Mathematics
Scope and Sequence
Number and Algebra Foundation to Level 10
Introduction
What is a Scope and Sequence?
scope

The breadth and depth of
content to be covered in a curriculum at any one time (e.g. week, term, year,
over a student’s school life.) All that you do in a given period.

sequence

The order in which content
is presented to learners over time. The order in which you do it.

Together a scope and
sequence of learning bring order to the delivery of content, supporting the
maximising of student learning and offering sustained opportunities for
learning. Without a considered scope and sequence there is the risk of ad hoc
content delivery and the missing of significant learning.
http://activated.act.edu.au/ectl/design/scope_and_sequence.htm

Why does a school need a scope and sequence?
An agreed Scope and Sequence for a Learning
Area, provides a sound basis for a school being able to offer a guaranteed and viable curriculum by
addressing gaps in students’ leaning and eliminating unnecessary repetition. A shared Scope and Sequence within a
school enables teachers to have clarity about the knowledge, skills and
dispositions that students will acquire in their learning and what they need to
learn next. A Scope and Sequence supports teachers with effective unit and
lesson planning and enables teachers to maintain a developmental focus on
student learning as students progress through the school.
The Mathematics Scope and Sequence developed
by WMR
This document has been developed to support schools
with the transition to AusVELS Mathematics for 2013. While it provides examples
of yearly overviews and learning sequences based on the content descriptors in
the Australian Curriculum, it is not a complete curriculum. Each individual
school can use the documents as a basis for developing a guaranteed and viable curriculum that caters for the needs of
their school community.
Levels Foundation to 10A each include a set of
learning goals/ intentions for each content substrand intended to provide a
user friendly guide to the essential learnings around which teachers and teams
could base their unit and lesson development.
Proficiency strands are listed next to each learning
goal / intention as a guide only and teachers / teams are encouraged to
consider all proficiencies equally whilst planning units and lessons. Where a
particular proficiency is not listed for a content substrand teachers and
teams should endeavour to contextualise the learning goals to address these
proficiencies. Please note the following:
Sequence of teaching
The
learning goals/intentions are listed adjacent to the content descriptions to
assist teachers when developing a teaching program. They are not necessarily in
the order to be taught – teachers /teams will make their own decisions
regarding this. The third column has been included to assist teams to develop
ideas for unit planning.
A
sample Scope and Sequence Overview is also provided for each of the year levels
from F to 10A. The number of weeks given to each unit in the overview acts as a
guide and the total number of weeks allows for the many interruptions in a
typical school year.
Links between the Learning
Goals/Intentions and the proficiency strands
(a) The Learning Goals/Intentions have
been identified to relate most closely to one of the four proficiency strands
(shown in 3 below). This identification is shown in brackets at the end of each
Learning Goal/Intention:
·
Understanding
is identified by (U)
·
Fluency
is identified by (F)
·
Problem
Solving is identified by (PS)
·
Reasoning
is identified by (R)
(b) In this document there are less
Problem Solving and Reasoning proficiency strands identified than those for
Understanding and Fluency. Should teachers wish to include more of these
proficiencies in their curriculum, they are encouraged to emphasise them when
teaching, and to develop appropriate learning tasks.
Proficiency strands
The
proficiency strands describe the actions in which students can engage when
learning and using the content. While not all proficiency strands apply to
every content description, they indicate the breadth of mathematical actions
that teachers can emphasise. The proficiencies listed next to each learning
goal / intention are examples of how students might achieve the goal or what
they have demonstrated by achieving the goal but are dependent on the context
in which the learning takes place.
Understanding
Students
build a robust knowledge of adaptable and transferable mathematical concepts.
They make connections between related concepts and progressively apply the
familiar to develop new ideas. They develop an understanding of the
relationship between the ‘why’ and the ‘how’ of mathematics. Students build
understanding when they connect related ideas, when they represent concepts in
different ways, when they identify commonalities and differences between
aspects of content, when they describe their thinking mathematically and when
they interpret mathematical information.
Fluency
Students
develop skills in choosing appropriate procedures, carrying out procedures
flexibly, accurately, efficiently and appropriately, and recalling factual
knowledge and concepts readily. Students are fluent when they calculate answers
efficiently, when they recognise robust ways of answering questions, when they
choose appropriate methods and approximations, when they recall definitions and
regularly use facts, and when they can manipulate expressions and equations to
find solutions.
Problem
Solving
Students
develop the ability to make choices, interpret, formulate, model and
investigate problem situations, and communicate solutions effectively. Students
formulate and solve problems when they use mathematics to represent unfamiliar
or meaningful situations, when they design investigations and plan their
approaches, when they apply their existing strategies to seek solutions, and
when they verify that their answers are reasonable.
Reasoning
Students
develop an increasingly sophisticated capacity for logical thought and actions,
such as analysing, proving, evaluating, explaining, inferring, justifying and
generalising. Students are reasoning mathematically when they explain their
thinking, when they deduce and justify strategies used and conclusions reached,
when they adapt the known to the unknown, when they transfer learning from one
context to another, when they prove that something is true or false and when
they compare and contrast related ideas and explain their choices.
Useful
references for teams
and teachers to use when planning units of work and lessons include the
following:
·
Ultranet
Design Space – DEECD Big Ideas in Number Maps  128428217
·
Ultranet
design Space – Mathematics eBookboxes  66512121
·
Teaching Mathematics Foundations to Middle Years
Dianne Siemon, Kim Beswick, Kathy
Brady, Julie Clark, Rhonda Faragher and Elizabeth Warren
·
Mathematics Domain Page DEECD
·
Building Numeracy – George Booker
·
Teaching Primary
Mathematics George Booker, Denise Bond, Len Sparrow, Paul Swan
·
What We Know About
Mathematics Teaching and Learning MCREL
·
WMR Numeracy Design Space
106126201
·
Acara Scope and Sequence
Documents http://www.australiancurriculum.edu.au/Download
·
VCAA – resources http://www.vcaa.vic.edu.au/Pages/foundation10/curriculum/index.aspx
Please note: Teachers will be required to join
each Ultranet design space before being able to access the resource. The number
associated with each space should be entered into the search box in ‘available
design spaces’ in order to find the space.
Foundation Level
Number and Algebra
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Number
and place value
·
Establish
understanding of the language and processes of counting by naming numbers in
sequences, initially to and from 20, moving from any starting point(ACMNA001)
·
Connect number names, numerals and quantities,
including zero, initially up to 10 and then beyond (ACMNA002)
·
Subitise small
collections of objects (ACMNA003)
·
Compare, order and
make correspondences between collections, initially to 20, and explain
reasoning (ACMNA289)
·
Represent practical
situations to model addition and sharing (ACMNA004)
Patterns and Algebra
·
Sort
and classify familiar objects and explain the basis for these
classifications. Copy, continue and create patterns with objects and drawings
(ACMNA005)

