HEATHCOTE HIGH SCHOOL
YEAR 8 MATHEMATICS PROGRAM
2004
TOPIC:
Patterns and Algebra
SUGGESTED TIME:
At least 3 weeks
CONTENT
Key Ideas for Stage 2
1. Generate, describe and record number
patterns using a variety of strategies
Key Ideas for Stage 3
1.Build simple geometric patterns
involving multiples
2.Complete a table of values for geometric
and number patterns
3.Describe a pattern in words in more
than one way
Heathcote High School
OUTCOMES:
Stage 2: PAS2.1 Generates, describes and records number patterns using a variety of strategies (p 79)
Stage 3: PAS 3.1a Records, analyses and describes geometric and number patterns that involve one operation using tables and
words (p 80)
Stage 4: PAS4.1 Uses letters to represent numbers and translates between words and algebraic symbols (p 82)
PAS4.2 Creates, records, analyses and generalises number patterns using words and algebraic symbols in a variety of
ways (p 83)
PAS4.3 Uses the algebraic symbol system to simplify, expand and factorise simple algebraic expressions (p 85)
Stage 5: PAS5.1.1 Applies the index laws to simplify algebraic expressions (p 87)
KNOWLEDGE AND SKILLS
RESOURCES
TERMINOLOGY
Signpost
8
Second
Edition
Number pattern
 identifying and describing patterns when counting
Chapter
5
Geometric pattern
forwards or backwards by threes, fours, sixes,
Table of values
sevens, eights or nines
Term
 creating, with materials or a calculator, a variety of
Equal sign
patterns using whole numbers, fractions or decimals
Number sentence
 finding a higher term in a number pattern given the
Rule
first five terms
Variable
 describing a simple number pattern in words
Pronumeral
Constant
 using the equals sign to record equivalent number
Sum
relationships and to mean ‘is the same as’ rather
Product
than as an indication to perform an operation
Algebraic expression
eg 4  3  6  2
Algebraic symbols
 completing number sentences involving one
Simplify
operation by calculating missing values
Expand
 transforming a division calculation into a
Factorise
multiplication problem eg find so that 30 ÷ 6 =
Substitute
becomes find so that  6 = 30.
Like terms
Grouping symbols
 working through a process of building a simple
geometric pattern involving multiples, completing a
table of values, and describing the pattern in words.
This process includes the following steps:
- building a simple geometric pattern using
materials
- completing a table of values for the geometric
pattern
- describing the number pattern in a variety of ways
and recording descriptions using words
- determining a rule to describe the pattern from the
YR8 program 3 patterns & algebra
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table
- using the rule to calculate the corresponding value
for a larger number
 working through a process of identifying a simple
number pattern involving only one operation,
completing a table of values, and describing the
pattern in words. This process includes the following
steps:
- completing a table of values for a number pattern
involving one operation (including patterns that
decrease)
- describing the pattern in a variety of ways and
recording descriptions using words
- determining a rule to describe the pattern from the
table
- using the rule to calculate the corresponding value
for a larger number
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.Use the algebraic symbol system to
simplify, expand and factorise simple
algebraic expressions
7.Substitute into algebraic expressions
 using letters to represent numbers and developing
the notion that a letter is used to represent a variable
 using concrete materials such as cups and counters
to model:
- expressions that involve a variable and a variable
plus a constant eg a, a  1
- expressions that involve a variable multiplied by a
constant eg 2a, 3a
- sums and products eg 2a  1, 2 (a  1)
- equivalent expressions such as
x  x  y  y  y  2x  2 y  y  2 ( x  y )  y
- and to assist with simplifying expressions, such as
(a  2)  (2a  3)  (a  2a)  (2  3)
 3a  5
 recognising and using equivalent algebraic
expressions
y  y  y  y  4y
eg
w w  w2
a  b  ab
a
a b 
b
Heathcote High School
YR8 program 3 patterns & algebra
WORKING
MATHEMATICALLY
WMS3.1 Asks questions that
could be explored using
mathematics in relation to
Stage 3 content
WMS3.3 Describes and
represents a mathematical
situation in a variety of ways
using mathematical
terminology and some
conventions
WMS4.1 Asks questions that
could be explored using
mathematics in relation to
Stage 4 content
WMS4.3 Uses mathematical
terminology and notation,
algebraic symbols, diagrams,
text and tables to
communicate mathematical
ideas
DIAGNOSIS/ASSESSMENT
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 translating between words and algebraic symbols
and between algebraic symbols and words
 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
 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
 replacing written statements describing patterns with
equations written in algebraic symbols
 translating from everyday language to algebraic
language and from algebraic language to everyday
Heathcote High School
YR8 program 3 patterns & algebra
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language
Key Ideas for Stage 5
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
 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

Heathcote High School
YR8 program 3 patterns & algebra
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