TOPIC: 3
ALGEBRA
OUTCOMES:
Stage 4: PAS 4·1 Uses letters to represent numbers and translates between words and algebraic symbols (p82)
PAS 4·2 Creates, records, analyses and generalises number patterns using words and algebraic symbols in
SUGGESTED TIME:
a variety of ways. ( p83)
PAS 4·3 Uses the algebraic symbol system to simplify, expand and factorise simple algebraic
expressions (p85)
Stage 5: PAS 5·1·1 Applies the index laws to simplify algebraic expressions (p87)
CONTENT
Key Ideas for Stage 4
1. Use letters to represent numbers
2. Translate between words and algebraic symbols
and between algebraic symbols and words
3. Recognise and use simple equivalent algebraic
expressions.
4. Create, record and describe number patterns
using words
5. Use algebraic symbols to translate descriptions
of number patterns
6. Represent number pattern relationships as points
on a grid.
7. Use the algebraic symbol system to simplify,
expand and factorise simple algebraic expressions
8. Substitute into algebraic expressions
PAS 5.2.1 Simplifies, expands and factorises algebraic expressions involving fractions and negative and
fractional indices(p 88)
KNOWLEDGE AND SKILLS
RESOURCES
TERMINOLOGY
Pronumeral
Knowledge and Skills
Sum

Maths
Works
9
Int
Students learn about
Product
Ch 5
 using a process that consists of building a geometric
Simplify
Ch 7 p252 – 253
pattern, completing a table of values, describing the
Expand
P260 – 261
pattern in words and algebraic symbols and
Factorise
representing the relationship on a graph:
Substitute
 New Coarse Maths
- modelling geometric patterns using materials such as
Grouping symbols
Yr9 Adv
matchsticks to form squares
Like terms
Ch2
Algebraic expression
eg
,
,
,
,…
Ch 6 p168 – 172
Notation
- describing the pattern in a variety of ways that relate
Quotient

New
Century
Maths
to the different methods of building the squares, and
Variables
Int
9
recording descriptions using words
Ch 3, Ch 5
- forming and completing a table of values for the
geometric pattern
 New Century Maths
Number of
eg
Yr 9 Adv
1
2
3
4
5
10 100
squares
Ch 3, Ch 5
Number of
matchsticks
4
7
10
13
_
_
_
- representing the values from the table on a number
grid and describing the pattern formed by the points
on the graph (note – the points should not be joined to
form a line because values between the points have no
meaning)
- determining a rule in words to describe the pattern
from the table – this needs to be expressed in function
form relating the top-row and bottom-row terms in the
table
- describing the rule in words, replacing the varying
number by an algebraic symbol
Heathcote High School
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
Maths Works 10 Int
Ch 3 p 79 – 102

Mathscape Yr 9
Stage 5·2
Ch 2, Ch 8

Mathscape Yr 9
Stage 5·3
Ch 2, Ch 9
Page 1 of 5
- using algebraic symbols to create an equation that
describes the pattern
- creating more than one equation to describe the
pattern
- using the rule to calculate the corresponding value for
a larger number
 using a process that consists of identifying a number
pattern (including decreasing patterns), completing a
table of values, describing the pattern in words and
algebraic symbols, and representing the relationship on
a graph:
- completing a table of values for the number pattern
eg
a
1
2
3
4
5
10
100
b
4
7
10
13
_
_
_
- describing the pattern in a variety of ways and
recording descriptions using words
- representing the values from the table on a number
grid and describing the pattern formed by the points
on the graph
 determining a rule in words to describe the pattern
from the table – this needs to be expressed in function
form relating the top-row and bottom-row terms in the
table
 describing the rule in words, replacing the varying
number by an algebraic symbol
WORKING
MATHEMATICALLY
 ask questions about how
number patterns have been
created and how they can be
continued (Questioning)
 using algebraic symbols to create an equation that
describes the pattern
 creating more than one equation to describe the
pattern
 using the rule to calculate the corresponding value for
a larger number
 recognising like terms and adding and subtracting like
terms to simplify algebraic expressions
eg 2n  4m  n  4m  3n
 recognising the role of grouping symbols and the
different meanings of expressions, such as
2a  1 and 2a  1
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Page 2 of 5
 simplifying algebraic expressions that involve
multiplication and division
12a  3
eg
4x  3
2ab  3a
 simplifying expressions that involve simple algebraic
fractions
eg
a a

