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FoundationNumber and Algebra

Content Descriptions (what to teach/learn)

Essential Learnings with Proficiencies Progression Score 0.5

A student progressing towards Foundation may, for example:

Achievement Standard F.0

NUMBER AND PLACE VALUE (F-8)

Match individual objects with counting sequences up to and back from 10.

Connect number names and numerals with sets of up to 10 elements.

Order the first, second and third elements of a set.

Use counting strategies to solve problems that involve comparing, combining and separating these sets.

Copy and create simple patterns.

Match individual objects with counting sequences up to and back from 20.

Connect number names and numerals with sets of up to 20 elements.

Estimate the size of these sets (of up to 20).

Order the first 10 elements of a set.

Use counting strategies to solve problems that involve comparing, combining and separating these sets.

Represent, continue and create simple patterns.

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point

Know the names of the numbers (F) Count orally forwards and backwards (initially to and from 20) (F) Counting from any starting point to and beyond 20 (F) Understand and connect names, numerals and quantities (U) Understand that there are patterns in the way numbers are said (U)

Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond

Match the names to the numbers and quantities (F) Understand and connecting names, numerals and quantities (U) Understand that objects must be only counted once – use of one-

one correspondenceSubitise small collections of objects

Subitise up to 10 (F) Understand and connecting names, numerals and quantities (U)

Compare, order and make correspondences between collections, initially to 20, and explain reasoning

Use one-to-one correspondence to identify when two sets are equal in size and when one set is larger than another.

Compare larger and smaller of two numbers (R) Order 3 or more numbers with explanation (R) Fluent in counting numbers in sequences readily, continuing

patterns, and comparing objects directly to 20 by 1s Reason by explaining comparisons of quantities, creating patterns,

and explain processes for indirect comparisons Understand and use terms such as ‘first’ and ‘second’ to indicate

ordinal position in a sequence. To tenth(U)Represent practical situations to model addition and subtraction

Real world (authentic) problems modelling addition and subtraction (U)

Represent the problem using pictures, numbers or words (F) Convert between pictures, numbers and words (story problems) (PS) Problem Solve using materials to model authentic problems, sort

objects, use familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer

Use materials to model addition and subtraction of subtraction by the aggregation (grouping together) and disaggregation (moving apart) of objects.

They add and subtract by counting forward and backward using the numbers from 0 to 20.

Represent practical situations to model sharing

Real world (authentic) problems modelling sharing (U) Use a range of practical strategies for sharing small groups of

numbers, such as visual displays or concrete materials (U) Use verbal action stories to model situations that involve sharing (U)

MONEY AND FINANCIAL MATHEMATICSRepresent simple, everyday financial situations involving money

Use toy money to pay for goods in play situations (U)

PATTERNS AND ALGEBRA (F-10)Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings

Sort and classify objects with justification of the classification (U) Copy patterns with explanation of the repeating elements – two

elements (F) Continue patterns with explanation of the repeating elements (F) Create patterns with explanation of the repeating elements (R) Be Fluent when counting numbers in sequences readily, continuing

patterns, and comparing objects directly (F) Reason when explaining comparisons of quantities, creating

patterns, and explain processes for indirect comparisons (R) use of drawn simple symbols in place of objects; for example, B for

boyFollow a short sequence of instructions

Carry out a specified sequence of actions to move an object from one location to another (PS)

Play a simple rule-based game moving a specified number of places according to the result on a die in a chance-based game (U)

FoundationMeasurement and Geometry



Achievement

Victorian Curriculum – updated May 2017 – Anne Reciszen

A student progressing towards Foundation may, for example: Standard F.0

USING UNITS OF MEASUREMENT (F-10)Compare lengths and masses of familiar objects.

Identify measurement attributes of length and mass in practical situations.

Order events in a day.

Name the days of the week, in order.

Identify simple shapes in their environment.

Use simple location words.

Compare lengths, masses and capacities of familiar objects.

Identify measurement attributes in practical situations.

Order events and explain their duration.

Match days of the week to familiar events.

Identify simple shapes in their environment.

Sort shapes by their common and distinctive features.

Use simple statements and gestures to describe location.

Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language

Compare longer, shorter, same and explain reasoning (R) Compare heavier, lighter, same and explain reasoning (R) Compare which holds more, less or same and explain reasoning (R) Be Fluent in comparing objects directly (F) Reason by explaining comparisons of quantities and explaining

processes for indirect comparison of measurement (R) Use suitable language when comparing objects (U)

Compare and order the duration of events using the everyday language of time

Know and use the language of time (F) Use of a clock to determine the hour – o’clock Compare and order the duration of events using the language of

time (F) Be Fluent in sequencing and comparing the duration of events (F) Reason by explaining comparisons of time (R) Name and order the days of the week (F)

Connect days of the week to familiar events and actions

Connect days of the week to familiar events and actions (U) Understand connections between days of the week and familiar

events (U)SHAPE (F-7)Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment

Sort and describe squares, circles, triangles, rectangles, spheres and cubes (U)

Show Understanding by connecting names with objects (U) Problem Solve through sorting, describe and classify objects (PS) Reason by comparing and naming the shapes and attributes of

objects (R)LOCATION AND TRANSFORMATION (F-7)Describe position and movement Know the everyday language of location and direction (F)

Understand and use the language of location and direction (U) Follow and give simple directions using the language of location and

direction (PS)

FoundationStatistics and Probability



A student progressing towards Foundation may, for example:

Achievement Standard F.0

DATA REPRESENTATION AND INTERPRETATION (F-10)Answer simple yes/no questions about given categorical data that are sorted.

Sort familiar categorical data into sets and use these to answer yes/no questions and make simple true/false statements about the data.

Answer yes/no questions to collect information

pose questions about themselves and familiar objects and events (U)

represent responses to questions using simple displays (PS) use data displays to answer simple questions (R) Problem Solve through modelling authentic problems, using

familiar counting sequences to solve unfamiliar problems (PS) Discussing the reasonableness of the answers (R) Reason by explaining comparisons of quantities (R)

Organise answers to yes/no questions into simple data displays using objects and drawings

Represent responses to questions using simple displays, including grouping students according to their answers

Interpret simple data displays about yes/no questions

Use data displays to answer simple questions such as ‘how many students answered “yes” to having pets?’


Level 1Number and Algebra


Essential Teachings with Proficiencies Progression Score F.5A student progressing towards Level 1 may, for example:

Achievement Standard 1.0


Connect number names and numerals with sets of more than 20 elements, and order the first 20 elements of a set.

Subitise small collections of objects.

Represent and solve simple addition and subtraction problems, using materials.

Investigate simple patterns of objects and their images.

Describe number sequences resulting from skip counting by 2s, 5s and 10s.

Count to and from 100 and locate these numbers on a number line.

Partition numbers using place value.

Carry out simple additions and subtractions, using counting strategies.

Identify representations of one half.

Recognise Australian coins according to their value.

Continue simple patterns involving numbers and objects with and without the use of digital technology.

Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero

Count forwards and backwards to and from 100 from any number (F) Count beyond 100 by 1s from 0 (F) From a number beyond 100 count forwards and backwards from any given number

(F) Count orally by 2’s, 5’s, 10’s to and beyond 100 starting at 0 (F) Understand and connect names, numerals and quantities

Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line.

Order Number sequences (U) Use number lines and number grids to count forwards, backwards and by patterns

(F) Model counting using number lines (F) Fluent in counting numbers in sequences readily, continuing patterns, and

comparing objects directly Reason by explaining comparisons of quantities, creating patterns, and explaining

processes for indirect comparisonsCount collections to 100 by partitioning numbers using place value

Bundle ones to create ten and tens to create 100 (F) Create, name and order teen numbers as 10 and some more (F) Understanding partitioning of numbers and the importance of grouping in tens Understanding two digit numbers as comprised of tens and ones/units

Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts

calculation of the next number when asked to add 1 or 2 to any natural number from 0 to 10

drawing of diagrams to show subtraction activities addition and subtraction of two-digit multiples of ten by counting on and counting back *counting on from the larger of two collections to find their total *use of the number properties (commutative and associative) of addition in mental

computation, and recognition of complements to ten; for example, 3 + 4 + 7 + 6 = 3 + 7 + 4 + 6 = 10 + 10 = 20

Model with materials, number lines and number grids addition and subtraction within and including 10 (F)

Model with materials, number lines and number grids addition and subtractions within and including 20 (F)