Students
will:
·
Know the names of
the numbers (F)
·
Count orally
forwards and backwards (initially to and from 20) (F)
·
Counting from any
starting point to and beyond 20 (F)
·
Understand and connect names, numerals
and quantities (U)
·
Match the names to
the numbers and quantities (F)
·
Understand and connecting names,
numerals and quantities (U)
·
Subitise up to 10
(F)
·
Understand and connecting names,
numerals and quantities (U)
·
Compare larger and
smaller of two numbers (R)
·
Order 3 or more
numbers with explanation (R)
·
Fluent in counting numbers in
sequences readily, continuing patterns, and comparing objects directly
·
Reason by explaining comparisons of
quantities, creating patterns, and explaining processes for indirect comparisons
·
Real world
(authentic) problems modelling addition and sharing (U)
·
Represent the
problem using pictures, numbers or words (F)
·
Convert between
pictures, numbers and words (story problems) (PS)
·
Problem Solve using materials
to model authentic problems, sort objects, use familiar counting
sequences to
solve unfamiliar problems, and discussing the reasonableness of the answer
Students
will:
·
Sort and classify
objects with justification of the classification (U)
·
Copy patterns with
explanation of the repeating elements (F)
·
Continue patterns
with explanation of the repeating elements (F)
·
Create patterns
with explanation of the repeating elements (R)
·
Be Fluent when counting numbers in sequences readily,
continuing patterns, and comparing
objects directly (F)
·
Reason when explaining comparisons of quantities,
creating patterns, and explain
processes for indirect comparisons (R)


Achievement Standard
Students make connections
between number names, numerals and quantities up to 10. Students count to and
from 20 and order small collections.
Level 1
Number and Algebra
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Number and place value
·
Develop confidence with number sequences to
and from 100 by ones from any starting point. Skip count by twos, fives and
tens starting from zero (ACMNA012)
·
Recognise, model, read, write and order
numbers to at least 100. Locate these numbers on a number line (ACMNA013)
·
Count collections to 100 by partitioning
numbers using place value (ACMNA014)
·
Represent and solve simple addition and
subtraction problems using a range of strategies including counting on,
partitioning and rearranging parts (ACMNA015)
Fractions
and decimals
·
Recognise and describe one half as one of
two equal parts of a whole. (ACMNA016)
Money
and financial mathematics
·
Recognise, describe and order Australian
coins according to their value (ACMNA017)
Patterns and Algebra
·
Investigate and describe number patterns
formed by skip counting and patterns with objects (ACMNA018)

Students
will:
·
Count forwards and backwards
to and from 100 from any number (F)
·
Count orally by
2’s, 5’s, 10’s to and beyond 100 starting at 0 (F)
·
Understand and connect names, numerals
and quantities
·
Order Number
sequences (U)
·
Use number lines
and number grids to count forwards, backwards and by patterns (F)
·
Model counting
using number lines (F)
·
Fluent in counting numbers in
sequences readily, continuing patterns, and comparing objects directly
·
Reason by explaining comparisons of
quantities, creating patterns, and explaining processes for indirect
comparisons
·
Bundle ones to
create ten and tens to create 100 (F)
·
Create, name and
order teen numbers as 10 and some more (F)
·
understanding
partitioning of numbers and the importance of grouping in tens
·
understanding
two digit numbers as comprised of tens and ones/units
·
model with
materials, number lines and number grids addition and subtraction within and
including 10 (F)
·
Model with
materials, number lines and number grids addition and subtractions within and
including 20 (F)
·
Discuss and
compare strategies for addition and subtraction (R)
·
develop a range
of mental strategies for addition and subtraction problems (F)
·
Real world
(authentic) problems modelling addition and subtraction (U)
·
Represent the
problem using pictures, numbers or words (F)
·
Convert between
pictures, numbers and words (story problems) (PS)
·
Problem Solve using materials
to model authentic problems, sort objects, use familiar counting
sequences to
solve unfamiliar problems, and discussing the reasonableness of the answer
·
Model the
partitioning of one whole into two equal parts (U)
·
Model the
partitioning of a group into two equal parts (U)
·
Name equal parts
as halves, one equal part as one half (R)
·
sharing a
collection of readily available materials into two equal portions (F)
·
Show reasoning
by splitting an object into two equal pieces and describing how the pieces
are equal
·
Recognise Australian coins according to
their value (F)
·
Order Australian coins according to their
value (F)
·
Describe and order Australian coins according
to their value (R)
·
showing that
coins are different in other countries by comparing Asian coins to Australian
coins (U)
·
Understanding
that the value of Australian coins is not related to size
·
Show reasoning
by describing the features of coins that make it possible to identify them
·
Identify and say
patterns 1’s forwards and backwards from any point to 100 (F)
·
Identify and say
patterns 2’s to 50, 5’s to 100 and 10’s to and beyond 100 (F)
·
Identify and say
patterns with explanation of the repeating elements (R)
·
Investigate and
model patterns on a number grid and a number line as ‘skip counting’ (PS)
·
Create patterns
with explanation of the repeating elements (R)
·
Be Fluent when counting numbers in sequences readily,
continuing patterns, and comparing objects directly
Reason when explaining comparisons of quantities,
creating patterns, and explain
processes for indirect comparisons


Achievement Standard: Students describe number sequences resulting from skip counting by 2s,
5s and 10s. They identify representations of one half. Students count to and from 100 and locate
numbers on a number line. They carry out simple additions and subtractions
using counting strategies. They partition numbers using place value. They
continue simple patterns involving numbers and objects. They recognise
Australian coins according to their value.
Level 2
Number and Algebra
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Number and place value
·
Investigate number sequences, initially
those increasing and decreasing by twos, threes, fives and ten from any
starting point, then moving to other sequences. (ACMNA026)
·
Recognise, model, represent and order
numbers to at least 1000 (ACMNA027)
·
Group, partition and rearrange collections
up to 1000 in hundreds, tens and ones to facilitate more efficient counting
(ACMNA028)
·
Explore the connection between addition and
subtraction (ACMNA029)
·
Solve simple addition and subtraction
problems using a range of efficient mental and written strategies (ACMNA030)
·
Recognise and represent multiplication as
repeated addition, groups and arrays (ACMNA031)
·
Recognise and represent division as
grouping into equal sets and solve simple problems using these
representations (ACMNA032)
Fractions
and decimals
·
Recognise and interpret common uses of
halves, quarters and eighths of shapes and collections (ACMNA033)
Money
and financial mathematics
·
Count and order small collections of
Australian coins and notes according to their value (ACMNA034)
Patterns
and algebra
·
Describe patterns with numbers and identify
missing elements (ACMNA035)
·
Solve problems by using number sentences
for addition or subtraction (ACMNA036)

