# Quotition for Purchase - PDF

Document Sample

Correlation
QLD
Queensland

Early Years
(Kindergarten)

Topic                                          Relevant Exercise
Children build early mathematical
understandings about number, patterns &        Concept – Counting
algebra, measurement, chance & data and        Skill – Reading and Printing Numerals
space by:                                      Level A
counts small collections in           Skill – Estimating the number of objects
different arrangements and from       and reasonableness
different starting points             Level A
recognises familiar numbers           Concept – Operations
identifies how many in a small        Skill – Introduce
collection
“altogether”
recognises the required number of
Level A
items needed to complete a
Concept- Comparing and Ordering
recognises parts of a whole
Skill- locate numbers on a number line
identifies collections with           Level A
exaggerated differences for "more"    Skill – Introduce “Greater than” and “less
or "less"                             than”
represents the quantities of small    Level A
collections in different ways         Skill – Understanding “more” and “less”
imitates exchange processes as part   Level A
of play                               Skill – Understand Measurement of time
identifies and describes attributes   Level B (only The clock – An introduction
of objects as long, short, empty,     worksheet
full, heavy, light
uses comparative language when
comparing two objects or pictures
sorts collections by single
attributes such as shape, colour or
size of objects
identifies and describes attributes
of objects according to shape
uses familiar positional language
to communicate own position, the
position of others and objects
interprets familiar language of
position to place or locate objects
identifies the repeating element of
a simple pattern and continues
pattern
identifies patterns in the
environment
follows a simple sequence of
actions, or pattern, in order
represents sequences of familiar
events
identifies points in time, with
prompts
in discussions, sometimes
identifies that an event might or
might not happen
identifies ways of collecting data
own questions.
Level 1
(End Year 1)

Topic                                   Relevant exercise
Number
Key Ideas:                                     Concept – Counting
Number concepts:                               Skill – Reading and printing numerals
Whole numbers 0-100                     Level A, B, C
Number names 0-100                      Skill – Counting using Money
Parts of a whole – whole, part,         Level B
slice, bit, piece                       Skill – Skip counting and patterns
Conservation of number 0-10             Level C
Position and order of numbers 0-10      Skill – Introduce Fractions…Equal parts
Different representations of            Level B (two equal parts, one half, One
numbers (concrete, verbal, pictorial,   quarter)
symbolic)
Concept – Operations
Goods and services have a purchase
Skill – Introduce
price
Terms – saving, spending, cost
“altogether”
Attributes of coins and notes           Level A
Joining model                           Concretely…”and”
Language of joining                     Level A
Two or more addends                     Skill – Introduce the Symbolism.. # + # = #
Subtracts whole numbers to 10           Level A
Takeaway model                          Skill – Introduce the words…”plus” and
Language of take away                   “equals”
Makes connections i.e. addition         Level A
undoes subtraction and vice versa       Skill – Demonstrate Addition
Counts on in 1‟s and 2‟s                facts…Making 5, 6, 7, 8, 9, 10
Counts back in 1‟s and 2‟s              Level A
Can do mental computations              Skill – Introduce Subtraction
Understands written recordings i.e.     Concretely…”take away”
subtraction (cover up, takeaway,       Skill – Introduce subtraction Symbolism
left)                                  Level A
Understands symbols for                Skill – Fact Families…Add and Subtract
calculations (+, -)                    Level A
Understands multiplication             Skill – Introduce Multiplication Concretely
language i.e. set (equal groups)       Level C
Understands division language i.e.     Skill – Introduction to division.
partition (sharing equally)            Level C

