Mathematics
Content Descriptors with Learning Goals /
Indicators and Proficiencies
Level 9
All Content Strands
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.
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.
eBookbox:
Computation and rational numbers ebookbox
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.
eBookbox: Linear Equations ebookbox
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.
eBookbox:
Introducing Quadratic
Equations
Level
9 Measurement & Geometry
Units of
Measurement
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?

·
Calculate the
areas of composite shapes (ACMMG216)
·
Calculate the
surface area and volume of cylinders and solve related problems (ACMMG217)
·
Solve problems
involving the surface area and volume of right prisms (ACMMG218)

Students will:
·
deconstruct a
composite shape into simple shapes with the appropriate dimensions (U)
·
estimate the area
of a composite shape (R)
·
calculate the area
of a composite shape (F)
·
sketch and recognise the net
that applies to prisms and cylinders. (R)
·
estimate the surface area of a
right prism (R)
·
calculate the surface area of a
cylinders and right prisms (F)
·
calculate the volume of a
cylinder and right prisms (F)


Achievement Standard:
By the end of Level 9, students calculate areas of
shapes and the volume and surface area of right prisms and cylinders.
eBookbox:
Measurement: Circles and 3D
Level
9 Measurement and Geometry
Geometric
Reasoning & Pythagoras and Trigonometry
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?

Geometric Reasoning
·
Use the
enlargement transformation to explain similarity and develop the conditions
for triangles to be similar (ACMMG220)
·
Solve problems
using ratio and scale factors in similar figures (ACMMG221)
Pythagoras and Trigonometry
·
Investigate
Pythagoras’ Theorem and its application to solving simple problems involving
right angled triangles (ACMMG222)
·
Use similarity
to investigate the constancy of the sine, cosine and tangent ratios for a
given angle in rightangled triangles (ACMMG223)
·
Apply
trigonometry to solve rightangled triangle problems (AMMG224)

Students will:
·
explain why two shapes are
similar. (R)
·
explain the conditions for
similarity of triangles, (ASS, AAA).
(R)
·
determine ratio and scale
factor. (F)
·
use similar triangles to solve
geometric problems. (U)
·
identify the parts of a right
angle triangle, Opposite, Adjacent and Hypotenuse. (F)
·
explain the relationship
between the sides of the right angle triangle. (F)
·
calculate the length of the
hypotenuse of a right angle triangle. (F)
·
calculate the length of a short
side of a right angle triangle. (F)
·
apply Pythagoras Theorem to
real life problems. (PS)
·
explain the constancy of the trigonometric ratios for
rightangle triangles.
·
identify the adjacent, opposite
and hypotenuse sides of a right angle triangle. (U)
·
identify Sine, Cosine and
Tangent Ratios of a triangle. (U)
·
determine missing side lengths
of the triangle, using the ratios. (F)
·
find missing angles in a right
angle triangle, using the ratios. (F)


Achievement Standard:
By the end of Level 9, students interpret ratio and
scale factors in similar figures. They explain similarity of triangles.
Students recognise the connections between similarity and the trigonometric
ratios. They use Pythagoras’ Theorem and trigonometry to find unknown sides of
rightangled triangles.
eBookbox: Trig Ratios and Pythagoras Theorem ebookbox
Level
9 Statistics and Probability
Chance and
Data Representations
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?

Data Representations
·
Investigate
reports of surveys in digital media and elsewhere for information on how data
were obtained to estimate population means and medians (ACMSP227)
·
Identify
everyday questions and issues involving at least one numerical and at least
one categorical variable, and collect data directly from secondary sources (ACMSP228)
·
Construct
backtoback stemandleaf plots and histograms and describe data, using
terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282)
·
Compare data
displays using mean, median and range to describe and interpret numerical
data sets in terms of location (centre) and spread (ACMSP283)
Chance
·
List all
outcomes for twostep chance experiments, both with and without replacement
using tree diagrams or arrays. Assign probabilities to outcomes and determine
probabilities for events (ACMSP225)
·
Calculate
relative frequencies from given or collected data to estimate probabilities
of events involving 'and' or 'or' (ACMSP226)

Students will:
·
develop a question that will aid the
comparison of two or more sets of data. (U)
·
use appropriate investigative techniques to
collect data. (PS)
·
choose appropriate secondary data (F)
·
identify
everyday questions and issues involving at least one numerical and at least
one categorical variable (R)
·
display comparative data, such as
backtoback stemandleaf plots and histograms. (F)
·
explain comparative data, such as
backtoback stemandleaf plots and histograms. (R)
·
describe data , using spread, mean, medium,
outliers, skewed, symmetric . (U)
·
explain the data and draw conclusions. (R)
·
evaluate media
reports and use statistical knowledge to draw conclusions (U)
·
list all the outcomes for a two step chance
experiment using a tree diagram. (F)
·
assign probabilities, using the tree
diagram. (F)
·
use the tree diagram to solve problems,
including and, or and not. (F)
·
solve probability questions, using a tree
diagram for events ( without replacement). (F)
·
use Venn Diagrams to solve problems with
‘and’, ‘or’, and ‘not’. (PS)


Achievement Standard:
By the end of Level 9, students compare techniques
for collecting data in primary and secondary sources. They make sense of the
position of the mean and median in skewed, symmetric and bimodal displays to
describe and interpret data. Students calculate relative frequencies to
estimate probabilities, list outcomes for twostep experiments and assign
probabilities for those outcomes. They construct histograms and backtoback
stemandleaf plots.
eBookboxes
yet to be developed