Download Australian Curriculum Mathematics

Australian Curriculum: Mathematics Bridging Document
What’s new or different in relation to the Tasmanian Curriculum (P–10*)?
Mapping Australian Curriculum ‘Content Descriptions’ and Tasmanian Curriculum ‘Opportunities to Learn’
Prepared for Department of Education Schools, February, 2011
*A separate bridging document for Kindergarten will be available at the end of February 2011
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
1
General Comments:



The document is to be read in conjunction with the Australian Curriculum.
This document has been prepared in order to map the differences between the Australian Curriculum content descriptions and the Tasmanian
Curriculum opportunities to learn and serve as bridge between the two documents. It is not intended that it be used for assessment purposes.
Teachers will continue to use a rich range of teaching approaches based on the Learning, Teaching and Assessment principles as outlined in the
Tasmanian Curriculum.
Organisational features:

The Tasmanian Curriculum for mathematics has 6 strands: number, algebra, function and pattern, measurement, chance and data, space and working
mathematically. The Australian Curriculum is organised into three strands and 13 sub-strands, with 4 proficiency strands embedded throughout (see
table below).
Number and Algebra
Measurement and Geometry
Statistics and Probability
Number and place value (F-8)
Using units of measurement (F-10)
Chance (1-10)
Fractions and decimals (1-6)
Shape (F-7)
Data representation and interpretation (F-10)
Real numbers (7-10)
Geometric reasoning (3-10)
Money and financial mathematics (1-10)
Location and transformation (F-7)
Patterns and algebra (F-10)
Pythagoras and trigonometry (9-10)
Linear and non-linear relationships (8-10)
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
2
Curriculum area specific comments:



There is a high degree of similarity between the Tasmanian Curriculum and the Australian Curriculum for mathematics.
The Australian Curriculum places strong emphasis on the teaching and assessment of the mathematical proficiencies of understanding, fluency,
problem solving and reasoning. School programs should reflect this emphasis.
It is clear that there is a strong emphasis on the focused teaching of number in the primary years, with key focus on deeply understanding numbers
and the connections between operations. Explicit teaching for understanding of fractions and multiplication are two key areas for focus.

Statistics and probability in the Australian Curriculum are less complex than the Tasmanian Curriculum in the primary years – this has implications
for the focus in primary years i.e. increased focus on number and geometry.

In the secondary years in the Australian Curriculum there is a strong emphasis on geometry and algebra. There are some likely professional learning
needs in regard to both areas, particularly for junior secondary teachers.

The use of appropriate ICT will enhance teaching and learning.

The current focus in Tasmanian schools on the explicit teaching of mental computation should be continued and supported.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
3
Year Foundation: (Prep)
Content generally maps to Stage 3 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?

Implications for professional learning and/or teaching focus
Expectations for statistics and probability in Australian Curriculum are
less complex currently in the Tasmanian Curriculum.
Geometry

Sort, describe and name familiar two-dimensional shapes and three
dimensional objects in the environment.

Ensure students are exposed to three-dimensional objects and their
features (e.g. toothpaste boxes, balls, dice, and other everyday items) as
well as 2 dimensional shapes.

Ensure development of visual/mental images for number through
subitising.
Number and algebra

Subitise small collections of objects.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
4
Year 1:
Content generally maps to Stage 5, some elements in Stage 4 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus

Money has moved from measurement into number in the Australian
Curriculum.

Ensure students are exposed to features of shapes and objects,
including emphasis on vocabulary e.g. corners, faces, edges, sides.
Geometry:

Visualising and classifying two dimensional shapes and three
dimensional objects.
Number and algebra:

Count collections to 100 by partitioning numbers using place value.

This expectation is beyond that of the Tasmanian Curriculum. Focus
on numbers to 100 and experiences with bead strings, 1-100 boards,
number lines to build mental images. Flexible partitioning is the focus
for talking about, modelling and representing numbers.

Recognise and describe one half as two equal parts of a whole.

Introduce half as two equal parts of a whole – ensure many models are
used, not just fraction diagrams. Connect the idea of half to the clock
(half hour).

Investigate and describe number patterns formed by skip counting.

Focus on skip counting in composite groups.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
5
Year 2:
Content generally maps Stages 5/6/7 to predominately Stage 6 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus
Number and algebra:

Investigate number sequences, initially those increasing and decreasing
by twos, threes, fives and 10s from any starting point, then moving to
other sequences.

Recognise, model, represent and order numbers to at least 1000.

