Mathematics
Content Descriptors with Learning Goals /
Indicators and Proficiencies
Level 7
All Content Strands
Introduction  Mathematics Scope and
Sequence Documents
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
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.
eBookbox: Working with Numbers
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.
eBookbox: Common fractions decimals and Percentages
Linking fractions decimals and percentages
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.
eBookboxes: Working with Patterns
Patterns and
Relationships
Level 7
Measurement and Geometry
Using 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?

· Establish
the formulas for areas of rectangles, triangles and parallelograms and use
these in problem solving (ACMMG159)
· Calculate
volumes of rectangular prisms (ACMMG160)

Students will:
· Explain
the difference between perimeter and area, and their respective units.(U)
· Deduce
the formula for the area of a rectangle by counting square units and finding
a pattern. (R)
· Deduce
the formula for the area of triangles and parallelograms using visual
constructions. (R)
· Calculate
the perimeter and area of rectangles, triangles and parallelograms. (F)
· Solve
problems involving the area of rectangles, triangles and parallelograms, and
the surface area of related prisms. (PS)
· Choose
the best unit to use when measuring volume. (U)
· Use
cubic units when estimating the volume of 3D shapes (F)
· Use
concrete materials to deduce the formula for the volume of cubes and other
rectangular prisms. (R)
· Calculate
the volume and surface area of cubes and other rectangular prisms.(F)


Achievement Standard
By the end
of Level 7, students use formulas for the area and perimeter of rectangles and
calculate volumes of rectangular prisms.
eBookbox: Measuring the world around us
Level
7 Measurement and Geometry
Shape &
Location and Transformation
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?

Shape
· Draw
different views of prisms and solids formed from combinations of prisms (ACMMG161)
Location and Transformation
· Describe
translations, reflections in an axis, and rotations of multiples of 90° on
the Cartesian plane using coordinates. Identify line and rotational
symmetries (ACMMG181)

Students will:
·
Draw isometric
diagrams of prisms and solids formed from combinations of prisms. (F)
·
Draw plan and elevation views (front and
side) of prisms and solids formed from combinations of prisms. (F)
·
Perform the following transformations on 2D
shapes: translation, reflection in an axis, and rotation in multiples of 90^{0}.
(F)
·
Describe translation, reflection in an
axis, and rotation in multiples of 90^{0} using coordinates. (U)
·
Create patterns with combinations of
translations, reflections and rotations, including using digital
technologies. (PS)
·
Identify line and rotational symmetries.
(U)


Achievement Standard:
By the end
of Level 7, students describe different views of three dimensional objects.
They represent transformations in the Cartesian plane.
eBookbox: Transforming and Visualising
Level 7 Measurement
and Geometry
Geometric
Reasoning
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
conditions for two lines to be parallel and solve simple numerical problems
using reasoning (ACMMG164)
· Identify
corresponding, alternate and
cointerior angles when two straight lines are crossed by a transversal (ACMMG163)
· Demonstrate
that the angle sum of a
triangle is 180° and use this to find the angle sum of a
quadrilateral (ACMMG166)
· Classify
triangles according to their side and angle
properties and describe quadrilaterals (ACMMG165)

Students will:
·
Deduce and then
describe the conditions for two lines to be parallel. (R)
·
Construct a pair of parallel lines with a
transversal intersecting with them using concrete materials or geometry
software. (F)
·
Define and classify pairs of angles as
complementary, supplementary, adjacent and vertically opposite. (U)
·
Define and classify alternate,
corresponding and cointerior angles. (U)
·
Deduce the missing angle in a
parallel/transversal line situation. (R)
·
Deduce and verify the angle sum of a
triangle using concrete materials. (R)
·
Calculate the missing angle in a triangle.
(F)
·
Deduce the angle sum of a quadrilateral
from knowing the angle sum of a triangle.(R)
·
Calculate the missing angle in a
quadrilateral.(F)
·
Justify and classify triangles as scalene,
isosceles or equilateral according to their side properties. (R)
·
Justify and classify triangles as
rightangled, obtuseangled and acute angled according to their angle properties. (R)
·
Describe key features of quadrilaterals
including squares rectangles, rhombuses, parallelograms, kites and
trapeziums. (U)


Achievement
Standard:
By the end
of Level 7, students solve simple numerical problems involving angles formed by
a transversal crossing two parallel lines. Students classify triangles and
quadrilaterals. They name the types of angles formed by a transversal crossing
parallel line.
eBookboxes: Properties of shapes and solids, Transforming and visualising
Level
7 Statistics and Probability
Data
Representation and Interpretation and Chance
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 Representation and
Interpretation
·
Identify and investigate issues
involving numerical data collected from primary and secondary sources (ACMSP169)
·
Construct and compare a range
of data displays including
stemandleaf plots and dot plots (ACMSP170)
·
Calculate mean, median, mode and range for sets
of data. Interpret these
statistics in the context of data (ACMSP171)
·
Describe and interpret data displays using median, mean and range (ACMSP172)
Chance
·
Construct sample spaces for
singlestep experiments with equally likely outcomes (ACMSP167)
·
Assign probabilities to the
outcomes of events and determine probabilities for events (ACMSP168)

Students will:
· Describe the difference between primary and secondary data. (U)
· Collect, organise and describe numerical data collected from primary
sources. (PS)
· Analyse numerical data collected from secondary sources. (PS)
· Explain why some data representations are more appropriate than others
for particular data sets. (U)
· Construct and compare data displays including ordered stem and leaf
plots, and dot plots. (F)
· Calculate the mean, median, mode and range for sets of data. (F)
· Explain and interpret data, including referring to the mean, median,
mode and range of the data. (R)
· Compare data sets from real life, including using the location of the
mean and median on graphs. (R)
· Describe how outliers may affect the comparison of data sets when the
mean, median and range are used.(U)
· Define key terms, including probability, sample space, favourable
outcomes, trial, events and experiments. (U)
· Identify equally likely outcomes and outcomes that are not equally
likely.(F)
· Construct sample spaces for singlestep experiments with equally likely outcomes. (U)
· Calculate the probability of an event as a decimal, fraction or
percentage. (F)


Achievement Standard:
By the end
of Level 7, students determine the sample space for simple experiments with
equally likely outcomes and assign probabilities to those outcomes. They
calculate mean, mode, median and range for data sets. They construct stem and
leaf plots and dot plots.
eBookbox: Working with Data
Summary Statistics