Patterns and Algebra                          Concept – Counting
Key Ideas:                                    Skill – Skip counting and patterns
Understands repeating patterns and     Level C
non patterns and spatial.              Skill – Counting Backwards
Understands translating patterns       Level A and B
into different representations         Skill – Recognize and count solids
Can skip counting with calculators     Level B
(addition and subtraction              Skill – Count on from a Given number
Understands rules describing           Level A
consistent change of one attribute     Concept Proble m Solving
both forwards and backwards            Strategies
(backtracking).                        Skill – Guess and Check:
Understands conservation and           Lesson: The Camp.
language of equal to, same as and
different from
Grasps representations of objects
and pictures
Measurement                                   Concept – Comparing and Orde ring
Key Ideas:                                    Skill _ described elapsed time:
Understands measurement terms          Level C and C
and attributes such as length, mass,   Skill – Understand Measurement of time:
covering (area), fill and pack         Level B
(volume)                               Skill – Introduce “Greater Than”, “less
Understands direct and indirect        than”:
comparisons                            Level A and C
Understands descriptive and            Skill – working with Whole Numbers >, <,
comparative terms associated with      =:
length, mass, area and volume          Level A, B, C and D
Understands units of measure such
as non standard units and              Concept – Counting
recognises measuring instruments       Skill – Estimating the number of Objects
such as balance scales                 and Reasonableness:
Understands time with non standard     Level A and B
and standard units (days, weeks,
months)
Can use comparative language for
time (e.g. later, earlier, more time,
less time)
Can class calendars
Understands relationships such as
points in time (e.g. home time, start
time), times of day (e.g. morning),
days of week and duration (times
between start and finish)
Chance and Data                                Concept – Counting
Key Ideas:                                     Skill - Estimating the Number of objects
Familiar with chance and the            and Reasonableness
language of chance (always,             Level A and B
sometimes, never, will, will not or     Skill – 1 to 1 correspondence of # to
might not happen, maybe, fair, not      objects
fair, lucky, unlucky)                   Level A
Understands concept of judgements
especially subjective judgements        Concept – Proble m Solving
(personal opinions, personal            Strategies
statements)                             Skill-Make a Graph: Lesson Animals
Can collect and handle data with        Skill-Make a table: Lesson Muffins
knowledge of collection methods         Skill-Make a graph: Classroom shoes.
(observation and questioning)
Can classify and check data             Concept – Operations
Understands simple displays (lists,     Skill – Given Graph…Perform operations
tables, people graphs, object graphs,   Level D
picture graphs, student generated)
Has grasp of sources of variation
(recording methods and
observational conditions) and
natural variation.
Space                                          Concept – Counting
Key Ideas:                                     Skill - Recognize and count solids:
Has general understanding of 3D         Level B and C
and 2D shapes such as cubes,            Skill – Recognize and count Two
rectangular prisms, spheres,            dimensional figures:
cylinders, cones and pyramids           Level B and C
Understands everyday examples of
3D shapes (e.g. ice cream cones,
balls, dice)
Also understands circles, triangles,
rectangles including squares.
Has understanding of geometric
terms and properties such as open
and closed figures.
Has understanding of terms such as
flat, straight, curved, round
Understanding of geometric
properties of 3D shapes (shapes of
faces, function “will roll”) and 2D
shapes (Straight and curved lines,
number of sides, number of
corners)
Can visualise „mind pictures of 3D
and 2D shapes
Can visualise 3D objects from
different view points.
Can visualise 2D shapes in different
orientations
Can visualise and represent shapes
within shapes (Through folding,
cutting and joining halves)
Can visualise shapes within picture,
illustrations, puzzles.
Understands lines and angles
(straight and curved lines and
corners – angles)
Understands language of location
and movement i.e. position (on,
between, beside, near, before,
after), direction (over, under. up,
down, left, right…), movement
(forwards, backwards, sideways…)
and non verbal (signs, symbols and
gestures)
Can make mind pictures of familiar
pathways
Can visualise alternative pathways
Understands language of direction
and angle such as turns (change in
direction)
Level 2
(End of Year 3)

Topic                                           Relevant Exercise
Number                                          Concept – Counting
Key Ideas:                                      Skill – Introduce Fraction…Equal Parts
Understands whole numers to 99,          Level B
then to 999                              Skill – Counting Using Money
Place value to 100‟s                     Level B, C and D
Understands equals (=) and does          Skill – Introduce common Fractions as
not equal (≠)                            parts of a whole
Can put fractions in context such as     Level B and C
equal parts of a whole, half (1 part     Skill – Introduce Fraction of a set
out of 2 equal parts), quarter (1 part   Level C
out of 4 equal parts)
Understands conservation of              Concept – Place Value
number (whole numbers)                   Skill – Break numbers into Groups
Understands position and order of        Level B and C
numbers (relationships between           Skill – Model Numbers Grouped in
numbers, different representations       Packages
of numbers and subset of whole           Level C
numbers –odd and even)                   Skill – Identify Value Patterns (to 20)
Level C
Understand that goods and services
Skill – Identify Place value Patterns (to
have a purchase price – tendering
100)
cash for purchases
Level C
Understands equivalent values and
Skill – Identify Place value Patterns (to
1000)
recording dollars and sense
Level C and D
Can add totals to 999, can two or
more addends                             Concept – Place Value
Can recall or work out addition          Skill – break numbers into Groups
facts to 9+9                             Level B
Can subtract numbers to 999              Skill – Identify Place Value Patters (to 100)
Understands models and languages         Level C
of subtraction i.e. takeaway,
(difference)                          Concept – Operations
Can recall or work out subtraction    Skill – Demonstrate Addition
facts                                 Facts…Patterns
Has understanding of mental           Level A, B
computation strategies and work       Skill – Add 3 or 4 numbers
out basic facts such as count on,     Level A and B
count back, doubles, near doubles,    Skill – Add 2 Digit numbers…concretely
make to ten, turnarounds.             Level C
Understands models and language       Skill – Fact Families…Add & Subtract
of multiplication (set, area and      Level A and B
linear) and division (partition and   Skill – Subtract 2 digit
quotition)                            Numbers...concretely
Understands that multiplication       Level C
undoes division and vice versa        Skill – Subtract 2 digit
Can work out basic multiplication     numbers…abstractly
computation strategies such as skip   Level C
counting, doubles, double doubles     Skill – Introduce Multiplication Sentences
and turnarounds.                      Level C
Skill – Introduce Multiplication
Understands symbols for
Facts…2,3,4,5
multiplication and division and
Level C
language of multiplication (groups
Skill – Patterns in Multiplication
of, rows of, jumps of) and division
Level C
(share between, share)
Skill – Demonstrate Commutative Property
Level C
Skill – Introduction to Arrays
Level c
Skill – Note patterns in 10 x 10
multiplication Table
Level D
Skill – Introduction to Division
Level C
Skill – Introduce Division Facts 2,3,4,5
Level C
Skill – Introduce Division Facts, 6,7,8,9
Level D

