Ways Forward

Ways Forward with the New Syllabus K-6
WESTERN SYDNEY REGION: SUZANNE GIBSON
ROWENA WHITTLE
PAMELA ARMOUR
November 2012

The Australian Curriculum:
Mathematics
 First published Dec 2010 (V1.0), Oct 2011 (V2.0)
 „Complete version‟ V3.0 published January 2012
 The world‟s first online curriculum: presented as a
database from which you can select and print
 Content organised by Year levels, not Stages
 Three content strands:
 Each strand has a number of sub-strands

Number
and Algebra
Measurement
and Geometry
Statistics
and Probability
Number and place value Using units of
measurement
Chance
Real numbers Shape Data representation
and interpretation
Money and financial
mathematics
Geometric reasoning
Patterns and algebra Location and
transformation
Linear and non-linear
relationships
Pythagoras and
trigonometry
Mathematics

Number
and Algebra
Measurement
and Geometry
Statistics
and Probability
Computation with integers Length Data collection and
representation
Financial mathematics Area and surface area
Proportion Volumes Single variable
data analysis
Fractions, decimals and percentages Numbers of any
magnitude
Algebraic techniques Time Bivariate
data analysis
Indices Properties of
geometrical figures
Probability
Equations Angle relationships
Linear relationships Right-angled triangles
Non-linear relationships Trigonometry and
Pythagoras‟ theorem
Logarithms / Polynomials /
Functions
Circle geometry
What NSW did .....

Australian curriculum in NSW
• NSW implementation delayed from 2013 to
2014
• So ... 2nd draft published February 2012
• Final draft published September 2012
• Announced 31.7.12: Implementation in 2014 to
begin with Years 7 and 9 (all Phase 1 subjects)
• Implementation of K-6 Mathematics in 2015

 Less content overall, to provide more depth and time for
key skills and the proficiency strands
 Focus on process and fluency rather than long
checklists of content
 For advanced students, greater emphasis on extension
rather than acceleration; not learning more skills but
applying the same skill to more advanced problems
………
Mathematics

 More statistics and probability: met every year from
primary school
 Use of ICT in calculation, statistics, graphing and
geometry: opportunities for graphics and CAS
calculators, spreadsheets, dynamic geometry
Mathematics

The AC proficiency strands
 Three content strands = „nouns‟ of mathematics
curriculum
 Four proficiency strands = „verbs‟ of mathematics
curriculum:
 Understanding
( knowing)
 Fluency (applying)
 Problem solving
( modeling)
Reasoning
(generalising)

What NSW did next .....
 Replaced the four proficiency strands with one
„Working mathematically‟ strand with five components:
 Understanding
 Fluency
 Problem solving
 Reasoning
Communicating

Working mathematically
 Communicating is …
 Describing and explaining mathematics
 Representing mathematical theory and solutions in
written, oral and graphical form
 Using words, algebraic symbols, special notations,
diagrams, graphs and tables

Additional
NSW
content
description
NSW
outcomes
Australian
curriculum
content
description
NSW elaborations
of Australian
curriculum content
Working
mathematically +
Learning across
the curriculum
components
tagged to content:
• Problem solving
• Numeracy [N]
• Critical and
creative thinking
[CCT]
Strand +
NSW substrand
Background
information and
language notes

New Syllabus:
http://syllabus.bos.nsw.edu.au/

Planned support: (CLIC)
General Professional Learning:
1. The learner and the new curriculum (2h)
2. Teaching for the new curriculum (2h)
3. Your school and the new syllabuses (5h)
4. Programming, teaching and assessing (10–
20h)

Content specific support: Curriculum Support
K-6
1. Fractions
2. Stacked dot plots
3. Using the numeracy continuum
7-10
1. Statistics in Stage 4
2. Statistics in Stage 5

Year 6 Number and Algebra
o Percentage discounts of 10%, 25%, 50% (NEW)
o Missing: Roman numerals

Year 7 Number and Algebra
o Associative, commutative and distributive laws (NEW)
o Ratio problems, best buys (NEW)
o Missing: Divisibility tests, history of number, special
numbers (eg Pascal‟s triangle, Fibonacci)
o Divisibility tests
o Long division
o Moved to „Additional content‟ section: Roman
numerals, history of number
Index laws, power of zero, irrational numbers (NEW)

