Mathematics
Content Descriptors with Learning Goals /
Indicators and Proficiencies
Level 10 and 10A
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 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.
eBookbox: Linear Functions and Modeling, Introducing Quadratic Functions
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.
eBookboxes: Linear Functions and
Modeling, Introducing
Quadratic Functions
Level 10
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?

 Solve problems involving surface area
and volume for a range of prisms, cylinders and composite solids
(ACMMG242)

Students will:
l Explain
the difference between surface area and volume including the use of square
and cubic units(U)
l Use
a variety of strategies to calculate surface area and volume of prisms,
cylinders, cones, pyramids, spheres and composite solids (R) (F) (U)
l Solve
worded problems involving surface area and/or volume calculations and/or
comparisons using a variety of strategies (F) (U) (R) (PS)


Achievement Standard
Students
solve surface area and volume problems relating to composite solids.
eBookbox: In development
Level 10
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?

·
Formulate proofs involving congruent triangles and
angle properties (ACMMG243)
·
Apply logical reasoning, including the use of
congruence and similarity, to proofs and numerical exercises involving plane
shapes (ACMMG244)

Students will:
·
Identify a shape by its properties (U)
·
Identify congruent triangles (U)
·
Use congruent triangles and angle
properties to prove that a quadrilateral with equal length diagonals
bisecting at right angles is a square (R)
·
present formal geometric arguments to
develop skills in mathematical reasoning and present reasoned arguments
(proofs) (R) (U)
·
use mathematical language and
notation, based on congruence and similarity (U)
·
apply an understanding of
relationships to deduce properties of geometric figures (for example the base
angles of an isosceles triangle are equal) (R) (PS) (U)
·
distinguish between a practical
demonstration and a proof (for example demonstrating triangles are congruent
by placing them on top of each other, as compared to using congruence tests
to establish that triangles are congruent) (U) (R)


Achievement Standard: Students apply
deductive reasoning to proofs and numerical exercises involving plane shapes.
They use triangle and angle properties to prove congruence and similarity.
eBookbox: Transformation, Location and Angle
Properties (in development), Describing, constructing and transforming shapes and
3D objects
Level 10
Measurement and Geometry
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?

·
Solve rightangled triangle problems including those
involving direction and angles of elevation and depression (ACMMG245)

Students will:
·
Identify a right angled triangle (F)
·
Recall Pythagoras’s Theorem (F)
·
Calculate the lengths of sides of
triangles using Pythagoras’s Theorem (F) (U)
·
Apply Pythagoras’s Theorem to worded
problems and real life situations to solve problems (PS) (R) (U)
·
Label sides of a triangle according to
their location in relation to an angle (e.g. opposite, adjacent ) (F)
·
Recall trigonometric relationships (F)
·
Use trigonometric relationships to
calculate lengths of sides and sizes of angles (F)
·
Represent real life situations
diagrammatically in order to apply trigonometry to solve a problem (R)
·
Apply trigonometric relationships to
real life situations to solve problems (PS) (R)
·
Solve problems involving angles of
elevation and depression using Pythagoras’s Theorem and Trigonometry (R) (PS)


Achievement Standard: Students use
trigonometry to calculate unknown angles in rightangled triangles.
eBookboxes: Trigonometric Ratios and Pythagoras Theorem
Level 10 Statistics and Probability
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?

·
Describe the results of two and
threestep chance experiments, both with and without replacements, assign
probabilities to outcomes and determine probabilities of events. Investigate
the concept of independence (ACMSP246)
·
Use the language of ‘if ....then,
‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and
identify common mistakes in interpreting such language (ACMSP247)

Students will:
·
Recognise chance events that are
dependent on previous results
·
Recognise chance events that are
independent of each other
·
Determine possible outcomes for chance
events of two or three steps
·
Determine the probability of an event
including those involving two or three steps with and without replacement
·
Recognise that for independent events
P(A) x P(B) = P(A and B)
·
Use an understanding of statistics and
probability to critically analyse, evaluate and explain data presented in a
wide range of contexts (e.g. media reports)


Achievement Standard: Students list outcomes
for multistep chance experiments and assign probabilities for these experiments.
eBookbox: Probability
Level 10 Statistics and Probability
Data representation and Interpretation
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?

·
Determine quartiles and interquartile range (ACMSP248)
·
Construct and interpret box plots and use them to
compare data sets (ACMSP249)
·
Compare shapes of box plots to corresponding histograms
and dot plots (ACMSP250)
·
Use scatter plots to investigate and comment on
relationships between two continuous variables (ACMSP251)
·
Investigate and describe bivariate numerical data where
the independent variable is time (ACMSP252)
·
Evaluate
statistical reports in the media and other places by linking claims to
displays, statistics and representative data (ACMSP253)