2 3
2x x

5 3
 expanding algebraic expressions by removing grouping
symbols (the distributive property)
3( a  2)  3a  6
eg
 5( x  2)  5 x  10
a ( a  b)  a 2  ab
 factorising a single term eg 6ab  3  2  a  b
 factorising algebraic expressions by finding a common
factor
eg
6a  12  6(a  2)
x 2  5 x  x( x  5)
5ab  10a  5a(b  2)
 4t  12  4(t  3)
 distinguishing between algebraic expressions where
letters are used as variables, and equations, where
letters are used as unknowns
 substituting into algebraic expressions
 generating a number pattern from an algebraic
expression
eg
x
1
2
3
4
5
6
10
100
x3
4
5
6
_
_
_
_
_
 replacing written statements describing patterns with
equations written in algebraic symbols
eg ‘you add five to the first number to get the second
number’ could be replaced with ‘ y  x  5 ’
translating from everyday language to algebraic
language and from algebraic language to everyday
language
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Page 3 of 5
Key Ideas for Stage 5·1
1. Apply the index laws to simplify algebraic
expressions (positive integral indices only)
 using the index laws previously established for
numbers to develop the index laws in algebraic form
eg
2 2  2 3  2 2 3  2 5
a m  a n  a mn
2 5  2 2  2 5 2  2 3
a m  a n  a mn
2   2
(a m ) n  a mn
2 3
6
WORKING
MATHEMATICALLY
DIAGNOSIS/ASSESSMENT
 verify the index laws using a
calculator
eg use a calculator to compare
the values of (34 ) 2 and 38
(Reasoning)
 establishing that a0  1 using the index laws
eg
a3  a3  a33  a0
and
a3  a3  1

a0  1
 simplifying algebraic expressions that include index
notation
eg
5x 0  3  8
2 x 2  3x 3  6 x 5
12a 6  3a 2  4a 4
2m 3 (m 2  3)  2m 5  6m 3

Key Ideas for Stage 5·2
 simplifying algebraic expressions involving fractions, such as
2x 2x

5
3
7 a 5a

8 12
2y y

3 6
2ab 6

3
2b
Simplify, expand and factorise algebraic
expressions including those involving fractions or
with negative and/or fractional indices
 applying the index laws to simplify expressions involving
pronumerals
 establishing that
 a 
2
a  a  a  a  a2  a
WORKING
MATHEMATICALLY
 state whether particular
equivalences are true or
false and give reasons
eg Are the following true or
false? Why?
5x 0  1
9 x 5  3x 5  3x
a5  a7  a 2
1
2c 4  4
2c
(Applying Strategies,
Reasoning, Communicating)
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Page 4 of 5
 using index laws to assist with the definition of the fractional
index for square root
 a  a
2
given
2
1
and  a 2   a


1
a  a2
then
 using index laws to assist with the definition of the fractional
index for cube root
 using index notation and the index laws to establish that
a 1 
1
1
1
, a 2  2 , a 3  3 , …
a
a
a
 applying the index laws to simplify algebraic expressions such
as
(3 y 2 ) 3
4b 5  8b 3
9 x 4  3x 3
1
1
3 x 2 5 x 2
1
1
6 y 3 4 y 3
 expanding, by removing grouping symbols, and collecting like
terms where possible, algebraic expressions such as
2 y ( y  5)  4( y  5)
4 x(3x  2)  ( x  1)
 3x 2 (5 x 2  2 xy )
 factorising, by determining common factors, algebraic
expressions such as
3x 2  6 x
14ab  12a 2
21xy  3x  9 x 2
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