Year 6 Measurement and Geometry
o The metric system: length, mass, capacity
o Length, area, volume and capacity
o Timetables
o Prisms and pyramids
o Transformations: translation, reflection, rotation (NEW)
o The number plane: all 4 quadrants (NEW)
o Angles on a straight line, at a point, vertically opposite
angles (NEW)
o Moved to Year 7: Area of a triangle (Australian Curriculum).
NSW Curriculum - In Year 7, students will use the formula, whereas in
year 6 they are investigating, comparing and using words.
o Moved to Year 8: Time differences
o Missing: Timelines and time zones

Stage 3 Measurement and Geometry
What NSW added
o Moved back from Year 7: Area of a triangle (NSW)
o Moved from Year 7: Volume of a rectangular prism
o Moved back from Year 8: Time differences
o Timelines and Australian time zones
o Diagonals of plane shapes
o Parts of a circle

STAGE 3 AREA 2 – YEAR 6 (NSW)
 investigate the area of a triangle by comparing the area
of a given triangle to the area of the rectangle of the same
length and perpendicular height, eg use a copy of the
given triangle with the given triangle to form a rectangle
 explain the relationship between the area of a triangle
and the area of the rectangle of the same length and
perpendicular height (Communicating, Reasoning)
 establish the relationship between the base length,
perpendicular height and area of a triangle
 record, using words, the method for finding the area of
any triangle, eg
'Area of triangle = 1/2 × base × perpendicular height'

Stage 4 - Measurement and Geometry (NSW)
 develop, with or without the use of digital technologies,
and use the formulas to find the areas of
parallelograms and triangles, including triangles for
which the perpendicular height needs to be shown
outside the shape:
Area of parallelogram=b x h where b is the length of the
base and h is the perpendicular height
Area of triangle=1/2 x b x h where b is the length of the
base and h is the perpendicular height
 identify the perpendicular heights of parallelograms and
triangles in different orientations (Reasoning)

Year 6 Statistics and Probability
o Probability using fractions, decimals, percentages
(NEW)
o Chance experiments, expected frequencies (NEW)
o Statistical graphs and displays, including side-by-side
column graphs
o Interpreting secondary data
o Moved to Year 7: The mean

Stage 3 Statistics and Probability
What NSW added
o No changes

The 7 General Capabilities
of the Australian Curriculum
o Literacy
o Numeracy
o ICT competence
o Critical and creative thinking
o Ethical behaviour
(acting with moral integrity, eg unbiased statistics)
o Personal and social competence
(life and community skills, eg budgeting, reading timetables)
o Intercultural understanding
(respecting diversity, eg how other cultures perceive number, time,
geometry, measurement)

The 3 Cross-curriculum priorities
of the Australian Curriculum
o Aboriginal and Torres Strait Islander
histories and culture
o Asia and Australia‟s engagement with Asia
o Sustainability (environmentally-friendly living)

NSW made these into 11
‘Learning across the curriculum’ areas
1. Literacy [L]
2. Numeracy [N]
3. ICT competence [ICT]
4. Critical and creative thinking [CCT]
5. Ethical behaviour understanding [EU]
6. Personal and social competence [PSC]
7. Intercultural understanding [IU]
8. Work and enterprise [WE]
9. Aboriginal and Torres Strait Islander histories and
culture [AHC]
10. Asia and Australia‟s engagement with Asia [A]
11. Sustainability and environment [SE]

‘Learning across the curriculum’ icons

New Syllabus:
http://syllabus.bos.nsw.edu.au/
ADDITIONAL ASSESSMENT ADVICE
Support materials, available later this year, will provide further advice
about assessment, including:
planning and designing effective teaching, learning and
assessment activities
sharing learning and assessment intentions
providing effective feedback
differentiating assessment
integrating information and communication technologies (ICT)
recording evidence for assessment.