Patterns and Algebra:                        Concept – Proble m Solving
Key Ideas:                                   Skill – Find a Pattern
Understands missing terms, non-       Johnny‟s Pennies
patterns or patterns with errors,     Toy Animals
spatial, translating patterns into    Skill – Number Sentence
number patterns.                      Lesson Oranges
Understands functions input ->        Lesson Bills Ball
output (function machines,
Understands backtracking (inverse)     Concept – Operations
addition or subtraction, reversing a   Skill – Given Graph…Perform Operations
change.                                Level D
Understands rules relating two sets
of data.
Understands equivalence such as
conservation, balance, transitive
relation, language (equal to, same
as, not equal to, different from)
and check)
Understands representations of
objects, equations (number
sentences), symbols (equals =, does
not equal ≠, for unknowns – shapes
boxes, question marks, spaces,
lines)
Measurement:                                  Concept – Comparing and ordering
Key Ideas:                                    Skill – Described elapsed Time..Hours, 5
Understands measurement terms          minutes
and attributes and associates with     Level C and D
the attributes of length (height,      Skill – Describe Elapsed Time…Minutes
width, depth, distance), mass          Level D
(weighing), area (covering), volume    Skill – Describe Bank in Time….Hours, 5
(pouring, packing, layers.)            minutes
Understands units of measure –         Level C and D
metres (m), centimetres (cm),          Skill – Describe Back in Time…minutes
Kilograms (kg) and parts of            Level D
kilograms, litres (L) and parts of     Skill – Understand Measurement of Time
litres, non-standard units for         Level B, C and D
volume (e.g. layers of blocks).
Can use measuring instruments          Concept – Operations
such as rulers, tape measures,         Skill – Finding the area of a Shape
scales, area grids, litre jugs.        Level D
Has an understanding of related
historical units of measure.
Understands units and conventions
of time such as seconds (s), minutes
(min), hours (hr) and years (yr)
Can read 12 hour display in
analogue (o‟clock, half hour, 5
minute interval markings) and
digital (all times)
Understands the calendar
(abbreviations for days e.g. mon
and months in words), understands
seasons, and representations i.e. that
9:30 is nine-thirty.
Understands relationships between
days and months, weeks and a year,
months and a year, analogue and
digital displays and duration such as
estimation of seconds and minutes.
Chance and Data:                                Concept – Counting
Key Ideas:                                      Skill – Estimating the number of Objects
Understands the language of chance       and Reasonableness
such as likely, unlikely, and            Level A and B
impossible.                              Skill – 1 to 1 correspondence of # to
Can make subjective judgements on        objects
comparisons and predictions and          Level A
the independence of an event from a
previous event.                          Concept – Operations
Has understanding of collection          Skill – Given Graph…Perform operations
methods through observation and          Level D
simple surveys.
Can classify record and check data.
Can make displays such as tables,
picture graphs, bar graphs and
understands main elements of
displays such as titles and axes.
Can identify and interpret variation
and understand the effects of
variation.
Space
Key Ideas:
Understands common
characteristics of cubes and prisms,
spheres, cylinders, cones and
pyramids.
Understands geometric terms and
properties such as face, corner, side,
edge.
Understands properties of 3D
shapes such as shape, number of
faces, function…
Understands properties of 2D
shapes such as number of sides,
number of angles…
Understands the nets of 3D shapes
with flat surfaces.
Can visualise mind pictures of 3D
and 2D shapes,
Can represent 3D objects from a
different viewpoint.
Can represent and visualise 2D
shapes in different orientations
Can partition 2D shapes e.g.
triangles within a square.
Understands depth in 3D shapes
Understands right angles (Square
corner) and angles (greater than,
less than, same as a right angle)
Can sketch simple maps and simple
plans (e.g. of rooms)
Understands relative size of objects
and locations.
Can understand non labelled grids
and alphanumeric grids
Understands movements (E.g.
paces, steps, grid spaces.)
Understands different view points
(above, birds eye view, front,
behind, side.) and alternate
pathways.
Understands language of direction
and angle such as full, half, quarter,
and three quarter turns, left and
right turns, clockwise and anti
clockwise.
Level 3
(End year 5)

Topic                                          Relevant Exercise
Number                                         Unde rstanding Whole Numbe rs and
Key Ideas:                                     Integers
Understands: whole numbers to               1) The meaning of whole Numbers
9999, decimal fractions in context              Can/Us.
(tenths, hundredths), place values          2) Adding and Subtracting Whole
from thousands to hundredths,                   Numbers
greater than (>), equals to (=), less       3) Multiplying and Dividing Whole
than (<), fractions in context (equal           Numbers
parts of a whole, common fraction              Multiplication facts
format and decimal fraction format)            Commutative Property
Understands conservation of                     The 10 x 10 Multiplication Table
number (whole numbers, decimal               9) Order of Operations
and common fractions)
Understands position and order of
numbers, relationships between          Unde rstanding Fractions
numbers and sensible adjustment of         2) The multiplication Table
numbers.                                   1) The Meaning of Fractions
Has grasp of different                     5) Introduction to decimals.
representation of numbers and              6) Percents…Fractions…Decimals
subsets of whole numbers
(multiples and factors)                 Unde rstanding Percent
Understands cash transactions,             1) The meaning of Percent
cashless transactions (e.g. EFTPOS         2) Percent to Fraction/Decimal
and Pre paid card accounts),               4) Fraction/Decimal to Percent
equivalent values, conventions
for cash purchases), and change.
understands decimals to 2 places in
context with the same number
places and can recall addition facts
to 9+9.
Can subtract whole number to 9999
and make mental computation with
money (change) and recall
subtraction facts.
Can make mental computations
strategies for larger numbers and
decimal fractions in context (to
make numbers manageable, count
on and back, doubles, changing
operations, and turnarounds.
Understands computation methods
such as mental computations of
exact and approximate.
Understands model and language of
multiplication and division
Understands combinations of whole
numbers and decimal fractions in
context
Fractions and proportion
• reducing numbers by ´
• enlarging numbers by multiples
of ½ (e.g. 1½)
Mental computation strategies
Multiplication
• to work out basic facts
− double, double doubles (x 8)
− build up, build down to
known facts
− turnarounds (commutativity)
• extend basic facts strategies to
larger numbers
• student-generated
Division
• related multiplication facts
• extend basic facts to other
numbers
• student-generated
• mental computations
− exact
− approximate
• written recordings
− student- generated
(single-digit whole number
multipliers and divisors)
• calculators/computers
− link × and † with * and / symbols

