraic fractions
(page 169)
Using indices with algebra
(page 170)
Multiplication using
indices (page 170)
WE 20, 21, 22, 23
Ex 4L Multiplication using
indices (page 172)
Division using indices
(page 173)
WE 24, 25, 26, 27
Ex 4M Division using
indices (page 175)
Raising a power to another
power (page 176)
WE 28a-b, 29, 30
Ex 4N Raising a power to
another power
(page 178)
SkillSHEET 4.10:
Operations with
fractions (page 169)
Mathcad: Algebraic
fractions (page 169)
PAS4.3
 simplifying
expressions that
involve simple
algebraic fractions
Excel: Multiplying with
PAS5.1.1
indices (page 172)
 using the index laws
Mathcad: Multiplying with
previously established
indices (page 172)
for numbers to develop
the index laws in
algebraic form
 simplifying algebraic
expressions that
include index notation
Excel: Dividing with
PAS5.1.1
indices (page 175)
 using the index laws
Mathcad: Dividing with
previously established
indices (page 175)
for numbers to develop
the index laws in
algebraic form
 simplifying algebraic
expressions that
include index notation
Excel: Raising a power to
PAS5.1.1
a power (page 178)
 using the index laws
Mathcad: Raising a power
previously established
to a power (page 178)
for numbers to develop
the index laws in
algebraic form
 simplifying algebraic
expressions that
7
Working with indices
(page 179)
Ex 4O Working with
indices (page 179)
Summary (page 180)
Chapter review (page 181)
include index notation
PAS5.1.1
 simplifying algebraic
expressions that
include index notation
‘Test yourself’ multiple
choice questions
(page 182)
Topic tests (2)