Mathematics
Scope and Sequence
Measurement and Geometry 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
Measurement and Geometry
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?

Using units of
measurement
·
Use direct and
indirect comparisons to decide which is longer, heavier or holds more, and
explain reasoning in everyday language (ACMMG006)
·
Compare and order the
duration of events using the everyday language of time (ACMMG007
·
Connect days of the
week to familiar events and actions (ACMMG008)
Shape
·
Sort, describe and
name familiar twodimensional shapes and threedimensional objects in the
environment (ACMMG009)
Location and
Transformation
·
Describe position and
movement (ACMMG010)

Students
will:
·
Compare longer, shorter, same and explain
reasoning (R)
·
Compare heavier, lighter, same and explain
reasoning (R)
·
Compare which holds more, less or same and
explain reasoning (R)
·
Be Fluent in comparing
objects directly (F)
·
Reason by explaining comparisons of quantities and
explaining processes for indirect comparison of measurement (R)
·
Know and use the language of time (F)
·
Compare and order the duration of events
using the language of time (F)
·
Be Fluent in sequencing and comparing the duration of
events
(F)
·
Reason by explaining comparisons of
time (R)
·
Connect days of the week to familiar events
and actions (U)
·
Understand connections between days of the week and
familiar events (U)
Students will:
·
Sort and describe
squares, circles, triangles, rectangles, spheres and cubes (U)
·
Show Understanding by
connecting names with objects (U)
·
Problem Solve through sorting, describe and classify objects (PS)
·
Reason by comparing and naming the shapes and attributes
of objects (R)
Students
will:
·
Know the everyday
language of location and direction (F)
·
Understand and use the language of location and direction (U)
·
Follow and give simple
directions using the language of location and direction (PS)


Achievement Standard: They compare objects using mass, length and
capacity. Students connect events and the days of the week. They explain the
order and duration of events. They use appropriate language to describe
location. They group objects based on
common characteristics and sort shapes and objects.
Level 1
Measurement and Geometry
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?

Using units of measurement
·
Measure and compare the lengths and
capacities of pairs of objects using uniform informal units (ACMMG019)
·
Tell time to the half hour (ACMMG020)
·
Describe duration using months, weeks, days
and hours (ACMMG021)
Shape
·
Recognise and classify familiar two
dimensional shapes and three dimensional objects using obvious features
(ACMMG022)
Location
and transformation
·
Give and follow directions to familiar
locations (ACMMG023)

Students
will:
·
Use uniform informal units to compare
longer, shorter, same and explain reasoning (R)
·
Use uniform informal units to compare
heavier, lighter, same and explain reasoning (R)
·
Use uniform informal units to compare which
holds more, less or same and explain reasoning (R)
·
Understand that
in order to compare objects, the unit of measurement must be the same size
(U)
·
Be Fluent in comparing objects
directly (F)
·
Reason by explaining comparisons of
quantities and explaining processes for indirect comparison of measurement
(R)
·
To know and use the language of time (F)
·
Compare and order the duration of events
using the language of time (PS)
·
read time on
analogue and digital clocks and observing the characteristics of half hour
times (F)
·
Be Fluent in sequencing and comparing the duration of
events
(F)
·
Reason by explaining comparisons of
time (R)
·
Connect months, weeks and days to familiar
events and actions (U)
·
Describe durations using months, weeks,
days and hours (U)
·
Understand connections between days,
weeks and months
·
Understand and order relative size of months, weeks, days and hours
·
Sort and describe
squares, circles, triangles, rectangles, spheres and cubes (F)
·
Connect shape names to
everyday objects (F)
·
Explore
geometric features and describe shapes and objects using everyday words such
as 'corners', 'edges' and 'faces' (R)
·
Show Understanding by connecting
names with objects
·
Problem Solve through sorting,
describe and classify objects by
corners, edges and faces
·
Reason by comparing and naming the
shapes and attributes of objects
·
Know the everyday
language of location and direction (U)
·
follow and give simple
directions using the language of location and direction (PS)
·
Understand the language of location and
direction (U)
·
Understand that
people need to give and follow directions to and from a place, and that this
involves turns, direction and distance (U)
·
Understand the meaning and
importance of words such as ‘clockwise’, ‘anticlockwise’, ‘forward’ and
‘under’ when giving and following directions interpreting and following
directions around familiar locations (U)


Achievement Standard: They recognise
Australian coins according to their value. Students explain time durations.
They describe two dimensional shapes and three dimensional objects. Students order objects based on lengths and
capacities using informal units. They tell time to the half hour. They use the
language of direction to move from place to place.
Level 2
Measurement and Geometry
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?