Students
will:
·
Count orally
forwards and backwards by 1’s from any number beyond 100 to 1000 (F)
·
Counting orally by
2’s, 5’s and 10’s to 100 and beyond (F)
·
Count backwards by
10’s from 3 digit multiple of 10 (F)
·
Count by 100’s to
1000 (F)
·
Investigate and
describe patterns in number sequences, such as adding 10 always results in
the same final digit (R)
·
Understand and describe final digit
patterns of familiar patterns (U)
·
Developing
fluency and confidence with numbers and calculations by saying number
sequences (F)
·
Fluent in counting numbers in
sequences readily, continuing patterns, and comparing objects directly (F)
·
Reason by explaining comparisons of
quantities, creating patterns, and explaining processes for indirect
comparisons (R)
·
Modelling
numbers with materials and diagrams (U)
·
recognising
there are different ways of representing numbers (U)
·
Order numbers in
ascending and descending order (F)
·
Compare numbers
on a number line (U)
·
identifying
patterns going beyond 100 (R)
·
developing
fluency with writing numbers in meaningful
contexts (F)
·
use materials to
model and represent numbers understanding three digit numbers as comprised of
hundreds, tens and ones/units (U)
·
demonstrate and
use models to compare value of numbers in base 10 places (U)
·
Use Place Value
chart bundling sticks, sticks of Unifix or MAB to model partitioning of 3
digit numbers (F)
·
Investigate and
discover strategies for efficient counting such as counting up by multiples
of 10 then some more on a number line (PS)
·
Show Understanding
of expanding numbers in 2 and 3 digit numbers through modeling, drawing
visuals and describing what is happening with the hundreds, tens and ones (U)
·
Real world
(authentic) problems modeling addition and sharing with 2 digit numbers (U)
·
Represent problems
using pictures, numbers and words (F)
·
Convert between
pictures, numbers and words (story problems) (PS)
·
Create addition and
subtraction story problems (PS)
·
Create, model and
record efficient methods for addition and subtraction (R)
·
Use number lines
and parts and totals models to show the connections between addition and
subtraction (U)
·
use countingon
to identify the missing element in an
additive problem
(F)
·
becoming fluent
with partitioning numbers to understand the connection between addition and
subtraction (F)
·
becoming fluent
with a range of mental strategies for addition and subtraction problems, such
as commutativity for addition, building to 10, doubles, 10 facts and adding
10 (F)
·
Problem Solve using materials
to model authentic problems, sort objects, use familiar counting
sequences to
solve unfamiliar problems, and discussing the reasonableness of the answer
(PS)
·
Show reasoning by
explaining strategies and understanding of connections between addition and
subtraction (R)
·
Use skip
counting on a number line to find ‘four twos’ as an additive concept (F)
·
represent array
problems with available materials and develop the language of rows and
columns (F)
·
Use skip
counting to count groups of and rows or columns in arrays (F)
·
represent array
problems with available materials and explain reasoning (R)
·
Show
understanding by visualising a group of objects as a unit and using this to
calculate the number of objects in several identical groups (U)
·
dividing the
class or a collection of objects into equal sized groups (U)
·
identify the
difference between dividing a set of objects into three equal groups and
dividing the same set of objects into groups of three (R & U)
·
develop the
language of equal sharing and ‘how many?’ (U)
·
Show
Understanding by modelling and creating word problems to represent division
concepts (U)
·
Making models of
common fractions such as ½ ¼ 1/3 (F)
·
recognise that
sets of objects can be partitioned in different ways to demonstrate fractions
(U)
·
Show
understanding by relating the number of parts to the size of a fraction
·
Naming the
fractions with connection to the sequence words (F)
·
identify
equivalent values in collections of coins or notes, such as two five cent
coins having the same value as one 10cent coin (F)
·
counting
collections of coins or notes to make up a particular value, such as that
shown on a price tag (U)
·
Solving real
life money problems using 5 cent and 10 cent combination
·
Showing
Reasoning through justifying solutions and finding alternate representations
·
describe a
pattern created by skip counting and representing the pattern on a number
line (R)
·
investigating
features of number patterns resulting from adding twos, fives or 10s, 3’s and
4’s (PS)
·
Use reasoning to
make connections between and describe number patterns
·
representing a
word problem as a number sentence (PS)
·
writing a word
problem to represent a number sentence (PS)
·
Interpret
between Pictures, Numbers and Words to show understanding of addition and
subtraction (U)
 Solve
authentic addition and subtraction problems, explaining strategies and
reasoning (R)


Achievement Standard: Students recognise increasing and decreasing number
sequences involving 2s, 3s and 5s. They represent multiplication and division
by grouping into sets. Students count to
and from 1000. They perform simple addition and subtraction calculations using
a range of strategies. They divide collections and shapes into halves, quarters
and eighths. They associate collections of Australian coins with their value.
Students identify the missing element in a number sequence.
Level 3
Number and Algebra
AusVELS Content Descriptors

Learning Goals/ Intentions and
Proficiencies
Essential
Learning

Unit Development Ideas
How is the
essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

Number and place value
·
Investigate the conditions required for a number to
be odd or even and identify odd and even numbers(ACMNA051)
·
Recognise, model, represent and order numbers to at
least 10 000 (ACMNA052)
·
Apply place value to partition, rearrange and
regroup numbers to at least 10 000 to assist calculations and solve
problems (ACMNA053)
·
Recognise and explain the connection between
addition and subtraction (ACMNA054)
·
Recall addition facts for singledigit numbers and
related subtraction facts to develop increasingly efficient mental strategies
for computation(ACMNA055)
·
Recall multiplication facts of two, three, five and
ten and related division facts (ACMNA056)
·
Represent and solve problems involving
multiplication using efficient mental and written strategies and appropriate
digital technologies(ACMNA057)
Fractions and decimals
·
Model and represent unit fractions including 1/2,
1/4, 1/3, 1/5 and their multiples to a complete whole(ACMNA058)
Money and financial mathematics
·
Represent money values in multiple ways and count
the change required for simple transactions to the nearest five cents (ACMNA059)
Patterns and algebra
·
Describe, continue, and create number patterns
resulting from performing addition or subtraction(ACMNA060)

Students will:
·
Explain if and why a number is odd
or even. (U)
·
Read, write and order numbers to 10
000. (F)
·
Rename larger numbers using
place value and using other non place value partitions. (F)
·
Partition larger numbers
into place value parts to use to assist calculations (Partial sums, Partial
products). (R,F)
·
Understand subtraction is the inverse of addition
(U)
·
Be able to write addition and subtraction fact
family number sentences for a set of numbers. (F)
·
Know addition facts and strategies such as
compliments to ten, doubles and near doubles and counting by tens and ones
forwards and backwards. (F)
·
Apply a range of mental and written strategies to
solve the result of addition and subtraction calculations such as partial
sums and compensation. (U,F)
·
Know multiplication facts for 2’s, 3’s, 5’s and
10’s. (F)
·
Relate skip counting to multiplication to division.
(U)
·
Use a range of strategies for multiplication such as
the area model and the partitioning of numbers.(U,F)
·
Understand and model unit
fractions. Find and relate unit fractions of a group through sharing (such as
shared between (÷) 3 is 1/3)
·
Count by ½’s, 1/3’s and
1`/4’s to 1. (F)
·
Partition money amounts using place value
denominations ($100’s, $10’s, $1’s) and also with other denomination
partitions.(F)
·
Calculate change using strategies such as counting
up. (F)
·
Solve addition and subtraction
problems using money as a context using strategies such as counting on for
addition and counting up for subtraction. (F)
·
Understand and apply skip counting
number patterns in solving problems involving repeated addition and repeated
subtraction (U,F)


