Mathematics
Content Descriptors with Learning Goals /
Indicators and Proficiencies
Level 1
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
1 Sequence
Level 1 document learning goals and
proficiencies are sequenced within each substrand by order of conceptual
development. Substrands are not in
difficulty order.
Number
and Algebra
– Number and Place value descriptors are in sequence for teaching and learning.
Patterns
and Algebra descriptor learning goals and proficiencies need to be integrated
and developed consistently within Number and linked to Geometry.
Measurement and Geometry – Sorting shape will
relate to the pattern and algebra concepts and be ongoing for students
throughout the year.
All
descriptors can be taught independently, the goals and proficiencies for each
are in difficulty order.
Statistics
and Probability
– Is not a unit of work, rather the Chance descriptor and Data descriptor
should be introduced and revisited frequently throughout each term, related to
other curriculum areas and other content within mathematics.
Level 1
Number and Algebra
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

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

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

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


Achievement Standard: Students describe number sequences resulting from
skip counting by 2s, 5s and 10s. They identify representations of one half. Students count to and from 100 and locate
numbers on a number line. They carry out simple additions and subtractions
using counting strategies. They partition numbers using place value. They
continue simple patterns involving numbers and objects. They recognise
Australian coins according to their value.
Level 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 1
Statistics
and Probability
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?

Chance
·
Identify outcomes of familiar events
involving chance anddescribe them using everyday language such as ‘will
happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024)
Data
representation and interpretation
·
Choose simple questions and gather
responses (ACMSP262)
·
Represent data with objects and drawings
where one object or drawing represents one data value. Describe the displays
(ACMSP263)

Students
will:
·
pose questions about
themselves and familiar objects and events (U)
·
identify outcomes of
familiar events involving chance, describing them using everyday language (R)
·
represent responses to
questions using simple displays such as a probability line (F)
·
Problem Solve through
modelling authentic problems, using familiar counting sequences to solve
unfamiliar problems, and discussing the reasonableness of the answer (PS)
·
Reason by explaining comparisons of
quantities (R)
·
use data displays to
answer simple questions, developing the language of least, most, same amount
(U)
·
Use tally marks to
record (F)
·
determinine
which questions will gather appropriate responses for a simple investigation
(R)
·
Problem Solve through
modelling authentic problems, using familiar counting sequences to solve
unfamiliar problems, and discussing the reasonableness of the answer (PS)
·
Reason by explaining comparisons of
quantities (R)
·
Understand that one
object or drawing represents on data value (U)
·
Explain the display
and what it tells us about the data (U)
Compares categories using language such as greatest or least (R


Achievement Standard: Students describe data displays. Students classify
outcomes of simple familiar events. They collect data by asking questions and
draw simple data displays.