Patterns and Algebra                  Unde rstanding Algebra
Key Ideas:                               1) Introduction to Algebraic Thinking
Patte rns                                2) Tiles and Algebra
• number (including patterns with        3) Patterns, Patterns, Patterns
decimals)
− rules based on previous term        Unde rstanding Graphing
− calculators (whole and                 1) Reading and Sketching Graphs
decimal numbers involving                2) Statistics
any operations)
− missing term                        Unde rstanding Equations
− non-patterns or patterns with          1) Tiles, Balances and Equations
errors
− rules based on the position
of terms (one operation only)
Functions
• input −› output (function
machines)
• backtracking (inverse)
− multiplication or division
− reversing a change
• representations of relationships
− rules, tables, graphs
Equivalence
• conservation
• balance
• language
− same and different
− more and less
− equal, not equal
− greater than, less than
• unknowns
− guess and check
Representations
• equations (number sentences)
• symbols
− equals (=)
− does not equal (≠)
− greater than (>)
− less than (<)
− for unknowns (shapes, boxes,
question marks, spaces, lines)

Measurement                         Unde rstanding Measurement
Key Ideas:                             1) An introduction to Measurement
Measure ment terms and
attributes
• boundaries
• square units
• metric prefixes
− milli-, centi-, kilo-
Units of measure
• metres (m) and centimetres (cm)
• grams (g) and kilograms (kg)
• square centimetres (cm2)
• square metres (m2)
• millilitres (mL) and litres (L)
• non-standard units for volume
(e.g. layers of blocks)
• measuring instruments
− square centimetre grids
• equivalent forms of standard
units (e.g. 1.5 kg/1500 g;
600 mL/0.6 L)
• personal referents
• related historical units of
measure
Relationships
• the larger the unit the fewer
required to measure and vice
versa
− millilitres and litres
− grams and kilograms
− centimetres and metres
Units and conventions
• units
− fortnight
− leap year
• 12-hour displays (analogue and
digital)
− quarter past, quarter to
− five- minute intervals
• timelines
• timetables (e.g. school, bus,
train)
• diaries (e.g. personal, school,
class)
• calendars
− abbreviations for days
(e.g. M for Monday),
months (e.g. Feb for
February)
• conventions
− dates (e.g. dd/mm/yy)
− ante meridiem (a.m.)
− post meridiem (p.m.)
Relationships
• digital and analogue time
• seconds and a minute
• minutes and an hour
• minutes and parts of hours
(quarter, half)
• hours and days
• duration
− personal referent (for
seconds, minutes, half hour)

Chance and Data                        Unde rstanding Probability
Key Ideas:                                1) Introduction to Probability
Likelihood                                2) What‟s the Chance
• language of chance                      3) Dice Probabilities
− more likely, less likely, equally
likely                                 Unde rstanding Graphing
− most likely, least likely               1) Reading and Sketching Graphs
− certain                                 2) Statistics
− multiple outcomes
− relate everyday language or
colloquialisms to likelihood
(e.g. „no chance‟)
− experimental probability
(e.g. one in four chance)
− sample space (all possible
outcomes)
Judgments
• subjective and numerical judgments
− comparisons and predictions
based on experimental data
− fairness of rules
− independence and dependence
of subsequent outcomes
(randomness)
Collecting and handling data
• collection methods
− surveys
− observations
− experiments
• classify, record and check data
• existing data sources
− publications
Exploring and presenting data
• displays
− tables
− picture graphs (one-to-many
representations)
− bar graphs
• main elements of displays
− titles
− axes
− scales
Identifying and interpreting
variation
• comparative and quantitative
language
• variety of displays to illustrate
data features and variation

Space                                     Unde rstanding Measurement
Key Ideas:                                   1) An Introduction to Measurement
3D shapes and objects and 2D                 2) Perimeter and area of polygons
shapes                                       4) Solids…Volume and Surface Area
• definition of:                                  Classifying Solids
− prisms                                          Volume of a Solid
− spheres                                    5) Angles and their measure
− cylinders
− cones
− pyramids
rectangles, trapeziums, rhombuses
including diamonds)
• triangles (right-angled triangles,
isosceles triangles, scalene triangles,
equilateral triangles)
Geometric te rms and
properties
• vertex, base, apex
• congruence (same shape and size)
• parallel sides, faces, lines
• equal sides and angles
• conventions for labelling shapes and
angles
− letters for naming shapes
(ABC …)
− arrows to identify parallel lines
− marks to identify equal sides of
shapes
− symbols for angles
• surfaces of 3D shapes
• nets (excluding spheres)
• line symmetry of 2D shapes
• symmetrical/asymmetrical shapes
• transformations of 2D shapes
− enlargements and reductions of
shapes
• tessellating properties of triangles
Visualisations and
representations
• „mind pictures‟ of a single flip, slide
or turn of 2D shapes
• „mind pictures‟ of 3D shapes
• different viewpoints and
orientations
• nets of shapes
• shapes within shapes, angles within
angles
• conventions for representing
connecting overlays)
Lines and angles
• vertical, horizontal and oblique lines
• parallel lines
• degrees
• right angle (90 degrees)
• acute, obtuse, straight and reflex
angles
Location and movement
• combinations of alphanumeric
grids and maps (e.g. local area)
• plans (e.g. school layout)
• conventions
− keys and legends (symbols
and explanations of the
symbols)
− grid references (regions
and/or points)
− orientation to north
Direction and angle
• the four compass points
(N, S, E, W)
• connection between compass
points and the amount of turn
Level 4
(End Year 7)