Achievement Standard: By the end of Level 3, students
recognise the connection between addition and subtraction and solve problems
using efficient strategies for multiplication. They model and represent unit
fractions. They represent money values in various ways. Students count to and
from 10 000. They classify numbers as either odd or even. They recall addition
and multiplication facts for single digit numbers. Students correctly count out
change from financial transactions. They continue number patterns involving
addition and subtraction.
Level 4
Number and
Algebra
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Number
and place value
·
Investigate and use the properties of odd and even
numbers (ACMNA071)
·
Recognise, represent and order numbers to at least
tens of thousands (ACMNA072)
·
Apply place value to partition, rearrange and
regroup numbers to at least tens of thousands to assist calculations and
solve problems (ACMNA073)
·
Investigate number sequences involving multiples of
3, 4, 6, 7, 8, and 9 (ACMNA074)
·
Recall multiplication facts up to 10 × 10 and
related division facts (ACMNA075)
·
Develop efficient mental and written strategies and
use appropriate digital technologies for multiplication and for division
where there is no remainder(ACMNA076)
Fractions
and decimals
1.
·
Investigate equivalent fractions used in contexts(ACMNA077)
·
Count by quarters halves and thirds, including with
mixed numerals. Locate and represent these fractions on a number line (ACMNA078)
·
Recognise that the place value system can be
extended to tenths and hundredths. Make connections between fractions and
decimal notation(ACMNA079)
·
Money
and financial mathematics
·
Solve problems involving purchases and the
calculation of change to the nearest five cents with and without digital
technologies (ACMNA080)
Patterns
and algebra
·
Explore and describe number patterns resulting from
performing multiplication (ACMNA081)
·
Solve word problems by using number sentences
involving multiplication or division where there is no remainder (ACMNA082)
·
Use equivalent number sentences involving addition
and subtraction to find unknown quantities(ACMNA083)

Students will:
·
Explain why a number is odd or even.
(U)
·
Relate the properties of odd or
even to authentic contexts. (R)
·
Read, write and order numbers to 10
000’s. (F)
·
Rename larger numbers using
place value and using other non place value partitions. (F)
·
Partition larger numbers into
place value parts to use to assist calculations (Partial sums, Partial
products). (R,F)
·
Apply a range of mental strategies to solve and/or
estimate the result of calculations. (F)
·
Understand the number patterns for the multiples of 3 
9 and use in assisting with determining multiplication facts. (U)
·
Know multiplication facts to 10x10. (F)
·
Be able to relate all four fact family number facts for
multiplication and division to any multiplication or division number
sentence. (U)
·
Use a range of techniques for multiplication such as
the area model and the partitioning of numbers.(F)
·
Understand the relationship
between ½, 2/4 and 4/8 in authentic contexts and other equivalent fractions.
(U)
·
Count by ½’s, 1/3’s and 1`/4’s
with and without a number line. (F)
·
Understand the place value system into the hundredths
using real life contexts such as money. (U,R)
·
Relate fractions as another way of representing
division.
·
Relate fractions to decimals
through fractions of 100 (1 metre, $1.00, 100 piece block of chocolate). (R)
·
Solve addition and subtraction
problems using money as a context using strategies such as counting on for
addition and counting up for subtraction. (F)
·
Understand and apply the
multiplication (skip counting) number patterns in solving multiplication and
resulting products. (U,F)
·
Apply a variety of strategies
for multiplication and division including mental strategies for problem
solving. (F)
·
Rearrange subtraction number
sentences into addition and vise versa to solve for unknown quantities. (F)


Achievement Standard: By the end of Level
4, students choose appropriate strategies for calculations involving
multiplication and division. They recognise common equivalent fractions in
familiar contexts and make connections between fraction and decimal notations
up to two decimal places. Students solve simple purchasing problems. They
identify unknown quantities in number sentences. They describe number patterns
resulting from multiplication. Students use the properties of odd and even
numbers. They recall multiplication facts to 10 x 10 and related division
facts. Students locate familiar fractions on a number line. They continue
number sequences involving multiples of single digit numbers.
Level 5
Number and
Algebra
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Number
and place value
·
Identify and describe factors and multiples of whole
numbers and use them to solve problems(ACMNA098)
·
Use estimation and rounding to
check the reasonableness of answers to calculations(ACMNA099)
·
Solve problems involving multiplication of large
numbers by one or twodigit numbers using efficient mental, written
strategies and appropriate digital technologies (ACMNA100)
·
Solve problems involving division by a one digit number,
including those that result in a remainder(ACMNA101)
·
Use efficient mental and written strategies and
apply appropriate digital technologies to solve problems (ACMNA291)
Fractions
and decimals
·
Compare and order common unit fractions and locate
and represent them on a number line(ACMNA102)
·
Investigate strategies to solve problems involving
addition and subtraction of fractions with the same denominator (ACMNA103)
·
Recognise that the place value system
can be extended beyond hundredths (ACMNA104)
·
Compare, order and represent decimals(ACMNA105)
Money
and financial mathematics
·
Create simple financial plans (ACMNA106)
·
Patterns and algebra
·
Describe, continue and create patterns with
fractions, decimals and whole numbers resulting from addition and
subtraction (ACMNA107)
·
Use equivalent number sentences
involving multiplication and
division to find unknown quantities (ACMNA121)

Students
will:
·
Identify factors and multiples of
whole numbers. (F)
·
Know the difference between factors
and multiples. (U)
·
Identify the patterns involved in
identifying factors and multiples. (R)
·
Apply a range of mental strategies to estimate the
result of calculations and know the usefulness of this. (F)
·
Use a range of techniques for multiplication such as
the area model and the partitioning of numbers.(F)
·
Apply the distributive law and represent arrays to
model multiplication. (F,R)
·
Solve real life division
problems that result in a remainder. (F)
·
Use a range of written and
mental calculation strategies to solve division problems. (F)
·
Interpret the resulting remainder
in real contexts. (R)
·
Understand, model and order
unit fractions. (U)
·
Model and therefore add and
subtract fractions with similar denominators, such as using the area model
for adding and subtracting fractions. (U,R,F)
·
Understand the place value system into the
thousandths and smaller, including in real life situations such as mass and
volume. (R)
·
Know how to represent decimals in different ways,
such as words, numbers, fractions and models and compare relative sizes of
decimals. ((U)
·
Develop financial plans for
suitable relevant real life situations. (P)
·
Find, continue and create number
patterns using fractions, decimals and whole numbers. (R)
·
Make relevant fact family
number sentences for multiplication and division with known and unknown
multipliers and quotients. (F)


Achievement Standard: By the end of Level 5, students
solve simple problems involving the four operations using a range of
strategies. They check the reasonableness of answers using estimation and
rounding. Students identify and describe factors and multiples. They explain plans
for simple budgets. Students order decimals and unit fractions and locate them
on number lines. They add and subtract fractions with the same denominator.
Students continue patterns by adding and subtracting fractions and decimals.
They find unknown quantities in number sentences.
Level 6
Number and Algebra
AusVELS Content
Descriptors

Learning Goals/
Intentions and Proficiencies
Essential Learning

Unit Development Ideas
How
is the essential learning developed into units of work? How do students make connections
between the learning goals and those included in other content strands or
substrands? How do we ensure students become proficient in fluency,
understanding, reasoning and problem solving?