Students will:
·
determine the minimum and maximum
values in a set of data (F)
·
determine the range in a set of data
(F)
·
determine the median in a set of data
(F)
·
determine the upper and lower
quartiles in a set of data (F)
·
determine the interquartile range in a
set of data (F)
·
compare data sets numerically (U) (R)
·
represent data by constructing a box
plot (F)
·
compare data sets visually using box
plots (U) (R) e.g. the distribution of Aboriginal and Torres Strait Islander
people by age with that of the Australian population as a whole
·
understanding that box plots are an
efficient and common way of representing and summarising data and can
facilitate comparisons between data sets
·
represent the same set of data
visually in various ways such as box plots, histograms and dot plots(U)
·
compare the various visual
representations of a set of data and explain their features (U)
·
represent data sets as scatter plots (F)
·
use authentic data to construct
scatter plots, make comparisons and draw conclusions (R)
·
comment on relationships between continuous variables
using their scatter plots
·
investigate and describe relationships between
variables (F) (U)
·
construct and interpret data displays
representing bivariate data over time (F) (U) (R)
·
investigate and describe bivariate data where the
independent variable is time (F) (U)
·
Use real life data to explain and evaluate statistical
reports presented in the media (F) (U) (R)
·
Investigate data in different ways to make comparisons
and draw conclusions (R) (PS) (U) (F)


Achievement Standard:
Students
compare data sets by referring to the shapes of the various data displays. They
describe bivariate data where the independent variable is time. Students
describe statistical relationships between two continuous variables. They
evaluate statistical reports. They calculate quartiles and interquartile
ranges.
eBookbox: Data
(in development)
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 including
rationalizing denonminators(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)


Level 10A 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?

·
Solve problems involving surface area and volume of
right pyramids, right cones, spheres and related composite solids (ACMMG271)

Students
will:
 Use
length, area and volume relationaships to solve problems (F) (R)
 Calculate
simple surface areas and volumes using a variety of strategies (F)
 Solve
problems involving surface area of right pyramids (R) (PS) (U) (F)
 Solve
problems involving surface area of right cones (R) (PS) (U) (F)
 Solve
problems involving surface area of spheres (R) (PS) (U) (F)
 Solve
problems involving surface area of composite solids (R) (PS) (U) (F)
 Solve
problems involving volume of right pyramids (R) (PS) (U) (F)
 Solve
problems involving volume of right cones (R) (PS) (U) (F)
 Solve
problems involving volume of spheres (R) (PS) (U) (F)
 Solve
problems involving volume of composite solids (R) (PS) (U) (F)


Level 10A 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?

·
Prove and apply angle and chord properties of circles
(ACMMG272)

Students will:
·
Describe a variety of parts of circles (U)
·
Calculate arc lengths (F)
·
Calculate angles and chord lengths using circle
theorems (R)
·
Prove angle and chord properties of circles (R)


Level 10A Measurement and Geometry
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?

·
Establish the sine, cosine and area rules for any triangle
and solve related problems (ACMMG273)
·
Use the unit circle to define trigonometric
functions, and graph them with and without the use of digital technologies
(ACMMG274)
·
Solve simple trigonometric equations (ACMMG275)
·
Apply Pythagoras’ theorem and trigonometry to
solving three dimensional problems in rightangled triangles (ACMMG276)

Students will:
·
apply knowledge of sine, cosine and area rules to
authentic problems such as those involving surveying and design (PS) (R) (U)
(F)
·
understand the relationship of the unit circle to
trigonometric functions for angles of any magnitude (U)
·
graph trigonometric functions with and without
digital technologies (U)
·
understand the graphs of trigonometric functions (U)
·
solve simple trigonometric equations (F)
·
solve problems related to trigonometric functions as
periodic e.g. those describing motion (PS) (R)
·
represent reallife problems using right angled
triangles where appropriate in three dimensions (R) (U)
·
Solve authentic problems using Pythagoras’s Theorem
and Trigonometry (PS) (R) (U) (F)


Level 10A Statistics and Probability
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?

·
Investigate reports of studies in digital media and
elsewhere for information on the planning and implementation of such studies,
and the reporting of variability (ACMSP277)

Students will:
·
Evaluate media reports that refer to data from a range
of contexts (R)
·
Evaluate the visual representation of data in media
reports (R)
·
Evaluate the size and type of samples used for data
collection in a variety of contexts (R)
·
Discuss appropriate methods of sampling for data
collection (U)
·
Generate data by posing appropriate questions and
making decisions about sampling a population (U)(R)


Level 10A Statistics and Probability
Data Representation and Interpretation
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 and interpret the mean and standard
deviation of data and use these to compare data sets (ACMSP278)
·
Use information technologies to investigate
bivariate numerical data sets. Where appropriate use a straight line to
describe the relationship allowing for variation (ACMSP279)

Students will:
·
Calculate the mean for a data set (F)
·
Calculate the standard deviation for a data set (F)
·
Compare data sets using their standard deviations
and mean values (R) (U)
·
Discuss data sets by interpreting their mean and
standard deviations (R) (U)
·
Represent bivariate numerical data sets graphically
using digital technologies (F)
·
Use straight lines (line of best fit) to represent
scatter plots and to describe the relationships between variables (F) (U)

