Australian Mathematics Curriculum – AusVELS – Level 6
These levels [levels 3 – 6] emphasise the importance of students studying coherent, meaningful and purposeful mathematics that is relevant to their lives.
Students still require active experiences that allow them to construct key mathematical ideas, but also gradually move to using models, pictures and symbols
to represent these ideas.
The curriculum develops key understandings by extending the number, measurement, geometric and statistical learning from the early levels; by building
foundations for future studies through an emphasis on patterns that lead to generalisations; by describing relationships from data collected and represented; by
making predictions; and by introducing topics that represent a key challenge in these levels, such as fractions and decimals.
In these levels of schooling, it is particularly important for students to develop a deep understanding of whole numbers to build reasoning in fractions and
decimals and to develop a conceptual understanding of place value. These concepts allow students to develop proportional reasoning and flexibility with
number through mental computation skills, and to extend their number sense and statistical fluency.
Suggested Yearly Overview – Term by Term Planner

The following overview has been developed using the Australian Mathematics Curriculum content and proficiency standards as a basis for the outline.
Teachers will therefore need to develop appropriate quality learning experiences, and use the outcomes from these activities to determine progress in
relation to the standards. Teachers need to make continual reference to the descriptors and elaborations listed in the AMC as this overview only
shows a suggested outline.

While the term by term topics have been divided up throughout the year for planning purposes, the content will often be interwoven with topics
featured in different terms. The selection of topics in different content strands will often complement each other [for e.g. length could connect to
addition, subtraction, decimals and graphing. Fractions could relate to clocks, shape, division and graphing.] Schools may need to alter the overviews
based on their needs. Local events, integrated curriculum topics, school camp and other circumstances will need to be considered.

While the structure is adjustable to suit the needs of the school, the basic outline works on the premise that at least five hours per week is timetabled
for mathematics. To help cover the content listed teachers should endeavor to address several outcomes in the one lesson by integrating across the
strands but still have a clear focus for the lessons planned. Opportunities for teachers to link mathematics to other learning areas such as English,
Science or History will help students make connections across learning domains.

There are three cross curriculum priorities in the Australian Curriculum: Aboriginal and Torres Strait Islander histories and cultures: Asia and
Australia’s engagement with Asia: Sustainability. These priorities should be connected to tasks where there are natural and clear connections to the
content being taught. The AMC lists possible descriptors that naturally connect to these cross curriculum priorities.
© Michael Ymer ymermick@bigpond.com
Proficiency Strands -‘How’ content is explored or developed.
Understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making
reasonable estimations
Fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring
using metric units, and interpreting timetables
Problem Solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays, and finding the size of unknown angles
Reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another, explaining why the actual results of chance
experiments may differ from expected results.
The proficiency strands need to be embedded in all content strands.
Term
Content Strands - ‘What’ is to be learnt.
Number and Algebra
.•
Consolidate place value of whole numbers. Ensure that students can see and understand the Second Place-Value Pattern which
involves the repeated use of hundreds, tens and ones to count certain units (e.g., thousands, millions, billions, trillions ...) from 1
to 999 instead of 1 to 9. Discuss the idea of infinity in relation to our number system.
•
Investigate everyday situations that use integers. Locate and represent these numbers on a number line. For example -3, -2, -1, 0,
1, 2, 3,..Use stories that help students see relationship between positive and negative integers such owing money, below ground
floor using an elevator, pool depth etc. Use ordered pairs of integers to represent coordinates of points and locate a point in any
one of the four quadrants on the Cartesian plane. Refer to work in geometry.
•
1
Consolidate place value work with decimal and common fractions listed at level 5 [refer to level 5 overview]
A clear understanding of how these numbers are the same but represented differently is essential. Make both digital and manual
models such as fraction walls that include both representations and use this wall to compare fractions with related denominators
demonstrating equivalence. Use these drawings and models as a reference for proof and justification of answers in the terms ahead
when operating with decimals and fractions.
•
Select and apply efficient mental strategies and appropriate digital technologies to solve problems involving all four operations
with whole numbers applying strategies already developed for solving problems involving small numbers to those involving large
numbers.
* For e.g. If I know that double 8 is 16 then I also know that double 8 hundred is 16 hundred and this is 1 600.
* Use a range of strategies to solve realistic problems and commenting on the efficiency of different strategies. It is probably
quicker to find the difference between two numbers by adding on from the smallest than taking away one from the other. Let’s
investigate this idea using problems with money, our heights, our family ages etc.
* Recognise the usefulness of estimation and rounding when mentally calculating and being able to check the answer for
reasonableness with and without calculators.
•
Identify and describe properties of prime, composite, square and triangular numbers. Use materials such as square tiles to make,
© Michael Ymer ymermick@bigpond.com
Statistics and
Probability
Measurement and Geometry

This term work in the Measurement and Geometry area
will be integrated into our work in the Number and
Algebra areas.
Specific Measurement and Geometry areas will be
covered in following terms.
Statistics
Interpret and compare a range
of data displays, including
side by- side column graphs
for two categorical variables
*Comparing different
student-generated diagrams,
tables and graphs, describing
their similarities and
differences and commenting
on the usefulness of each
representation for interpreting
the data
draw on grid paper, search for digital photos on line, take digital photos around school that show the properties of these numbers.
•
Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence.
Identifying and generalising the number patterns. Make connections in this area of algebra into the work mentioned earlier this
term on investigating numbers on fraction walls. Mix the sequences up with all three types of number.
•
Continue work from first term on prime, composite, square and triangular numbers. Begin to understand that some numbers have
special properties and that these properties can be used to solve problems.
* For example representing composite numbers as a product of their prime factors [12 has the prime factors of 2 x 2 x 3] and
using this form to simplify calculations. 8 x 12 could be 8 x 2 x 2 x 3. Apply this to other examples to simplify problems.
* Understanding that if a number is divisible by a composite number then it is also divisible by the prime factors of that number
(for example 216 is divisible by 8 because the number represented is also divisible by 2 and 4 which are the prime factors of 8.
* investigate highest common factors of two whole numbers [ this is the greatest common divisor – e.g. 8 and 12 have the highest
common factor of 4. ] and the lowest common multiple of two whole numbers [ 8 and 12 have the lowest common multiple of 24.]
•
Continue term one work on efficient strategies when mentally computing. Revisit and multiplication and division facts to 10 x 10
for students who need are yet to attain recall. [Refer to level 4 overview for ideas]

Explore the use of brackets and order of operations to write number sentences. Appreciate the need for rules to complete multiple
operations within the same number sentence. 2 + 3 x 4 could equal 20 or 14. Investigate the need for a rule or brackets.
•
Extend understanding of operations with all numbers and solve problems involving the four operations. Focus on multiplication
and division this term. Use a range of strategies such as materials and models, written, mental, estimation and digital technologies
with an emphasis on efficiency. Use measurement topics such as volume and area to support understanding in contexts. Create
and solve written number stories.
© Michael Ymer ymermick@bigpond.com