Number and place value
1.
·
Apply efficient Identify and describe properties of
prime, composite, square and
triangular numbers(ACMNA122)
·
Select and mental and written strategies and
appropriate digital technologies to solve problems involving all four
operations with whole numbers (ACMNA123)
·
Investigate everyday situations that use integers.
Locate and represent these numbers on a number line (ACMNA124)
Fractions
and decimals
1.
 Add and subtract decimals,
with and without digital technologies, and use estimation and rounding to
check the reasonableness of answers(ACMNA128)
 Multiply decimals by whole
numbers and perform divisions by nonzero whole numbers where the
results are terminating decimals, with and without digital technologies (ACMNA129)
 Multiply and divide decimals
by powers of 10(ACMNA130)
Money
and financial mathematics
1.
 Investigate and calculate percentage discounts
of 10%, 25% and 50% on sale items, with and without digital
technologies (ACMNA132)
2.
Patterns and algebra
 Continue and create sequences
involving whole numbers, fractions and decimals. Describe the rule used
to create the sequence (ACMNA133)

Students will:
·
Identify and describe properties of prime, composite, square and
triangular numbers. (F)
·
Use these properties to create patterns and solve
problems. (R)
·
Select between and use a
variety of written, mental and digital calculation strategies involving the
four operations to solve a variety of everyday problems. (F)
·
Become familiar with and use the range of integers.
(F)
·
Use a number line to solve addition and subtraction
problems using positive and negative integers. (F)
·
Apply integers in everyday situations. (F)
·
Understand, model and order
fractions with related denominators. (U)
·
Model and therefore add and
subtract fractions with related denominators, such as using the area model
for adding and subtracting fractions. (U,F)
·
Find fractional quantities
where a group is the whole. (F)
·
Apply a variety of strategies to add and subtract
decimals. (F)
·
Estimate the solution to
addition and subtraction problems involving decimals. (R)
·
Understand and use as
variety of strategies to multiply and divide problems involving decimals in
everyday situations (U,F)
·
Understand how multiplying
and dividing decimals by powers of ten affects the initial decimal. (U)
·
Know how to represent decimals in different ways,
such as words, numbers, fractions and models and compare relative sizes of
decimals. (R)
·
Use the understanding of
percentages to calculate the sale price of items in everyday situations.
(U,F)
·
Find, continue and create number
patterns using fractions, decimals and whole numbers. (R)
·
Find and describe the rule
used to create a pattern. (R)
·
Understand and
apply the rules for completing multiple operations within the same number
sentence including brackets (BODMAS,BOMDAS,PEMDAS,etc.) (F)


Achievement Standard: By the end of Level 6, students
recognise the properties of prime, composite, square and triangular numbers.
They describe the use of integers in everyday contexts. They solve problems
involving all four operations with whole numbers. Students connect fractions,
decimals and percentages as different representations of the same number. They
solve problems involving the addition and subtraction of related fractions.
Students make connections between the powers of 10 and the multiplication and
division of decimals. They describe rules used in sequences involving whole
numbers, fractions and decimals. Students locate fractions and integers on a
number line. They calculate a simple fraction of a quantity. They add, subtract
and multiply decimals and divide decimals where the result is rational.
Students calculate common percentage discounts on sale items. They write
correct number sentences using brackets and order of operations.
Level 7
Number and Algebra
Number and Place Value
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

·
Investigate index notation
and represent whole numbers as products of powers of prime numbers (ACMNA149)
·
Investigate and use square roots of
perfect square numbers (ACMNA150)
·
Apply the associative, commutative and distributive laws to
aid mental and written computation (ACMNA151)
·
Compare, order, add and subtract integers (ACMNA280)

Students will:
·
Define and compare prime and composite numbers and
explain the difference between them. (U)
·
Apply knowledge of factors to strategies for
expressing whole numbers as products of powers of prime factors, such as
repeated division by prime factors or creating factor trees. (R)
·
Solve problems involving lowest common multiples and
greatest common divisors (highest common factors) for pairs of whole numbers
by comparing their prime factorization (F)
·
Use diagrams to investigate perfect square numbers
such as 25 and 36 and their square roots.
(R)
·
Estimate between which two whole numbers a square
root lies. (R)
·
Use the associative, commutative and distributive
laws to show the equivalence of different number sentences, and then apply
them when calculating mentally or in writing.(F)
·
Apply the associative, commutative and distributive
laws when calculating mentally or on paper. (PS)
·
Compare and order integers. (U)
·
Add and subtract integers. (F)


Achievement Standard
By the end of Level 7, students
solve problems involving the comparison, addition and subtraction of integers.
They make the connections between whole numbers and index notation and the
relationship between perfect squares and square roots.
Level 7 Number and Algebra
Real Numbers and Money and Financial Mathematics
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Real
Numbers
· Compare fractions using equivalence. Locate and represent
positive and negative fractions and mixed numbers on a number line (ACMNA152)
· Solve problems involving addition and subtraction of
fractions, including those with unrelated denominators (ACMNA153)
· Multiply and divide fractions and decimals using efficient
written strategies and digital technologies (ACMNA154)
·
Express one
quantity as a fraction
of another, with and without the use of digital technologies (ACMNA155)
·
Round
decimals to a specified number of decimal places (ACMNA156)
·
Connect
fractions, decimals and percentages and carry out simple conversions (ACMNA157)
·
Find
percentages of quantities and express one quantity as a percentage
of another, with and without digital technologies. (ACMNA158)
·
Recognise and
solve problems involving simple ratios (ACMNA173)
Money
and Financial Mathematics
· Investigate and calculate 'best buys', with and without
digital technologies (ACMNA174)

Students will:
·
Locate positive and negative fractions and mixed
numbers on a number line. (U)
·
Compare fractions using equivalence, including
using visual representations or
concrete materials such as fraction walls or number lines (R)
·
Add and subtract fractions, including using visual
representations such as fraction walls or rectangular arrays. (F)
·
Multiply fractions using strategies including visual
representations, repeated addition and written. (F)
· Deduce the process
for division of fractions as the inverse of multiplication (R)
· Divide fractions
using visual representations and written strategies. (F)
· Multiply decimals,
using strategies including patterning and repeated addition. (F)
· Divide decimals,
using strategies including patterning. (F)
·
Calculate one quantity as a fraction of another, using real life examples. (F)
· Round decimals to a
specified number of decimal places. (U)
· Know that a
fraction can be expressed as a decimal and a percentage, and vice versa. (U)
· Carry out simple
conversions between fractions, decimals and percentages, including showing
visual representations. (F)
· Calculate
percentages of quantities in real life situations, including using multiples of 10%
and 25%. (F)
· Calculate one
quantity as a percentage of another. (F)
· Calculate a part to
part relationship as a ratio. (F)
· Calculate at part
to whole relationship as a ratio. (F)
· Calculate
proportions of a given ratio such as converting quantities of a recipe for 4
people to one for 6 people. (PS)
· Calculate, estimate
and make judgements when shopping. (PS)
· Apply the unitary method to identify the cheapest of several
like products. (F)


Achievement Standard:
By the end of Level 7, students
solve problems involving percentages and all four operations with fractions and
decimals. They compare the cost of items to make financial decisions. Students
use fractions, decimals and percentages, and their equivalences. They express
one quantity as a fraction or percentage of another.
Year
7 Number and Algebra
Patterns and Algebra & Linear and NonLinear Relationships
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Patterns
and Algebra
· Introduce the concept of variables as a way of
representing numbers using letters (ACMNA175)
· Create algebraic expressions and evaluate them by
substituting a given value for each variable (ACMNA176)
· Extend and apply the laws and properties of arithmetic to
algebraic terms and expressions (ACMNA177)
Linear
and NonLinear Relationships
·
Given
coordinates, plot points on the Cartesian plane, and find coordinates for a
given point (ACMNA178)
·
Solve simple
linear equations (ACMNA179)
· Investigate, interpret and analyse graphs from authentic data (ACMNA180)