Topic                                    Relevant Exercise
Numbers:                                 Unde rstanding Whole Numbe rs and
Key Ideas:                               Integers
Numeration                                   1) The Meaning of Whole numbers
• whole numbers                                  Can/us
• decimal fractions                          2) Addition and Subtraction of Whole
• key percentages (100%, 50%,                    Numbers
25%, 20%, 10%,1%)                            3) Multiplying and dividing whole
• fractions                                      numbers
− common fraction format                     8) Dividing Integers
− terms (vinculum, numerator,                9) Order of Operations
denominator)
− decimal fraction format                Unde rstanding Fractions
− percentage format                         4) Equivalent Fractions
− equivalence                               5) Introduction to Decimals
• square and cubic notation                 6) Percents…fractions…decimals
• position and order of numbers             13) Improper Fractions and Mixed
− relationships between                          Numbers
numbers                                     14) Addition and Subtraction of
numbers
• connections between key                Unde rstanding Percent
percentages, unit fractions and             1) The meaning of Percent
decimal fractions                           2) Percent to Fraction/Decimal
• everyday representations of               3) Fraction/decimal to Percent
numbers (e.g. 20K/20 000,
\$1.5m/\$1.5 million,
\$3b/\$3 billion)
• subsets of numbers
− prime and composite
− square
− triangular
Money
• financial decisions
discounts)
− methods of payment
− budgets for specific events
• key percentages
− simple interest
− discounts
• cashless transactions
(e.g. cheques, money orders,
EFTPOS, store cards)
• whole numbers
• common fractions (same
denominators)
• decimal fractions including
different numbers of decimal
places
Mental computation strategies
• for whole numbers and decimal
fractions
− making numbers manageable
− count on and back
− doubling
− changing operations
• for common fractions
and subtraction
Computation methods
• mental computations
− exact
− approximate
• written recordings
− student- generated
• calculators, computers
Multiplication
• whole numbers
• common fractions
• decimal fractions to hundredths
• recall multiplication facts to 9 x 9
Division
• whole numbers
• decimal fractions to hundredths
• recall division facts
Connections
• relationship between division
and common fractions
• inverse (backtracking)
Fractions and proportion
Fractions
• unit fractions as operators
(e.g. 1/8 of 120)
• vinculum for division
(horizontal line separating
the numerator from the
denominator)
unit fractions and decimal
fractions
Rates
• simple everyday rates such as
kilometres per hour
Mental computation strategies
• for beyond basic facts
− extensions of all multiplication
and division facts
− doubling
− halving
− student- generated
− place value
− build up, build down
multiplication and division
Computation methods
• mental computations
− exact
− approximate
• written recordings
− student- generated
two-digit multipliers; single digit
whole number divisors)
• formats for recording division
− 13/4, 13 † 4, 4 ) 13,
• calculators, computers
Patterns and Algebra                  Unde rstanding Algebra
Key Ideas:                               4) Patterns Patterns Patterns.
Patte rns
• rules based on the position         Unde rstanding Graphing:
of terms (combinations of             3) Points on a grid
operations)
• calculator number patterns
• ordered pairs and graphs
(with discrete data only)
Functions
• input −› output (with
combinations of operations)
• rules relating two sets of data
• backtracking (inverse)
− with combination of
operations
• representations of relationships
− ordered pairs
− tables, line graphs, equations
(number sentences)
− trends
− discrete data
− continuous data
− electronic, manual
Equivalence
• order of operations
• methods for solving equations
− balance
− guess and check
Representations
• symbols
− equals (=)
− does not equal (≠)
− brackets
− for unknowns (shapes, boxes,
question marks, spaces, lines)
• arrow diagrams
Measurement                          Unde rstanding Measurement and
Key Ideas:                           Geometry