Discuss and compare strategies for addition and subtraction (R) develop a range of mental strategies for addition and subtraction problems (F) Real world (authentic) problems modelling addition and subtraction (U) Represent a given problem using pictures, numbers or words (F) Convert between pictures, numbers and words (story problems)(show

understanding and interpretation) (PS) Problem Solve using materials to model authentic problems, sort objects, use

familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer (PS)

Represent practical situations that model sharing

drawing of diagrams to show sharing of up to 20 items sharing a set of objects, such as a packet of sweets, equally between a small group

of people using one-to-one correspondence recognising whether there is a remainder or not after sharing equally

FRACTIONS AND DECIMALS (1-6)Recognise and describe one-half as one of two equal parts of a whole

Model the partitioning of one whole into two equal parts (U) Model the partitioning of a group into two equal parts (U) Name equal parts as halves, one equal part as one half (R) sharing a collection of readily available materials into two equal portions (F) Show reasoning by splitting an object into two equal pieces and describing how the

pieces are equalMONEY AND FINANCIAL MATHEMATICS (1-10)Recognise, describe and order Australian coins according to their value

Recognise Australian coins according to their value (F) Order Australian coins according to their value (F) Describe and order Australian coins according to their value (R) showing that coins are different in other countries by comparing Asian coins to

Australian coins (U) Understanding that the value of Australian coins is not related to size Show reasoning by describing the features of coins that make it possible to identify

themPATTERNS AND ALGEBRA (F-10)Investigate and describe number patterns formed by skip counting and patterns with objects

Identify and say patterns counting by 1’s forwards and backwards from any point to 100 (F)

Identify and say patterns counting by 2’s to 50, 5’s to 100 and 10’s to and beyond 100 (F)

Identify and say patterns with explanation of the repeating elements (R) Investigate and model patterns on a number grid and a number line as ‘skip

counting’ (PS) Create patterns with explanation of the repeating elements (R) Be Fluent when counting numbers in sequences readily, continuing patterns, and

comparing objects directly Reason when explaining comparisons of quantities, creating patterns, and explain

processes for indirect comparisons

Recognise the importance of repetition of a process in solving problems

using one-to-one correspondence to determine which of two sets is larger, or if they are of equal size

dividing a set of blocks in a simple ratio such as ‘2 for me’, ‘1 for you

Level 1Measurement and Geometry


Essential Teachings with Proficiencies Progression Score F.5A student progressing towards Level 1 may, for example:



USING UNITS OF MEASUREMENT (F-10)Use direct and indirect comparisons to decide which of two objects is longer, heavier or holds more, and explain reasoning.

Place familiar events in time order.

Identify, sort and name familiar three-dimensional objects in their environment.

Describe movement, and follow and give simple directions.

Use informal units of measurement to order objects based on length, mass and capacity.

Tell time to the half-hour.

Explain time durations.

Describe two-dimensional shapes and three-dimensional objects.

Use the language of distance and direction to move from place to place.

Measure and compare the lengths, masses and capacities of pairs of objects using uniform informal units

Use uniform informal units to compare longer, shorter, same and explain reasoning (R)

Use uniform informal units to compare heavier, lighter, same and explain reasoning (R)

Use uniform informal units to compare which holds more, less or same and explain reasoning (R)

Understand that in order to compare objects, the unit of measurement must be the same size (U)

Be Fluent in comparing objects directly (F) Reason by explaining comparisons of quantities and explaining processes for

indirect comparison of measurement (R)Tell time to the half-hour To know and use the language of time (F)

Compare and order the duration of events using the language of time (PS) Knowledge of the relationship between analogue and digital clocks read time on analogue and digital clocks and observing the characteristics of

half hour times (F) Be Fluent in sequencing and comparing the duration of events (F) Reason by explaining comparisons of time (R)

Describe duration using months, weeks, days and hours

Connect months, weeks and days to familiar events and actions (U) Describe durations using months, weeks, days and hours (U) Understand connections between days, weeks and months Understand and order relative size of months, weeks, days and hours

SHAPE (F-7)Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features

Sort and describe squares, circles, triangles, rectangles, spheres and cubes (F)

Connect shape names to everyday objects (F) Explore geometric features and describe shapes and objects using everyday

words such as 'corners', 'edges' and 'faces' (R) Use of labelling on diagrams of shapes Show Understanding by connecting names with objects Problem Solve through sorting, describing and classify objects by corners,

edges and faces Recognise the congruence of two shapes Reason by comparing and naming the shapes and attributes of objects