Mathematics Key:
In the Mathematics syllabus, Working Mathematically
and the strands are represented by the following
codes:
 Working Mathematically WM
 Number and Algebra NA
 Measurement and Geometry MG
 Statistics and Probability SP

Mathematics Key: for example
Outcome Interpretation
c ode
MAe-1WM Mathematics, Early Stage 1 - Outcome 1, Working
Mathematically
MA4-5NA Mathematics, Stage 4 - Outcome 5, Number and
Algebra
MA5.2-16SP Mathematics, Stage 5.2 - Outcome 16, Statistics and
Probability
MALS-27MG Mathematics, Life Skills - Outcome 27, Measurement
and Geometry

Australian Curriculum coding
Code Interpretation
ACMNA Australian Curriculum, Mathematics,
Number and Algebra
ACMMG Australian Curriculum, Mathematics,
Measurement and Geometry
ACMSP Australian Curriculum, Mathematics,
Statistics and Probability

NSW Glossary: Mathematics K-10

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What's changed for K-6?
Syllabus
element
Changes
Content for
Early Stage1
to Stage 3
Content related to money strengthened.
‘Two-Dimensional Space’ sub-strand re-sequenced.
Statistics and Probability strand revised.
Content on place-value strengthened.
Content for ‘Whole Numbers’ in Stage 2 limited to
five-digit numbers.

Two-Dimensional Space
ES1 S1 S2 S3
New
syllabus
Manipulates,
sorts and
describes
representations
of two-
dimensional
shapes using
everyday
language
Manipulates,
sorts,
represents,
describes and
explores two-
dimensional
shapes
Manipulates,
classifies and
sketches two-
dimensional shapes,
including
quadrilaterals, and
describes their
features
Manipulates,
classifies and draws
two-dimensional
shapes, including
triangles, and
describes their
properties

Syllabus
element
Changes
Content for Stage
3
Content on other number systems moved to the
‘Additional Content’ section.
Sector graphs and divided bar graphs included in
Stage 4.
Cartesian plane reviewed to make it more
accessible.
-Order of operations revised:
-importance of index notation (indices)
- importance of working left to right for addition/
subtraction and for multiplication / division

Link to Laptop Wrap -
http://lrrpublic.cli.det.nsw.edu.au/lrrSecure/Sites/LRRView/14118
/14118_04.htm
OR
http://bit.ly/NewS3Stat
Stage 3 – Statistics and Probability

The Cartesian Plane
Syllabus BITES courtesy of the
NSW Curriculum and
Learning Innovation Centre

Battleships – using the Cartesian
coordinate system
• Each player places 5 ships on the grid (make sure they are on the lines
not in the boxes)
• Use the following letters to represent each ship
Aircraft carrier AAAAA
Battleship BBBB
Crusier CCC
Submarine SSS
Destroyer DD
• Take turns calling out coordinates on the grid. The other player says hit if
they have a boat on that spot, or a miss of they do not. Keep track of your
guesses by writing a “H” for hit or “M” for miss.
• You must guess all the coordinates for a certain ship to “sink” it.
• When a player has a ship sunk they must report it by saying “you have sunk
my battleship”. The first player to sink all their opponents ship wins.

Table group task using a stacked dot plot
 As a table group collect data to create a stacked dot plot.
 Some suggestions are: your height, your shoe size...
 You can use the paper rulers to measure your height.
You should know your shoe size.
 As a whole group, determine an appropriate scale for
creating a stacked dot plot.
 Use a paper streamer for the scale and the coloured dots
to create a stacked dot plot to represent the data you
collected.
 Label the dot plot.
 What questions could you ask about your graph and
data?

Features of a dot plot
Features include:
 An automatic sorting of data - once the axis is chosen the
data points can be plotted in any order but are actually
sorted by the plotting process.
 A good choice of scale in a dot plot can make the shape of
the data clearer
 Easy identification of the range and highlighting of
extreme values („outliers‟).
 Reveals any peaks and/or mode/s in the data.

 Use real data, relevant to the students
 Students need to determine an appropriate scale from the
data collected. Identify the lowest score and the highest
score.
 In a dot plot, the dots must align vertically and horizontally.
 Dot plots only give a good pictorial representation of
frequency when the 'dots' are aligned.
Teaching Implications
This is an example
of a poor stacked
dot plot

Ways Forward

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