Measure ment terms and                  1) An introduction to measurement
attributes                                  Converting between metric units.
• perimeter                             2) Perimeter and Area of Polygons
• circumference                         3) Solids…Volume and Surface Area
• square and cubic units                7) Projective Geometry
Units of measure                        4) Angles and their Measure
• millimetres (mm), centimetres         5) Angles and Polygons.
(cm), metres (m) and
kilometres (km)
• tonnes (t) and kilograms (kg)
• square metres (m²)
• square centimetres (cm²)
• cubic metres (m³)
• cubic centimetres (cm³)
• measuring instruments
• related historical units of
measure
Relationships
• the larger the unit the fewer
required to measure and vice
versa
− metres, centimetres and
millimetres
− kilograms and tonnes
− square centimetres and
square metres
• relationships between:
− length, width and area of
rectangle
− length, width and height, and
volume of a prism
− length of side and perimeter
Units and conventions
• units
− century (e.g. 21st century is
2001–2100)
• 24-hour time
• personal timetables, diaries
(electronic or manual)
• timelines
• calendars
Relationships
• days, weeks, months and years
• hour and minutes (e.g. 90
minutes = 1½ hours)
• 24-hour time and 12-hour time
• duration
− time calculations
Chance and Data                            Unde rstanding Probability
Key Ideas:                                    1) Introduction to Probability
Likelihood                                    2) What‟s the chance
• language of chance                          3) Dice Probabilities.
− frequency table                          Unde rstanding Graphing:
− relative frequency                          3) Statistics
• probability values                          5) Relations, Equations and Functions
− impossible to certain, 0 to 1,
key percentages between 0%
and 100%
− relate colloquialisms to
probability values (e.g. „fifty- fifty‟,
„Buckley‟s chance‟)
Judgments
• subjective and numerical
judgments
− comparisons and predictions
based on experimental and
given data
− fairness of rules
Collecting and handling data
• plans and methods for data
collection
− design of data record
templates
− extraction of data from
existing data sources
• classify data
• check data
• discrete data
− categorical data
− count data
• continuous data
Exploring and presenting data
• displays
− pie charts
− bar graphs
− dot-plots
− line graphs
− two-way tables
− lists
Identifying and interpreting
variation
• features of data
− measures of location (central
tendency)
º mean
º median
º mode (for discrete data)
• limitations of measures of
location
Space                               Unde rstanding Measurement and
Key Ideas:                          Geometry:
3D shapes and objects and 2D           4 ) Solids… Volume and Surface Area.
shapes                                 1) Angles and their measure
• triangular prisms and hexagonal      2) Angles and Polygons
prisms                                  9) Rations for areas and volume
• square-based pyramids,
tetrahedrons
concentric circles
• regular and irregular polygons
pentagons, hexagons, octagons,
dodecagons)
• non-polygons (e.g. ellipse)
• Platonic solids (cube tetrahedron,
octahedron, dodecahedron,
icosahedron)
Geometric te rms and
properties
• perpendicular faces,
perpendicular lines
• congruence
• symmetry
• rotational symmetry
• sum of internal angles of shapes
Visualisations and
representations
• 3D shapes from different
viewpoints
• 2D shapes in different
orientations
• shapes embedded within other
shapes
Lines and angles
• intersecting lines
• diagonal lines
• perpendicular lines
• degrees
• geometric tools
− 360 degrees protractor
− pair of compasses
Location and movement
• conventions
− simple scale on maps (linear
form or 1 cm:1 km)
− coordinates
º grid references
º movement between grid
reference points
− latitude and longitude
º key lines of reference
(prime meridian, equator)
º polar limits
• maps
− flat maps
− globes
• plans (e.g. shopping centre)
Direction and angle
• eight compass points
(N, NE, E, SE, S, SW, W, NW)
• connection between the eight
compass points and the amount
of turn
• angle as a difference in direction
• estimation and measurement of
angles in degrees
Level 5
(Year 8 and 9)