LOCATION AND TRANSFORMATION (F-7)Give and follow directions to familiar locations

Know the everyday language of location and direction (U) follow and give simple directions using the language of location and direction

(PS) Understand the language of location and direction (U) Understand that people need to give and follow directions to and from a place,

and that this involves turns, direction and distance (U) Understand the meaning and importance of words such as ‘clockwise’,

‘anticlockwise’, ‘forward’ and ‘under’ when giving and following directions interpreting and following directions around familiar locations (U)

Level 1Statistics and Probability

CHANCE (1-10)

Describe outcomes of simple familiar events using 'will happen', 'won't happen' or 'might happen'.

Sort objects into designated categories on diagrams and create their own visual records by sorting objects or their images.

Classify outcomes of simple familiar events.

Ask questions to collect data and draw simple data displays.

Describe data displays.

Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’

Pose questions about themselves and familiar objects and events (U) Identify outcomes of familiar events involving chance, describing them using

everyday language (R) Represent responses to questions using simple displays such as a probability line

(F) Problem Solve through modelling authentic problems, using familiar counting

sequences to solve unfamiliar problems, and discussing the reasonableness of the answer (PS)

Reason by explaining comparisons of quantities (R)

DATA REPRESENTATION AND INTERPRETATION (F-10)Choose simple questions and gather responses

Use data displays to answer simple questions, developing the language of least, most, same amount (U)

Use tally marks to record (F) determine which questions will gather appropriate responses for a simple

investigation (R) Problem Solve through modelling authentic problems, using familiar counting

sequences to solve unfamiliar problems. (PS) Discuss the reasonableness of the answers (PS) Reason by explaining comparisons of quantities (R)

Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays

Understand that one object or drawing represents on data value (U) Explain the display and what it tells us about the data (U) Compares categories using language such as greatest or least (R)



Essential Teachings with Proficiencies Progression Score 1.5



Recognise increasing and decreasing number sequences involving 2s, 3s, 5s and 10s.

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

Count orally forwards and backwards by 1’s from any number beyond 100 to 1000 (F)

Counting orally by 2’s, 5’s and 10’s to 100 and beyond (F) Count backwards by 10’s from 3 digit multiple of 10 (F) Count by 100’s to 1000 and beyond (F)


Investigate and describe patterns in number sequences, such as adding 10 always results in the same final digit (R)

Understand and describe final digit patterns of familiar patterns (U) Developing fluency and confidence with numbers and calculations by saying

number sequences (F) Fluent in counting numbers in sequences readily, continuing patterns, and

comparing objects directly (F) Reason by explaining comparisons of quantities, creating patterns, and

explaining processes for indirect comparisons (R)

Count to and from, and order numbers up to hundreds.

Recognise different ways of writing the same number.

Group collections of objects in units, tens and hundreds.

Write and solve number sentences involving addition or subtraction.

Recognise and interpret common uses of halves and quarters.

Count to and from, and order numbers up to 1000.

Perform simple addition and subtraction calculations, using a range of strategies.

Use digital technology to produce sequences by constant addition.

Represent multiplication and division by grouping into sets.

into halves, quarters and eighths

Recognise, model, represent and order numbers to at least 1000

Modelling numbers with materials and diagrams (U) recognising there are different ways of representing numbers (U) Order numbers in ascending and descending order (F) Compare numbers on a number line (U) Identifying patterns going beyond 100 (R) Developing fluency with writing numbers in meaningful

contexts (F) Use materials to model and represent numbers understanding three digit

numbers as comprised of hundreds, tens and ones/units (U) Demonstrate and use models to compare value of numbers in base 10 places (U)

Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting

Use Place Value chart bundling sticks, sticks of Unifix or Base Ten Blocks to model partitioning of 3 digit numbers (F)

Investigate and discover strategies for efficient counting such as counting up by multiples of 10 then some more on a number line (PS)

Show Understanding of expanding numbers in 2 and 3 digit numbers through modeling, drawing visuals and describing what is happening with the hundreds, tens and ones (U)