Using units of
measurement
·
Compare and order several shapes and objects
based on length, area, volume and capacity using appropriate uniform informal
units (ACMMG037)
·
Compare masses of objects using balance
scales (ACMMG038)
·
Tell time to the quarter hour, using the
language of 'past' and 'to' (ACMMG039)
·
Name and order months and seasons
(ACMMG040)
·
Use a calendar to identify the date and
determine the number of days in each month (ACMMG041)
Shape
·
Describe and draw two dimensional shapes,
with and without digital technologies (ACMMG042)
·
Describe the features of three dimensional
Objects (ACMMG043)
Location
and transformation
·
Interpret simple maps of familiar locations
and identify the relative positions of key features (ACMMG044)
·
Investigate the effect of onestep slides
and flips with and without digital technologies (ACMMG045)
·
Identify and describe half and quarter
turns (ACMMG046) l

Students
will:
·
Compare shapes and determine attributes of
length, area, volume and capacity (R)
·
Order shapes by one attribute, discuss
using the language of larger, smaller, longer, shorter, least, most, same,
equal value (F)
·
comparing lengths using finger length, hand
span or a piece of string (U)
·
estimate and use MAB minis and longs to
measure length in centimetres (PS)
·
compare areas using the palm of the hand or
a stone (R)
·
Use uniform grid paper to find the area in
squares of given shapes (U)
·
Estimate and compare capacities using a
range of containers and pouring materials (U)
·
Estimate and stack containers with uniform
cubes (unifix or MAB minis) to find volume in cubes (U)
·
Compare capacity of a range of containers
using the same uniform cubes (R & U)
·
Show Understanding by using length, area,
volume and capacity in problem solving contexts (U)
·
Show understanding by making and drawing
models and recording measurements of length, area, volume and capacity of
objects (U)
·
Estimate mass by hefting, using the
language of heavier, lighter and similar when comparing objects (R)
·
using balance scales to determine whether
the mass of different objects is more, less or about the same, or to find out
how many single items are need to balance a different item (PS)
·
Use a uniform object to compare items to on
the balance scale (U)
·
Estimate and compare objects using uniform
metric weights to compare items on the balance scale (U)
·
Show fluency through using units
iteratively to compare measurements (F)
·
Identify and mark quarters on the analogue
clock (U)
·
Identifying the quarter after an hour as
quarter past an hour and the quarter before an hour as quarter to an hour (U)
·
Link the quarter past as 15 minutes and the
quarter to as 45 minutes (U)
·
describe the characteristics of ‘quarter
past’ times on an analogue clock, and identifying that the small hand is
pointing just past the number and the big hand is pointing to the three (R)
·
describe the characteristics of ‘quarter
to’ times on an analogue clock, and identifying that the small hand is
pointing almost to the next number and
the big hand is pointing to the nine (R)
·
Show fluency
through describing and comparing time durations (F)
·
Problem Solving using time and formulating
problems from authentic situations to represent quarter past and quarter to
(PS)
·
Identify and describe features of a
calendar (U)
·
Create a calendar to represent a specific
time period (PS)
·
Understand the
current use of Seasons representing a specific time period
·
Use a calendar as an ongoing tool to record
time and specific events each month (U)
·
Use a calendar to predict time frames by
month, week and days (PS)
·
Use a calendar to identify the date and to
determine the number of days in each month (PS & R)
·
use calendars to locate specific
information, such as finding a given date on a calendar and saying what day
it is, and identifying personally or culturally specific days (F)
·
investigate the seasons used by Aboriginal
people and compare them to those used in Western society, recognising the
connection to weather patterns (U)
·
Show understanding
by connecting knowledge of time from smallest time frame to largest time
frame (U)
·
Identify and name 2 dimensional shapes (F)
·
Compare and describe 2D shapes to develop
the vocabulary of straight and curved lines, edges, points and corners,
number of sides (U)
·
identifying key features of squares,
rectangles, triangles, kites, rhombuses and circles, such as straight lines
or curved lines, and counting the edges and corners (R)
·
Show reasoning
by sorting shapes by key features and describing the categories
·
Identify and name known 3 dimensional
shapes such as cube, cone, sphere, pyramid (F)
·
identifying geometric features of known
shapes such as the number of faces, corners or edges (U)
·
Investigate and identifying geometric
features of prisms and other 3D shapes through the use of models, such as the
number of faces, corners or edges (R)
·
Use Pictures, Numbers, Words to show what
is known about 3D shapes (PS)
·
Show reasoning
by describing connections between 2D and 3D representations
·
Understand and use
directional language left and right, up (top) and down (bottom) on a page and
transfer this to reading a map
·
Use directional language of beside,
between, next to, to tell directions on a map (PS)
·
construct arrangements of objects from a
set of directions (PS)
·
Use problem
solving strategies to plan problems for others by planning routes on maps
and recording the directions (PS)
·
Through problem solving match transformations with their original shape
(PS)
·
Understand
that
we use representations of objects and their positions, such as on maps, to
allow us to receive and give directions and to describe place (U)
·
Investigate one step slides using models
(PS)
·
Investigate one step flips using models
(PS)
·
Show understanding
by using Pictures, Numbers, Words to show, describe and compare slides and
flips (U)
·
Students model half and quarter turns
related to analogue clock (F)
·
predict and reproduce a pattern based
around half and quarter turns of a shape and sketching the next element in
the pattern (PS)
·
Investigate the real world application of
flips, slides and turns (PS)
·
understand that
objects can be moved but changing position does not alter an object’s size or
features (U)