Topic                                     Relevant Exercise
Number                                    Unde rstanding Whole Numbe rs and
Key Ideas:                                Integers
Numeration                                    4) The meaning of Integers
• index notation (whole number                6) Subtracting Integers
indices only)                                 7) Multiplying Integers
• square root                                 8) Dividing Integers
• percentage                                  9) Order of operations
− whole percentages                       Unde rstanding Fractions
(e.g. 65%, 110%)                              7) Ratios and Proportions
− fractional (e.g. 6.5%, 12´%)                8) Adding Fractions
− greater than 100%                           9) Subtracting Fractions
Number sense                                  10) Multiplying Fractions
• position and order of numbers               11) Dividing Fractions
including integers                            12) Order of Operations
− relationships between                       13) Improper Fractions and Mixed
numbers                                       Numbers
numbers                                       Decimals
• connections between squares                 15) Multiplication and Division of
and square roots                              Decimals.
• connections between
percentages and fractions                 Unde rstanding Exponents:
Money                                     1) The meaning of Exponents
• financial decisions                     5) Square root
− credit and debit transactions
− charges/fees (including GST)            Unde rstanding Percent
− advertising (of financial               5) Percent of a number
services)                                 6) Problems involving percent
− short-term benefits and/or              7) Percent in Business
long-term consequences
− methods of saving
• cashless transactions
(e.g. direct debit, BPAY)
• percentages
− interest
− discounts
• positive rational numbers
− whole numbers
− decimal fractions
− common fractions
º related denominators
Mental computation strategies
• relevant to whole numbers,
common fractions and decimal
fractions
and subtraction
Computation methods
• mental computations
− exact
− approximate
• written recordings
− student- generated
• calculators, computers
Multiplication
• positive rational numbers
− whole numbers
− common fractions
− decimal fractions
− numbers with indices
Division
• positive rational numbers
− whole numbers
− common fractions
− decimal fractions
Fractions and proportion
Fractions
• percentages, common fractions,
decimal fractions
Rates
• calculations involving everyday
rates (e.g. mobile phone charges)
Ratio
• simple everyday ratios (e.g. 1 part
juice concentrate to 4 parts
water)
• symbol for ratio ( : )
Direct proportion
• calculations with direct
proportion (including graphical
representations)
Mental computation strategies
• relevant to whole numbers,
common and decimal fractions,
percentages
− student-preferred
multiplication and division
Patterns and Algebra                 Unde rstanding Algebra:
Key Ideas:                              1) Introduction to Algebraic thinking
Functions                               2) Tiles and algebra
• ordered pairs (four quadrants)        3) Patterns, Patterns, Patterns
• representations of variables          4) Patterns, Formulas, Substitution
− symbols                               6) Subtracting Expressions
• linear models                         7) Multiplying expressions
− representations (tables, line         8) Factorising expressions
graphs, linear equations,               9) Dividing Expressions
proportion equations)
− dependent and independent          Unde rstanding Equations
variables                               2) Solving one-step equations
− discrete and continuous data
− trends                             Unde rstanding Graphing:
• non-linear models                  3) Points on a grid
− dependent and independent          6) Linear Relations
variables                            2) Statistics
− discrete and continuous data       5) Relations, Equations and Functions
− representations (tables,
line graphs)
− trends
• representations of relationships
− electronic, manual
Equivalence
• methods for solving equations
− substitution
− balance
− backtracking
− guess and check
− graphical displays
− tabular data
Representations
• variables
− words
− letter symbols
• algebraic conventions
− implied multiplication (3t)
− implied division ( )
− computer format (*, / )
• arrow diagrams
• linear
• proportion equations
Measurement                          Unde rstanding Measurement and
Key Ideas:                           Geometry
Measure ment terms and                  3) The circle
attributes                              4) Solids… Volume and Surface Area.
• perimeter                             5) Angles and their measure
• circumference                         6) Angles and Polygons
• diameter
• pi (π)                                7) Pythagoras Theorem
Units of measure
• square metres (m²)
• hectares (ha) and square
kilometres (km²)
• measuring instruments
• historical units of measure
Relationships
• the larger the unit the fewer
required to measure and vice versa
− millilitres and cubic
centimetres
− hectares and square metres
• relationships between:
− diameter and circumference
of circle (pi)
− length and width (height),
and areas of triangles and
parallelograms
− areas of triangles and areas of
rectangles
− areas of rectangles and
areas of parallelograms (same
length, same width or height)
− areas of circles and irregular
shapes
• formulae
− area of rectangle
− volume of prism
− perimeter of rectangles
including squares
Units and conventions
• Australian time zones
− Eastern Standard Time (EST)
− Central Standard Time (CST)
− Western Standard Time
(WST)
− daylight saving time
• timetables
Relationships
• decimal representations of time
units (e.g. 2.25 hours = 2 hours
15 minutes)
• duration
− time calculations
− timetables of more than one
week duration
Chance and Data                       Unde rstanding Probability:
Key Ideas:                            2) Statistics
Likelihood                            4) Binomial Probabilities
• language of chance                  5) Geometric probabilities
− theoretical probability (of a       6) Pascal‟s Triangle
single event)                         7) Independent Events
• probability models                  8) Dependent events
− lists, tables
− computer simulations
− experiments
Judgments
• quantitative judgments
− probability of events with
equally likely outcomes
− fair, unfair and biased judgments
− probability to support
statements and decisions
(single events)
− experimental and theoretical
− extrapolations from simplified
explorations
Collecting and handling data
• studies involving observations,
experiments and surveys
• templates for recording data
• consistency of units and
conditions
• detect errors
• discrete data
• continuous data
• groups (bins)
Exploring and presenting data
• displays
− two-way tables
− compound bar graphs
− histograms
− stem and leaf plots
Identifying and interpreting
variation
• features of data
− range
− measures of location (central
tendency) and limitations
− shape (e.g. asymmetry, unusual
features)
• histograms and stem and leaf
plots as picture estimates
Space                               Unde rstanding Measurement and
Key Ideas:                          Geometry:
3D shapes and objects and 2D           4) Solids… Volume and Surface Area.
shapes                                 5) Angles and their measure
• plans and elevations                 6) Angles and Polygons
• compound shapes                      7) Constructions
• embedded shapes
Geometric te rms and
properties
• similarity
− similar shapes (reductions and
enlargements)
• congruence
− symbol for labelling
• scale plans
Visualisations and
representations
• conventions for representing 3D
shapes (perspective)
• sections and cross-sections
Lines and angles
• external angles
• simple constructions using
geometric tools
− perpendicular line
(90 degrees)
− angle of 60 degrees
− bisect a line
Location and movement
• conventions
− scale on maps expressed as a
simple ratio (e.g. 1:10; 1:1000)
− coordinates
º latitude and longitude
expressed in whole degrees
º location of points and places
using latitude and longitude
− distance and bearing (local
environment)
• maps
− flat maps including world,
atlas, street directory and
orthophoto
− globes
• simple floor plans with scale
Direction and angle
• bearings in whole degrees
(measured clockwise from north)
• estimation of bearings in degrees
• application of scales to maps to
find actual distances
Level 6
(End Year 10)