Students will:
·
Identify patterns in the way that numbers increase or
decrease. (F)
·
Describe
mathematical relationships in patterns. (U)
·
Define variables
and constants. (U)
·
Describe a
pattern using pronumerals (as variables). (U)
·
Know that
number patterns can be described using algebra. (U)
·
Know that expressions on either side of an equals
sign have the same value. (U)
·
Create algebraic expressions (using variables and
constants) from authentic situations. (PS)
· Substitute
numbers into algebraic expressions and authentic formulas to evaluate them.
(F)
· Use brackets and the order of operations to write number
sentences, and then extend their use to algebraic terms and expressions. (R)
· Use commutative, associative and distributive properties
to write number sentences, and
then extend their use to algebraic terms and expressions. (R)
· Use algebra to describe a situation described in words, and
vice versa. (F)
·
Specify the location of a point on the Cartesian
plane using coordinates. (F)
·
Plot points on the Cartesian plane when given
coordinates. (U)
·
Describe simple patterns (such as linear) from
points plotted from a table of integer values.(F)
·
Solve linear equations using concrete materials,
including using the balance model. (F)
·
Describe the need to do the same thing to each side
of an equation. (U)
·
Check the solution to an equation by substitution.
(F)
·
Describe situations depicted by graphs of everyday
events, including travel graphs. (R)
·
Describe the shape and features of a graph. (U)
·
Make predictions from graphs of authentic data. (R)


Achievement Standard:
By the end of Level 7, students
represent numbers using variables. They connect the laws and properties for
numbers to algebra. They interpret simple linear representations and model
authentic information. Students solve simple linear equations and evaluate
algebraic expressions after numerical substitution. They assign ordered pairs
to given points on the Cartesian plane.
Level 8 Number and Algebra
Number and Place Value
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

·
Use index notation with numbers to establish the index laws with positive integral indices and the zero index (ACMNA182)
·
Carry out the four
operations with rational numbers and integers, using efficient mental and
written strategies and appropriate digital technologies (ACMNA183)

Students
will:
·
Evaluate numbers expressed as
powers of positive integers. (F)
·
Know that any number expressed to the power of zero
is 1 and why. (R)
·
Understand how and why we use index notation. (U)
·
Add, subtract, multiply and divide positive and
negative numbers using written and digital technologies. (F)
·
Develop a range of mental strategies for calculating
involving the four operations. (F)


Achievement Standard:
By the end of Year 8, students
recognise index laws and apply them to whole numbers. Students use efficient
mental and written strategies to carry out the four operations with integers.
Level 8
Number and Algebra
Real
Numbers and Financial Maths
AusVELS Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential Learning

Unit
Development Ideas
How
is the essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

Real Numbers
·
Investigate terminating
and recurring decimals(ACMNA184)
·
Investigate the concept
of irrational numbers, including π (ACMNA186)
·
Solve problems involving
the use of percentages, including percentage increases and decreases, with and without digital
technologies (ACMNA187)
·
Solve a range of problems
involving rates and ratios, with and without digital technologies (ACMNA188)
Financial Maths
·
Solve problems involving
profit and loss, with and without digital technologies (ACMNA189)

Students
will:
·
Recognise terminating,
recurring and nonterminating decimals and choose their appropriate
representations. (F)
·
Give examples of
terminating, recurring and nonterminating decimals. (F)
·
Define and identify
rational and irrational numbers and give examples of each. (U)
·
Explain that the real
number system includes Irrational numbers. (U)
·
Explain why the Real
Number system includes Irrational numbers.(R)
·
Locate the approximate
position of an irrational number on a number line. (R)
·
Describe certain subsets
of the real number and explain their particular properties. Eg. Square
numbers, primes, etc (U)
·
Use percentages to solve
problems, including those involving markups, discounts, profit and loss and
GST. (F)
·
Develop mental strategies for calculating percentage
discounts using 10% as a reference. (F)
·
Solve rate and ratio
problems using fractions or percentages and chooses the most efficient form
to solve a particular problem. (F)
·
Express profit and loss
as a percentage of cost or selling price, comparing the difference eg.
Investigate the methods used in retail stores to express discounts. (F)


Achievement Standard:
By the end of Level 8, students
solve everyday problems involving rates, ratios and percentages. They describe
rational and irrational numbers. Students solve problems involving profit and
loss.
Level 8 Number and Algebra
Patterns and Algebra and
Linear and NonLinear Relationships
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Patterns and Algebra
·
Extend and apply
the distributive law to the expansion of algebraic expressions (ACMNA190)
·
Factorise algebraic expressions by identifying numerical factors (ACMNA191)
·
Simplify algebraic
expressions involving the four operations (ACMNA192)
Linear
and NonLinear Relationships
·
Plot linear relationships
on the Cartesian plane with and without the use of digital technologies(ACMNA193)
·
Solve linear equations
using algebraic and graphical techniques. Verify solutions by substitution(ACMNA194)

Students
will:
·
Expand and simplify one
bracket expressions eg 2(a +7) = 2a+14 (F)
·
Use the Area Model to
expand algebraic expressions. (F)
·
List all factors of an
algebraic term. (F)
·
Recognise that
factorising is the opposite of expanding. (U)
·
Identify the highest
common factor of algebraic expressions. (F)
·
Gather like terms. (F)
·
Factorise an expression
by taking out the highest common factor. (F)
·
Use the Area Model to
factorise algebraic expressions. (F)
·
Plot points on the
Cartesian plane.(F)
·
Complete a table of
values, plot the data and discuss the resulting linear relationship. (U)
·
Plot points from a linear
relationship and describe the shape, steepness and where it cuts the y
axis.(F,R)
·
Find the rule for a
linear relationship. (R)
·
Use variables to
symbolise simple linear equations and use a variety of strategies to solve
them. (F)
·
Solve equations using
concrete materials, such as the balance model, and explain the need to do the
same thing to each side of the equation. (U)
·
Use strategies, such as
backtracking and guess, check and improve to solve equations. (F)
·
Apply solving linear equations
to real life problems and discuss the resultant findings. (P)



Achievement Standard:
By the end of Year 8, students make
connections between expanding and factorising algebraic expressions. They
simplify a variety of algebraic expressions. They solve linear equations and
graph linear relationships on the Cartesian plane.
Level 9
Number and Algebra
Real
Numbers
AusVELS
Content Descriptors

Learning Goals/
Intentions and Proficiencies
Essential Learning

Unit Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

·
Apply index laws to
numerical expressions with integer indices (ACMNA209)
·
Extend and apply the
index laws to variables, using positive integer indices and the zero index (ACMNA212)
·
Express numbers in
scientific notation (ACMNA210)
·
Investigate very small
and very large time scales and intervals (ACMMG219)
NB: Mention only of positive
indices but this makes it impossible to refer to scientific notation of very
small numbers so Law 5 needs to be included