Group, partition and rearrange collections up to 1000 in 100s, 10s and
ones to facilitate more efficient counting – the expectation that students
deal with numbers to 1000 is beyond where they would currently be
working – a new emphasis.

Recognise and interpret common use of halves, quarters and eighths of
shapes and collections.

Numbers to 1000 are a focus. Ensure that students deal with larger
numbers and apply solid understandings of place value patterns to build
understandings.

Includes eighths as well as halves and quarters (currently in the
Tasmanian Curriculum halves and quarters are at Stage 6). Build
understanding through paper folding and models based on halving and
halving again and again and looking at patterns.
Geometry and measurement:

Identify and describe half and quarter turns (as pre cursors to
understanding angles) – not evident in Tasmanian Curriculum at this
stage (currently at Stage 7).

Links to fractions and time should be made when dealing with angles.
Ensure the focus is on the questions: “What turns?” and “How far does
it turn?”

Use a calendar to identify the date and determine the number of days in
each month.

Greater emphasis on calendar work.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
6
Year 3:
Content generally maps to Stage 7/8 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus
Number and algebra:

Investigate the conditions required for a number to be odd or even.
Identify odd and even numbers.

Focus on place value partitioning and renaming of numbers to
10 000 according to place value parts is significant.

Recognise, model, represent and order numbers to at least 10 000.

Focus on equivalence and connections between addition and
subtraction.

Apply place value to partition, rearrange and regroup numbers to at
least 10 000 to assist calculations and solve problems: Working with
numbers to 10 000 is beyond current curriculum expectations.

Recall of multiplication facts of 2, 3, 5 and 10 and related division facts.

Ensure students are provided with strategies to build recall of
multiplication and related division facts with understanding.

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their
multiples to a complete whole.

Build understanding of fractions through hands on experiences, relating
parts to the whole.
Measurement and geometry:

Tell the time to the minute and investigate relationship between units of
time.

Identify angles as measures of turn and compare angle sizes in everyday
situations (e.g. a wide or narrow angle, noticing angles in open doors,
pizzas and clocks).
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
7
Year 4:
Content generally maps to Stage 8 in all strands with some elements evident of Stage 9 opportunities to learn in the Tasmanian
Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus
Geometry:

Use scale to interpret information contained in basic maps.

Introduce simple scales when working with maps.

Build informal understanding of angles to focus on right angles i.e. use
informal angle measurers (strips of card joined with slit pins) to find
right angles in the environment e.g. desk corners, windows.

Focus on converting between units of time using contextual situations
and real world problems.
Angles:

Compare angles and classify them as equal to, greater than or less than a
right angle.
Time:

Convert between units of time.
Number and algebra:

Apply place value to partition, rearrange, and regroup numbers to at
least tens of thousands to assist calculations and solve problems.

Focus on place value, reading, writing and ordering larger numbers and
understanding place value parts and patterns.

Counting by quarters and halves.

Ensure use of number lines to support counting in fractional parts.

Investigate equivalent fractions in context.

Build understanding of equivalent fractions in contextual, real life
situations.

Recognise that the place value system can be extended to tenths and
hundredths. Make connections between fraction and decimal notation.

Ensure decimal fractions are introduced using decimal squares and
number lines to build mental images (research shows that using money
to introduce decimals is problematic and should be avoided).

Recall multiplication facts up to 10x10 and related division facts.

Ensure teaching of multiplication and associated division facts is
built up over all years of schooling. Ensure multiplication and
division strategies are taught and made explicit.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
8
Year 5:
Content mainly maps to Stage 9 with some aspects evident of Stages 7, 8 and 10 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Number and algebra:
 Describe, continue and create patterns with fractions, decimals and
whole numbers resulting from additions and subtraction.

Implications for professional learning and/or teaching focus

Focus on teaching for understanding of fractions and their connections to
decimals, including counting on a number line.
Investigate strategies to solve problems involving addition and
subtraction of fractions with the same denominator.
Geometry:

Estimate, measure and compare and construct angles using protractors.

Ensure angles are addressed in all year groupings and understandings
consolidated. Expose students to full and half circle protractors, as well
as dynamic interactive software.

Describe translations, reflections and rotations of two-dimensional
shapes. Identify line and rotational symmetries - not specifically
mentioned in Tasmanian Curriculum.

Increased focus on geometry.

Apply the enlargement transformation to familiar two-dimensional
shapes and explore the properties of the resulting image compared
with the original.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
9
Year 6:
Content mainly maps to Stage 10, with some elements evident of Stage 11 and 12 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus

Current research indicates the need for explicit focused teaching of
fraction concepts in the middle years using a range of tools and models.
Some professional learning may be required.
Measurement and geometry:

Convert between common metric units of length, mass and capacity.