Achievement
Standard: Students
recognise the features of three dimensional objects. They interpret simple maps
of familiar locations. They explain the effects of onestep transformations.
Students make sense of collected information. Students order shapes and objects
using informal units. They tell time to the quarter hour and use a calendar to
identify the date and the months included in seasons. They draw two dimensional
shapes.
Level 3
Measurement
and Geometry
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?

Using
units of measurement
·
Measure, order and compare objects using familiar
metric units of length, mass and capacity(ACMMG061)
·
Tell time to the minute and investigate the
relationship between units of time (ACMMG062)
Shape
·
Make models of threedimensional objects and
describe key features (ACMMG063)
Location
and transformation
·
Create and interpret simple grid maps to show
position and pathways (ACMMG065)
·
Identify symmetry in the environment (ACMMG066)
Geometric
reasoning
·
Identify angles as measures of turn and compare
angle sizes in everyday situations (ACMMG064)

Students
will:
·
Recognise the importance of using common units of
measurement. (R)
·
Recognise and use centimetres and metres, grams and
kilograms, and millilitres and litres. (F)
·
Tell and write time to the minute. (F)
·
Understand, use and order units of time. (U,F)
·
Use nets to make threedimensional objects and
identify faces, edges and vertices. (P)
·
Create simple maps. (P)
·
Use simple maps such as
theme park or zoo maps. (U)
·
Identify symmetrical patterns, pictures and shapes.
(P)
·
Identify comparative sizes
of angles in everyday situations including the hands on a clock. (R)


Achievement Standard: By the end of Level 3, students
identify symmetry in the environment. They match positions on maps with given
information. Students recognise angles in real situations. They interpret and
compare data displays. Students use metric units for length, mass and capacity.
They tell time to the nearest minute. Students make models of threedimensional
objects.
Level 4
Measurement
and Geometry
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?

Using
units of measurement
 Use scaled instruments to measure and compare
lengths, masses, capacities and temperatures(ACMMG084)
 Compare objects using familiar metric units of
area and volume (ACMMG290)
·
Convert between units of time (ACMMG085)
·
Use am and pm notation and solve simple time
problems (ACMMG086)
Shape
·
Compare the areas of regular and irregular shapes by
informal means (ACMMG087)
·
Compare and describe two dimensional shapes that
result from combining and splitting common shapes, with and without the use
of digital technologies(ACMMG088)
Location and transformation
·
Use simple scales, legends and directions to
interpret information contained in basic maps(ACMMG090)
·
Create symmetrical patterns, pictures and shapes
with and without digital technologies (ACMMG091)
Geometric
reasoning
·
Compare angles and classify them as equal to,
greater than or less than a right angle (ACMMG089)