Students
will:
·
Evaluate
numbers expressed as powers of positive integers. (U)
·
Express an
algebraic term in expanded form. (F)
·
Express an
expanded term in index form. (F)
·
Apply the
First Index Law. (F)
·
Deduce the
laws for division and expanding (laws 2 & 3) (R)
·
Apply the
Second Index Law. (F)
·
Apply the
Third Index Law. (F)
·
Explain the
effect of the zero power. (U)
·
Apply Index
Law 5. (F)
·
Combine
multiple laws to simplify an expression. (U)
·
Recognise
that an expression is in its simplest form. (U)
·
Express large
and small numbers in scientific notation. (F)
·
Add and
subtract numbers that are in scientific notation (F)


Achievement Standard:
By the end of Level 9, students apply the index
laws to numbers and express numbers in scientific notation.
Level 9
Number and Algebra
Linear
relationships and Money and financial mathematics
AusVELS
Content Descriptors

Learning Goals/
Intentions and Proficiencies
Essential Learning

Unit Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Linear
relationships
 Sketch
linear graphs using the coordinates of two points and solve linear
equations (ACMNA215)
·
Find the distance between
two points located on a Cartesian plane using a range of strategies,
including graphing software (ACMNA214)
·
Find the midpoint and
gradient of a line segment (interval) on the Cartesian plane using a range of
strategies, including graphing software (ACMNA294)
·
Solve problems involving
direct proportion. Explore the relationship between graphs and equations
corresponding to simple rate problems (ACMNA208)
Money
and financial mathematics
 Solve
problems involving simple interest (ACMNA211)

Students
will:
·
Sketch a linear graph given
two points (F)
·
Sketch a linear graph given
the gradient and one point (F)
·
Solve linear equations
algebraically (F)
·
Make predictions based on a
linear relationship (R)
·
Calculate the distance
between to points on a Cartesian plane using a formula (F)
·
Calculate the gradient of a
line from a graph (F)
·
Determine the gradient of a
line from an equation (F)
·
Calculate the midpoint of a
line segment using the formula (F)
·
Use graphing software to
determine the gradient, midpoint and line length of a line (F)
·
Identify variable and
constant in a worded linear relationship problem (PS, U)
·
Sketch a graph to show the
relationship of real world variables (PS)
·
Make decisions based on
information from a linear graph (R)
·
Calculate simple interest
(F)
·
Graph Total repayments
against principal (F)
·
Explain the financial impact
when factors vary when borrowing or investing (R)


Achievement Standard:
By the
end of Level 9, students find the distance between two points on the Cartesian
plane and the gradient and midpoint of a line segment. They sketch linear
relations. Students solve problems involving
simple interest.
Level 9
Number and Algebra
Patterns and Algebra &
NonLinear Relationships
AusVELS
Content Descriptors

Learning Goals/
Intentions and Proficiencies
Essential Learning

Unit Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

NonLinear Relationships
·
Graph simple nonlinear
relations with and without the use of digital technologies and solve simple
related equations (ACMNA296)
Patterns and Algebra
·
Apply the distributive
law to the expansion of algebraic expressions, including binomials, and
collect like terms where appropriate (ACMNA213)
·
NB: The following are
Year 10 Content descriptors but tend to be covered in Year 9 in Victoria
·
Factorise algebraic
expressions by taking out a common algebraic factor (ACMNA230)
·
Expand binomial products
and factorise monic quadratic expressions using a variety of strategies (ACMNA233)

Students will:
 Recognise a quadratic
pattern by determining second difference (U)
 Plot a parabola from an
equation. (F)
 describe the graphs shape and
key features (R)
 Identify and sketch a y translation
. (F)
 Identify and sketch an x
translation. (F)
 Identify and sketch a reflection. (F)
 Identify and sketch a
dilation. (F)
 Describe the transformation
shown on a graph (U)
 Connect a graph to it’s
equation (U)
 Expand one bracket (F)
 Expand two binomial
factors(F)
 Expand a perfect square
(F)
 Use the distributive
law and the index laws to factorise algebraic expressions (F)
 Factorise a
quadratic trinomial using sum and product technique (F)
 Factorise a
quadratic trinomial using by identifying a perfect square (F)
 Factorise a
quadratic expression using the difference of squares (F)
 Choose the
appropriate technique to factorise a quadratic (U)


Achievement Standard
By the
end of Level 9, students expand binomial expressions and sketch nonlinear
relations.
Level 10
Number and Algebra
Money and
Financial Mathematics
AusVELS Content
Descriptors

Learning Goals/ Intentions and Proficiencies
Essential
Learning

Unit Development Ideas
How is the essential learning developed
into units of work? How do students make connections between the learning
goals and those included in other content strands or substrands? How do we
ensure students become proficient in fluency, understanding, reasoning and
problem solving?

Money and Financial Maths
·
Connect the compound interest formula
to repeated applications of simple interest using appropriate digital
technologies (ACMNA229)

Students will:
·
Solve equations using substitution (F)
·
Define compound interest using examples (U)
·
Understand the difference between compound interest and
simple interest and the context in which each may be used (U)
·
Understand the connection between compound interest and
simple interest (U)
·
Calculate compound interest using a formula (F)
·
Transpose equations as required to perform calculations
(U)
·
Use digital technologies to calculate compound interest
(F)
·
Decide whether compound interest or simple interest
applies to a situation (R)
·
Solve authentic problems that involve calculations of
compound interest (F, U, R, PS)


Achievement
Standard: By the end of Level
10, students recognise the connection between simple and compound interest.
Level 10 Number and Algebra
Patterns and Algebra
AusVELS Content
Descriptors

Learning Goals/ Intentions and Proficiencies
Essential
Learning

Unit Development Ideas
How is the essential learning developed
into units of work? How do students make connections between the learning
goals and those included in other content strands or substrands? How do we
ensure students become proficient in fluency, understanding, reasoning and
problem solving?

·
Factorise algebraic expressions by taking out a common
algebraic factor (ACMNA230)
·
Simplify algebraic products and quotients using index
laws (ACMNA231)
·
Apply the four operations to simple algebraic fractions
with numerical denominators (ACMNA232)
·
Expand binomial products and factorise monic quadratic
expressions using a variety of strategies (ACMNA233)
·
Substitute values into formulas to determine an unknown
(ACMNA234)

Students will:
·
Determine factors of numbers and algebraic terms (U)
·
Determine common factors in a group of numbers or
algebraic terms (F, U)
·
Recognise the highest common factor in a group of
numbers or algebraic terms (F)
·
Recognise the highest common factor in algebraic
expressions (U)
·
Factorise an algebraic expression by recognising the
highest common factor (number or algebraic term or expression) and dividing
each term by this factor (R)
·
Simplify number sentences and
algebraic expressions using a range of index laws (F)
·
Represent large numbers and small
numbers using scientific notation (F)
·
Explain why index notation is used (U)
·
Explain, using indices, the meaning of
a negative index (U)
·
Simplify algebraic expressions
involving positive and negative indices and applying a range of index laws
(U) (R)
·
Simplify fractions using highest
common factors (U)
·
Add fractions using common
denominators (F)
·
Solve a range of linear equations (not
fractions) using the four operations (U) (R)
·
Solve linear equations, including
those with numerical denominators (U) (R) (PS)
·
Check solutions to linear equations
using substitution (R)
·
Multiply algebraic terms (U)
·
Expand binomial products (U)
·
Simplify expressions resulting from expansion
of binomial products (U)
·
Factorise monic quadratic equations
e.g. x^{2} + 7x + 12 using a variety of strategies (R) (PS)
·
Identify common factors including
binomial terms in algebraic expressions (U)
·
Factorise algebraic expressions with
four terms by using grouping in pairs (U) (R)
·
Recognise patterns for special
binomial products e.g. (a+b)(ab) and (a+b)^{2} to expand the
products (F) (U)
·
Recognise patterns to factorise special cases of
quadratic equations e.g. a^{2} – b^{2} (F) (U)
·
Use the area model to factorise quadratic
expressions such as ax^{2} +
bx + c where a = + 1 (U)
·
Factorise quadratic expressions using the method of
completing the square (U) (R)
·
Write linear equations to represent
word problems (U) (R) (PS)
·
Solve word problems using linear
equations (R) (PS) (U)