Provide realistic contexts to investigate conversions of common metric
units.

Connect volume and capacity and their units of measurement.

Ensure practical exploration of concepts of volume and capacity.

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.

Focus on angle relationships and properties including vocabulary and
practical investigations.

Investigate combinations of translations, reflections, and rotations, with
and without digital technologies.

Emphasis on geometry, including vocabulary, hands on experiences and
use of models and dynamic software.

Introduce Cartesian co-ordinate system using all four quadrants.

Focus on introducing Cartesian plane and its usefulness in representing
relationships.

Describe probability using fractions decimals and percentages.

New emphasis at this year level.

Compare observed frequencies across experiments with predicted
frequencies.

Focus on data experiments with and without digital technologies.

Interpret and compare a range of data displays including segmented bar
charts, and side by side column graphs for two categorical variables.

Critical analysis of sampling technique and identifying bias in data
representations.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
10
Year 7:
Content generally maps to Stages 10 to 12 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus
Geometry and measurement:

Calculate volumes of rectangular prisms.

Build understanding of volume relationships through hands-on
experiences.

Establish the formulas for areas of rectangles, triangles and
parallelograms and use these in problem solving.

Ensure there is an adequate focus on geometry. Build expertise in use
of appropriate ICT. Some teacher professional learning may be
required. Parallelograms are new in this content description.

Identify corresponding, alternate and co-interior angles when two
parallel straight lines are crossed by a transversal.

Continued emphasis on geometry.

A specific emphasis on translations, reflections and rotations on the
Cartesian plane using co-ordinates.

Continued emphasis on geometry.
Number and algebra:

Investigate index notation and represent whole numbers as products of
powers of prime numbers.

Ensure that number focus includes properties of numbers, composites
and primes, perfect square and square roots, and use suggested ideas in
Stage 12 of Tasmanian Curriculum including factor trees.

Understand and perform calculations with fractions.

Current research indicates the need for explicit focused teaching of
fraction concepts in the middle years using a range of tools and models.
Some professional learning may be required.

Write algebraic expressions and evaluate them by substituting a given
value for each variable.

New emphasis at this year level
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
11
Year 8:
Content generally maps to Stages 12 and 13, with some aspects of Stage 14 evident in algebra opportunities to learn in the Tasmanian
Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus
Geometry and measurement:

Specific focus on calculating perimeter and area of parallelograms, rhombuses and
kites. In Tasmanian Curriculum this was covered in Stage 12 compound shapes.

Ensure focus on use of dynamic software packages for geometry.

Establish properties of quadrilaterals using congruent triangles.

Congruence not specifically mentioned in the Tasmanian Curriculum.

Solve problems involving duration, including 12 and 24 hour time within a single
time zone.

New emphasis.

New emphasis for this grade level.

Not specifically mentioned in the Tasmanian Curriculum.
Number and algebra:

Requirements around expansion, factorisation and simplifying.
Statistics and probability:

Identify complementary events and use the sum of probabilities to solve
problems.

Describe events using language of ‘at least’ exclusive ‘or’ (A or B but not both)
inclusive ‘or’ (A or B or both) and ‘and’.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
12
Year 9:
Content maps to Stage 13/14 with some elements evident of Stage 15 opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus

Ensure focus on use of dynamic software packages for geometry.

Not specifically mentioned in the Tasmanian Curriculum.

Not specifically mentioned in the Tasmanian Curriculum.
Number and algebra:

Find distance and midpoint of a line segment using graphical and algebraic
techniques.

Sketch simple non-linear relations with or without the use of digital technologies.
Geometry and measurement:

Investigate very small and very large time scales.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
13
Year 10:
Content maps to Stages 14/15 (Year 10A – beyond Stage 15) opportunities to learn in the Tasmanian Curriculum
Australian Curriculum content descriptions:
What’s new or different?
Implications for professional learning and/or teaching focus

Ensure all areas covered in Stage 14/15 are covered during Year 10.

Ensure focus on use of dynamic software packages for geometry.

Not specifically mentioned in the Tasmanian Curriculum.
Number and algebra:

Solve linear inequalities and graph their solutions on a number line.
Measurement and geometry:

Formulate proofs involving congruent triangles and angle properties.
Australian Curriculum: Mathematics Bridging Document – What’s new or different in relation to the Tasmanian Curriculum?
14