Explore the connection between addition and subtraction

development and use of a ‘fact family’ linking 25 + 5 = 30 to 5 + 25 = 30, 30 − 5 = 25 and 30 − 25 = 5

Real world (authentic) problems modeling addition and sharing with 2 digit numbers (U)

Represent problems using pictures, numbers and words (F) Convert between pictures, numbers and words (story problems) (PS) Create addition and subtraction story problems (PS) Create, model and record efficient methods for addition and subtraction (R) Use number lines and parts and totals models to show the connections between

addition and subtraction (U) Use counting-on to identify the missing element in an

additive problem (F) Becoming fluent with partitioning numbers to understand the connection between

addition and subtraction (F)Solve simple addition and subtraction problems using a range of efficient mental and written strategies

Automatic recall of tens and twentys facts Use commutative and associative properties of + ‘n and x’n in mental

computation (for example, 3 + 4 = 4 + 3 and 3 + 4 + 5 can be done as 7 + 5 or 3 + 9).

Becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10 (F)

Problem Solve using materials to model authentic problems, sort objects, use familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer (PS)

Show reasoning by explaining strategies and understanding of connections between addition and subtraction (R)

Model and represent simple additive situations using materials such as 10 frames, 20 frames and empty number lines (F)

Recognise and represent multiplication as repeated addition, groups and arrays

Use skip counting on a number line to find ‘four twos’ as an additive concept (F) Describe and calculate simple multiplication as repeated addition, such as 3 × 5

= 5 + 5 + 5; and division as sharing, such as 8 shared between 4. Represent array problems with available materials and develop the language of

rows and columns (F) Use skip counting to count groups of and rows or columns in arrays (F) Represent array problems with available materials and explain reasoning (R) Show understanding by visualising a group of objects as a unit and using this to

calculate the number of objects in several identical groups (U)Recognise and represent division as grouping into equal sets and solve simple problems using these representations

Dividing the class or a collection of objects into equal sized groups (U) Identify the difference between dividing a set of objects into three equal groups

and dividing the same set of objects into groups of three (R & U) Develop the language of equal sharing and ‘how many?’ (U) Show Understanding by modelling and creating word problems to represent

division concepts (U)

FRACTIONS AND DECIMALS (1-6)Recognise and interpret common uses of halves, quarters and eighths of shapes and collections

Making models of common fractions such as ½ ¼ 1/3 (F) Recognise that sets of objects can be partitioned in different ways to

demonstrate fractions (U) Show understanding by relating the number of parts to the size of a

fraction Name the fractions, identify in a counting sequence and make

connection to the written words (U,F)MONEY AND FINANCIAL MATHEMATICS (1-10)Count and order small collections of Australian coins and notes according to their value

Identify equivalent values in collections of coins or notes, such as two five cent coins having the same value as one 10cent coin (F)

Counting collections of coins or notes to make up a particular value, such as that shown on a price tag (U)

Grouping of coins of the same denomination in sets of $1 Solving real life money problems using 5 cent and 10 cent combination Solving real life money problems using coin and note combinations Showing Reasoning through justifying solutions and finding alternate


representations

Describe patterns with numbers and recognise simple digit patterns in number sequences.

Write and solve number sentences involving addition or subtraction.

Find the total value of simple collections of Australian notes and coins.

Identify the missing element in a number sequence.

PATTERNS AND ALGEBRA (F-10)Describe patterns with numbers and identify missing elements

Describe a pattern created by skip counting and representing the pattern on a number line (R)

Investigating features of number patterns resulting from adding twos, fives or 10s, 3’s and 4’s (PS)

Use reasoning to make connections between and describe number patterns Solve problems by using number sentences for addition or subtraction

Representing a word problem as a number sentence (PS)Writing a word problem to represent a number sentence (PS)Interpret between Pictures, Numbers and Words to show understanding of

addition and subtraction (U)Solve authentic addition and subtraction problems, explaining strategies and

reasoning (R)Apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction

using technology to construct a sequence of numbers based on constant addition or subtraction from a given starting value

sharing a set of objects equally between a small number of groups


Content Descriptors (what to teach/learn)

Essential Teachings with Proficiencies Progression Score 1.5 Achievement Standard 2.0

USING UNITS OF MEASUREMENT (F-10)

Compare and order familiar objects by their length and relative mass.

Order shapes and objects, using informal units for a range of measures.

Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units

Compare shapes and determine attributes of length, area, volume and capacity (R) Order shapes by one attribute, discuss using the language of larger, smaller, longer, shorter,

least, most, same, equal value (F) Comparing lengths using finger length, hand span or a piece of string (U) Estimate and use base ten block minis and longs to measure length in centimetres (PS) Compare areas using the palm of the hand or a stone (R) Use uniform grid paper to find the area in squares of given shapes (U) Estimate and compare capacities using a range of containers and pouring materials (U) Estimate and stack containers with uniform cubes (unifix or base ten block (minis) to find

volume in cubes (U) Compare capacity of a range of containers using the same uniform cubes (R & U) Show Understanding by using length, area, volume and capacity in problem solving contexts

(U) Show understanding by making and drawing models and recording measurements of length,

area, volume and capacity of objects (U) Estimate mass by hefting, using the language of heavier, lighter and similar when comparing

objects (R)


Describe the duration of familiar events in terms of hours, days and weeks.

Recognise and classify familiar shapes and objects, using their features.

Give and follow directions to and from a place using everyday language for orientation, relative position, direction and distance.

Tell time to the quarter hour.

Use a calendar to identify the date, days, weeks and months included in seasons and other events.

Draw two-dimensional shapes, and specify their features.

Recognise the features of three-dimensional objects.

Interpret simple maps of familiar locations.

Explain the effects of one-step transformations.

Compare masses of objects using balance scales

Using balance scales to determine whether the mass of different objects is more, less or about the same, or to find out how many single items are need to balance a different item (PS)

Use a uniform object to compare items to on the balance scale (U) Estimate and compare objects using uniform metric weights to compare items on the balance

scale (U) Show fluency through using units iteratively (repeatedly) to compare measurements (F)

Tell time to the quarter-hour, using the language of 'past' and 'to'

Identify and mark quarters on the analogue clock (U) Identifying the quarter after an hour as quarter past an hour and the quarter before an hour as

quarter to an hour (U) Link the quarter past as 15 minutes and the quarter to as 45 minutes (U) Describe the characteristics of ‘quarter past’ times on an analogue clock, and identifying that

the small hand is pointing just past the number and the big hand is pointing to the three (R) Describe the characteristics of ‘quarter to’ times on an analogue clock, and identifying that the

small hand is pointing almost to the next number and the big hand is pointing to the nine (R) Show fluency through describing and comparing time durations (F) Problem Solving using time and formulating problems from authentic situations to represent

quarter past and quarter to (PS)Name and order months and seasons Identify and describe features of a calendar (U)Use a calendar to identify the date and determine the number of days in each month

Create a calendar to represent a specific time period (PS) Understand the current use of Seasons representing a specific time period Use a calendar as an ongoing tool to record time and specific events each month (U) Use a calendar to predict time frames by month, week and days (PS) Use a calendar to identify the date and to determine the number of days in each month (PS &

R) Use calendars to locate specific information, such as finding a given date on a calendar and

saying what day it is, and identifying personally or culturally specific days (F) Investigate the seasons used by Aboriginal people and compare them to those used in

Western society, recognising the connection to weather patterns (U) Show understanding by connecting knowledge of time from smallest time frame to largest

time frame (days, weeks, fortnight, month etc) (U)SHAPE (F-7)Describe and draw two-dimensional shapes, with and without digital technologies

Identify and name 2 dimensional shapes (F) Compare and describe 2D shapes to develop the vocabulary of straight and curved lines,

edges, points and corners, number of sides (U) Identifying key features of squares, rectangles, triangles, kites, rhombuses and circles, such

as straight lines or curved lines, and counting the edges and corners (R) Show reasoning by sorting shapes by key features and describing the categories

Describe the features of three-dimensional objects

Identify and name known 3 dimensional shapes such as cube, cone, sphere, pyramid (F) Identifying geometric features of known shapes such as the number of faces, corners or edges (U) Investigate and identifying geometric features of prisms and other 3D shapes through the use of

models, such as the number of faces, corners or edges (R)Use Pictures, Numbers, Words to show what is known about 3D shapes (PS)Show reasoning by describing connections between 2D and 3D representations

LOCATION AND TRANSFORMATION (F-7)Interpret simple maps of familiar locations and identify the relative positions of key features