Achievement
Standard: Students expand
binomial expressions and factorise monic quadratic expressions. They find
unknown values after substitution into formulas. They perform the four
operations with simple algebraic fractions.
Level 10 Number and Algebra
Linear and NonLinear Relationships
AusVELS Content
Descriptors

Learning Goals/ Intentions and Proficiencies
Essential
Learning

Unit Development Ideas
How is the essential learning developed
into units of work? How do students make connections between the learning
goals and those included in other content strands or substrands? How do we
ensure students become proficient in fluency, understanding, reasoning and
problem solving?

Linear and
NonLinear Relationships
·
Solve problems involving linear equations, including
those derived from formulas (ACMNA235)
·
Solve linear inequalities and graph their solutions on
a number line (ACMNA236)
·
Solve linear simultaneous equations, using algebraic
and graphical techniques including using digital technology (ACMNA237)
·
Solve problems involving parallel and perpendicular
lines (ACMNA238)
·
Explore the connection between algebraic and graphical
representations of relations such as simple quadratics, circles and
exponentials using digital technology as appropriate (ACMNA239)
·
Solve linear equations involving simple algebraic
fractions (ACMNA240)
·
Solve simple quadratic equations using a range of
strategies (ACMNA241)

Students
will:
·
Transpose equations (mathematical and
other) in order to solve for a particular unknown
·
use substitution as a checking strategy (R) (U)
·
solve linear inequalities (F)
·
graph linear inequalities and their
solutions (U)
·
identify word problems that can be
represented with simple linear inequalities (U)
·
represent word problems using simple
linear inequalities (R)
·
solve word problems through the use of
linear inequalities (PS)
·
solve linear equations (F)
·
solve pairs of simultaneous equations using a variety
of techniques e.g. elimination, graphing, substitution (R) (F)
·
identify the pairs of equations in worded problems (U)
·
solve worded problems involving simultaneous equations
(R) (PS)
·
recognise parallel and perpendicular lines from their
graphical representation (F)
·
identify parallel lines and perpendicular lines using
their algebraic representations (F) (U)
·
use geometric software to investigate parallel and
perpendicular lines (F)
·
Identify graphical representations of parabolas,
exponential functions and circles (F)
·
Match algebraic representations of parabolas,
exponential functions and circles to their graphs (U)
·
Describe the effect of changing an algebraic expression
on its corresponding graph (U)
·
Identify intercepts, turning points and transformations
from an algebraic expression and a graph (F)
·
Sketch graphs of parabolas, exponential functions and
circles from their algebraic representation (U)
·
Solve a wide range of linear equations including those
with simple algebraic fractions (F) (U)
·
Check solutions to equations using substitution (F)
·
Represent word problems using linear equations (R)
·
Solve word problems using linear equations (PS) (R)
·
Identify nonlinear relationships from their algebraic
or graphical representations (F)
·
Connect reallife situations to linear and non–linear
relationships (U)
·
Solve quadratic equations using a variety of strategies
(U)
·
Factorise quadratic expressions using a variety of
strategies including completing the square (U)
·
Represent quadratic equations graphically by first
solving and/ or factorising (U) (R)


Achievement Standard: Students make the
connections between algebraic and graphical representations of relations. They
solve simple quadratic equations and pairs of simultaneous equations. They
recognise the relationships between parallel and perpendicular lines.
Level 10A
Year 10A content descriptors indicate optional additional content suitable for development of student mathematical background in
preparation for further study of functions, algebra, and calculus; as well as
other additional content related to statistics and trigonometry. Teachers can
incorporate a selection of this
and other additional content in Year 10 mathematics courses, as applicable for
extension and enrichment purposes, and
to prepare students for subsequent study.
Level 10A Number and Algebra
Real Numbers
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the
essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

 Define rational and
irrational numbers and perform operations with surds and fractional
indices (ACMNA264)
 Use the definition of a
logarithm to establish and apply the laws of logarithms (ACMNA265)

Students will:
 define
a rational number (U)
 define
an irrational number (U)
 simplify
expressions involving surds (U)
 perform
operations (addition, subtraction and multiplication) with surds (F)
 represent
surds with fractional indices (U)
 perform
operations with fractional indices (F)
 evaluate
numeric expressions using index laws (U)
 simplify
algebraic expressions using index laws (U)
 define
a logarithm
 understand
the application of logarithms in reallife situations (U)
 understand
the relationship between exponential and logarithmic expressions (U)
 understand
the logarithmic scale and its use (U)
 use
the laws of logarithms to simplify expressions (R)


Level 10A Number and Algebra
Patterns and Algebra
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the
essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

·
Investigate the concept of a polynomial and apply
the factor and remainder theorems to solve problems (ACMNA266)

Students will:
 Identify a polynomial expression (F)
 Perform long division using numerals (F) (U)
 Perform divisions of polynomials using factors
and remainders (F) (U)


Level 10A Number and Algebra
Linear and NonLinear Relationships
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the
essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

·
Solve simple exponential equations (ACMNA270)
·
Describe, interpret and sketch parabolas,
hyperbolas, circles and exponential functions and their transformations
(ACMNA267)
·
Apply understanding of polynomials to sketch a range
of curves and describe the features of these curves from their equation
(ACMNA268)
·
Factorise monic and nonmonic quadratic expressions
and solve a wide range of quadratic equations derived from a variety of
contexts (ACMNA269)

Students will:
·
Understand that exponential equations can describe real
life data such as population growth (U)
·
Solve exponential equations (R) (U)
·
Solve problems involving multiplying by a constant
term (including negative terms) using a range of strategies (PS) (R)
·
Represent parabolas graphically given their
algebraic representation (F)
·
Represent hyperbolas graphically given their
algebraic representation (F)
·
Represent circles graphically given their algebraic
representation (F)
·
Represent exponential functions graphically given
their algebraic representation (F)
·
Transform graphs as a result of changes to their
algebraic representations (U)
·
Sketch polynomials efficiently given their algebraic
representation (U)
·
Describe the features of a polynomial given its
algebraic representation (U)
·
investigate the features of graphs of polynomials
using digital technology (F)
·
apply factorisation of a range of quadratic
expressions to solve word problems (PS) (U) (R)
·
apply the solving of quadratic equations using a
variety of strategies to solve word problems (PS) (U) (R)