Students will:
·
Read and interpreting
scales on a range of measuring instruments. (U)
·
Comparing areas using centimeter grid paper and volume
using centicubes and litres in authentic contexts. (R)
·
·
Convert between units of time including
hours to minutes and weeks to days and vise versa. (F)
·
Apply am and pm
appropriately. (R)
·
Calculate elapsed
time problems using counting on strategies. (F)
·
Comparing areas using informal means such as centimeter
grid paper or tiles. (R)
·
Identifying common twodimensional shapes that are part
of a composite shape by recreating it from these shapes. (R)
·
Understand and use
scales and directions in maps. (U)
·
Create symmetrical patterns, pictures and
shapes. (P)
·
Apply Acute, Right
and Obtuse correctly to angles in everyday situations. (F)


Achievement
Standard:
By the end of Level 4, students compare areas of regular and irregular shapes
using informal units. They solve problems involving time duration. They
interpret information contained in maps. Students use scaled instruments to
measure temperatures, lengths, shapes and objects. They convert between units
of time. Students create symmetrical shapes and patterns. They classify angles
in relation to a right angle.
Level 5
Measurement
and Geometry
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?

Using
units of measurement
1.
 Compare 12 and 24hour time
systems and convert between them (ACMMG110)
Shape
1.
·
Connect threedimensional objects with their nets
and other twodimensional representations(ACMMG111)
Location
and transformation
·
Use a grid reference system to describe locations.
Describe routes using landmarks and directional language (ACMMG113)
·
Describe translations, reflections and rotations of
twodimensional shapes. Identify line and rotational symmetries (ACMMG114)
·
·
·
·
·
Apply the enlargement transformation to
familiar two dimensional shapes and explore the properties of the resulting
image compared with the original(ACMMG115)
Geometric
reasoning
·
Estimate, measure
and compare angles using degrees. Construct angles using a protractor(ACMMG112)

Students
will:
·
Choose, use and describe appropriate units of
measurement for length, area, volume, capacity and
mass. (U,R)
·
Use a variety of strategies
in calculating the area and perimeter of rectangles. (F,R)
·
Compare 12 and 24hour time systems and convert
between them. (F)
·
Make and use nets of a
variety of 3D shapes. (R)
·
Use 2D representations of 3D
shapes. ®
·
Understand and use common
grids in everyday situations such as maps. (U)
·
Describe routes using the
language of direction. (U)
·
identify and describe the lines and rotational
symmetries of a range of twodimensional shapes, by manually cutting, folding
and turning shapes and by using digital technologies. (P)
·
identify the effects of transformations by manually
flipping, sliding and turning twodimensional shapes and by using digital
technologies. (R)
·
Enlarge 2D figures using
manual and digital technologies. (F)
·
Identify and measure the
angles in a figure. (F)
·
Estimate and compare angles
in a figure. (R)


Achievement Standard: By the end of Level 5, students
connect threedimensional objects with their twodimensional representations.
They describe transformations of twodimensional shapes and identify line and
rotational symmetry. They use appropriate units of measurement for length,
area, volume, capacity and mass, and calculate perimeter and area of
rectangles. They convert between 12 and 24 hour time. Students use a grid
reference system to locate landmarks. They measure and construct different
angles.
Level 6
Measurement and Geometry
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?

Using
units of measurement
·
Connect decimal representations
to the metric system (ACMMG135)
·
Convert between common metric units of length, mass
and capacity (ACMMG136)
·
Solve problems involving the comparison of lengths
and areas using appropriate units(ACMMG137)
·
Connect volume and capacity and
their units of measurement (ACMMG138)
·
Interpret and use timetables (ACMMG139)
Shape
·
Construct simple prisms and pyramids (ACMMG140)
Location
and transformation
·
Investigate combinations of translations,
reflections and rotations, with and without the use of digital
technologies (ACMMG142)
·
Introduce the Cartesian coordinate system using all four
quadrants (ACMMG143)
Geometric
reasoning
 Investigate, with and without
digital technologies, angles on a straight line, angles at a point and
vertically opposite angles. Use results to find unknown angles (ACMMG141)