Topic                                        Relevant Exercise
Number                                       Unde rstanding Exponents
Key Ideas:                                   4) Scientific Notation
Numeration
• rational numbers                           Unde rstanding Whole Numbe rs and
• index notation (integer indices)           Integers
• scientific notation (positive and              10) The meaning of Integers
negative powers of 10)                           11) Adding Integers
Number sense                                     12) Subtracting Integers
• position and order within the set              13) Multiplying Integers
of rational numbers                              14) Dividing Integers
− sensible adjustments of                        15) Order of operations
numbers                                      Unde rstanding Fractions
• connections between                            7) Ratios and Proportions
scientific notation and other                    8) Adding Fractions
representations of numbers                       9) Subtracting Fractions
Money                                            10) Multiplying Fractions
• financial decisions and budgeting              11) Dividing Fractions
− income (gross, net)                            12) Order of Operations
− expenditure                                    13) Improper Fractions and Mixed
− saving for a purpose                           Numbers
− borrowing                                      14) Addition and Subtraction of
− savings plan                                   Decimals
− planning for an event                          15) Multiplication and Division of
− consequences of overcommitment                 Decimals.
• percentages
− compound growth                            Unde rstanding Exponents:
• cashless transactions                      1) The meaning of Exponents
(e.g. internet and phone banking)            5) Square root
• comparisons of rates, fees and
charges                                      Unde rstanding Percent
Addition and subtraction                     5) Percent of a number
• rational numbers                           6) Problems involving percent
Mental computation strategies                7) Percent in Business
• relevant to integers and whole
numbers, common fractions and
decimal fractions
and subtraction
Multiplication
• rational numbers
− negative numbers
(with calculator)
Fractions and proportion
Fractions
• fractional percentages of numbers
Rates
• comparisons of rates expressed
in various forms
Ratio and proportion
• as direct proportion
• as inverse proportion
Mental computation strategies
• relevant to rational numbers
multiplication and division
Patterns and Algebra                  Unde rstanding Graphing:
Key Ideas:                               5) Relations, Equations and Functions
Functions                                6) Linear Relations
• linear models                          7) Slope of a line
− equations                              8) Equation of a straight line
(tables, graphs)
− trends                              Solving Equations:
• non-linear models                      3) Solving two step-equations
− representations                        4) Solving multi-step Equations
(tables, graphs)                         5) Problem Solving
− trends                                 6) Solving Linear systems
• representations of relationships       7) Solving Inequalities
− electronic, manual                     8) Solving Absolute Value equations
Equivalence
• methods for solving equations
− graphical methods
− substitution
− balance
− backtracking
− guess and check
• simplifying
• collecting like terms
• expanding
Representations
• linear, proportion equations
• life-related non- linear models
• algebraic conventions
− logical setting out
• models
Measurement                           Unde rstanding Equations
Key Ideas:                            4) Transformations
Measure ment terms and
attributes                                  Unde rstanding Exponents
• tangent                                      6) Pythagorean Theorem
• hypotenuse                                Unde rstanding Measurement and
Relationships                               Geometry
• within right-angled triangles             3) The Circle
− Pythagoras‟ Theorem                       4) Solids…Volume and Surface Area
− tangent ratio                             5) Angles and their measure
• formulae                                  6) Angles and Polygons
− circumference of circle                   7) Constructions
− area of circle                            8) Projective Geometry
− area of triangle
− volume of cylinder
− volumes of pyramids and
cones
• compound shapes
• objects
Units and conventions
• international time zones
− Greenwich Mean Time (GMT)
or Universal Time Coordinates
(UTC)
− International Date Line
• timetables
Relationships
• time zones and longitude
• synchronisation of events
• duration
– time calculations
Chance and Data                             Unde rstanding Probability:
Key Ideas:                                  4) Bionomial Probabilities
Likelihood                                  5)Geometric Probabilities
• language of chance                            6) Pascal‟s Triangle
− multi-outcome events                          7) Independent Events
− compound events                           8) Dependent Events
− conditional probability
(replacement and nonreplacement)            Unde rstanding Graphing
• theoretical probability of multioutcome      2) Statistics
and compound events                            3) Points on a grid
• probability models
− lists, tables, tree diagrams
− computer simulations
− experiments
Judgments
• quantitative judgments
− predictions and justifications
− experimental and theoretical
− extrapolations from simplified
explorations
Collecting and handling data
• data over time (time a major
focus)
• cross-sectional data (time not a
major focus)
• nature of types of data sets
− sample data
− census data
Exploring and presenting data
• displays
− plots over time
− scatterplots
− two-way tables
− histograms
− stem and leaf plots
Identifying and interpreting
variation
• comparisons of features of graphs
and plots
− location (mean, median)
− shape
• relationships between variables
− through scatterplots for
continuous data
− through two-way tables for
categorical data
Space                                 Unde rstanding Graphing
Key Ideas:                               4) Transformations
3D shapes and objects and 2D
shapes                                Unde rstanding Measurement and
• generalisations relating to 2D      Geometry
shapes                                   7) Constructions
• relationships between 2D and
3D shapes
Geometric te rms and
properties
• general patterns of triangles,
intersecting lines
• scale factor
Visualisations and
representations
• embedded shapes, lines and
angles
Lines and angles
• letter conventions
• angles produced when a
transversal crosses parallel lines
• generalisations relating angles
− vertically opposite
− at a point
− in a triangle
Location and movement
• conventions
− scale on maps expressed as
ratio (e.g. 1:25; 1:40)
− coordinates
º fractions of degrees
expressed as minutes
(mentally and on scientific
calculators)
º latitude and longitude
expressed in degrees and
minutes
− scale on floor plans expressed
in millimetres
• key referents for international
time zones
− Greenwich Mean Time (GMT)
or Universal Time
Coordinates (UTC)
− International Date Line
• link between longitude and time
• distance and bearing
Direction and angle
• maps (local environment) with
a given scale