Students will:
·
Understand the connection
between the Base 10 System of numbers and the Decimal system of
measurement. (U)
·
Convert between different
decimal units. (F)
·
Be able to use different
units of measurement in appropriate contexts to solve everyday problems
involving length and area. (P)
·
Use volume and capacity in
everyday situations. (F)
·
Use common timetables such
as public transport. (F)
·
Use a variety of materials
to construct and deconstruct prisms and pyramids. (P)
·
identify the effects of a combination of
transformations by flipping, sliding and turning twodimensional shapes. (R)
·
Use and relate the Cartesian
Plane to everyday situations. (U)
·
Identify the four quadrants
of a Cartesian plane and plot points into all four quadrants. (F)
·
Identify, define and measure right, acute, obtuse,
straight and reflex angles. (F)
·
Identify vertically opposite angles and use to
determine unknown angles such as intersecting roads. (U,R)


Achievement Standard: By the end of Level 6, students
connect decimal representations to the metric system and choose appropriate
units of measurement to perform a calculation. They make connections between
capacity and volume. They solve problems involving length and area. They
interpret timetables. Students describe combinations of transformations. They
solve problems using the properties of angles. Students locate an ordered pair
in any one of the four quadrants on the Cartesian plane. They construct simple
prisms and pyramids.
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.
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.
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.
Level 8
Measurement and 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?

·
Choose appropriate units
of measurement for area and volume and convert from one unit to another(ACMMG195)
·
Find perimeters and areas
of parallelograms, trapeziums, rhombuses and kites (ACMMG196)
·
Investigate the
relationship between features of circles such as circumference, area, radius
and diameter. Use formulas to solve problems involving circumference and
area (ACMMG197)
·
Develop the formulas for
volumes of rectangular and triangular prisms and prisms in general. Use
formulas to solve problems involving volume(ACMMG198)
·
SSolve problems involving
duration, including using 12 and 24hour time within a single time zone(ACMMG199)

Students
will:
·
Distinguish between area and volume and choose the
appropriate units of measurement for each. (U)
·
Convert between units of area and between units of
volume. (F)
·
Name and determine the perimeter and area of
parallelograms, rhombuses and kites. (F)
·
Determine the circumference and area of a circle by
direct measurement. (R)
·
Demonstrate that by knowing circumference of a
circle (its perimeter) we can determine its radius which in turn, can help me
find its diameter and area. Or knowing its radius, I can find the area,
circumference and diameter. (U, F, R)
·
Explain how, what and why Pi is used in equations
related to circles. (U)
·
Know how the formulae for all 3D shapes are related
and variations of Length x Width x Height.(U)
·
Solve problems involving duration, including using
12 and 24hour time within a single time zone. (PS)
·
Convert between 12 and 14 hour time and across time
zones. (U)
·
Determine the arrival time given a flight time and
time zones.(R)


Achievement Standard:
By the end of Level 8, students
convert between units of measurement for area and volume. They perform
calculations to determine perimeter and area of parallelograms, rhombuses and
kites. They name the features of circles and calculate the areas and
circumferences of circles. Students solve problems relating to the volume of
prisms. They make sense of time duration in real applications.
Level 8 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?

·
Define congruence of
plane shapes using transformations. (ACMMG200)
·
Develop the conditions
for congruence of triangles. (ACMMG201)
·
Establish properties of
quadrilaterals using congruent triangles and angle properties, and solve
related numerical problems using reasoning. (ACMMG202)

Students
will:
 Describe
transformations including: translations, rotations and reflections. (F)
 Define
congruence of plane shapes using transformations. (R)
 Use the conditions for
congruence of triangles including, congruence (SSS, SAS, ASA and RHS),
and demonstrating which conditions do not prescribe congruence (ASS,
AAA). (R)
 Use coordinates to describe
the transformation. (F)
 Describe properties of
quadrilaterals including squares, rectangles, parallelograms, rhombuses,
trapeziums and kites. (U)
 Determine the sum of internal
angles of a polygon, using triangles. (F)
 Solve problems using the sum
of internal angles for triangles and other polygons. (F)
 Determine lines of symmetry
in a given shape. (U)
 Identify properties related to side lengths, parallel sides,
angles, diagonals and symmetry. (R)


Achievement Standard:
By the end of Year 8, students identify conditions for
the congruence of triangles and deduce the properties of quadrilaterals.
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.
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.
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.
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.
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.
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 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 relationships 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)