Understand and use directional language left and right, up (top) and down (bottom) on a page and transfer this to reading a map

Use directional language of beside, between, next to, to tell directions on a map (PS) Construct arrangements of objects from a set of directions (PS) Use problem solving strategies to plan problems for others by planning routes on maps and

recording the directions (PS) Through problem solving match transformations with their original shape (PS) Understand that we use representations of objects and their positions, such as on maps, to

allow us to receive and give directions and to describe place (U)Investigate the effect of one-step slides and flips with and without digital technologies

Investigate one step slides using models (PS) Investigate one step flips using models (PS) Show understanding by using Pictures, Numbers, Words to show, describe and compare

slides and flips (U)Identify and describe half and quarter turns

Students model half and quarter turns related to analogue clock (F) predict and reproduce a pattern based around half and quarter turns of a shape and

sketching the next element in the pattern (PS) Investigate the real world application of flips, slides and turns (PS) understand that objects can be moved but changing position does not alter an object’s size

or features (U)




A student progressing towards Level 2 may, for example:


CHANCE (1-10)Explain why they think an event is 'certain' or 'impossible'.

Use everyday language to describe outcomes of familiar events.

Collect data from relevant

Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’

Create a probability meter to place everyday events to match the language of chance (R)

Identify practical activities and everyday events that involve chance. (U)

Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (U)

Classify a list of everyday events according to how likely they are to happen, using the language of chance, and explaining reasoning

Make conjectures about chance events and test these (PS) Show fluency through listing possible outcomes of chance events (F) Formulate problems from authentic situations, (PS)

DATA REPRESENTATION AND INTERPRETATION (F-10)Identify a question of interest based on one categorical

Determine questions for gathering data (R) Determine methods for gathering and recording data – including a


variable. Gather data relevant to the question

table (F)

Use tallies and tables to record answers to questions and summarise the answers by counting.

questions to create lists, tables and picture graphs with and without the use of digital technology.

Interpret data in context.

Collect, check and classify data Gather data relevant to the question (F) Recognise the usefulness of tally marks (F) Identifying categories of data and using them to sort data (R) Check and classify data (F)

Create displays of data using lists, table and picture graphs and interpret them

Create picture graphs to represent data using one to one correspondence (PS)

Create displays of data using lists, table and picture graphs (PS) Compare the usefulness of different data displays (R) Show reasoning by creating and interpreting simple representations

of data (R)







Count and order numbers to and from thousands.

Apply place value to partition, rearrange and regroup numbers to help with calculations and solve problems.

Classify numbers as either odd or even.

Count and order numbers to and from 10 000.

Recognise the connection between addition and subtraction.

Recall addition and multiplication facts for

Investigate the conditions required for a number to be odd or even and identify odd and even numbers

Explain if and why a number is odd or even. (U)

Recognise, model, represent and order numbers to at least 10 000

Read, write and order numbers to 10 000. (F) Model numbers to 10 000 (U,F)

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

Rename larger numbers using place value and using other non-place value partitions. (F)

Partition larger numbers into place value parts to use to assist calculations (Partial sums, Partial products). (R,F)

Apply knowledge of partitioning to problem solving situationsRecognise and explain the connection between addition and subtraction

Understand subtraction is the inverse of addition (U) Be able to write addition and subtraction fact family number sentences

for a set of numbers. (F)Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

Know addition facts and strategies such as compliments to ten, doubles and near doubles and counting by tens and ones forwards and backwards. (F)

Apply a range of mental and written strategies to solve the result of addition and subtraction calculations such as partial sums and


compensation. (U,F)

Recall multiplication facts for 2, 5 and 10.

Model and represent the unit fractions of halves, thirds, quarters, fifths and eighths.

Explore language differences associated with fractions.

Describe, continue and create number patterns formed by repeated addition or subtraction.

single-digit numbers.

Explore simple number sequences based on multiples.

Solve problems using efficient strategies for multiplication with and without the use of digital technology.

Model and represent unit fractions for halves, thirds, quarters, fifths and eighths, and multiples of these up to one.

Represent money values in various ways and correctly count out change from financial transactions.

Continue number patterns involving addition or subtraction.

Recall multiplication facts of two, three, five and ten and related division facts

Know multiplication facts for 2’s, 3’s, 5’s and 10’s. (F) Relate skip counting to multiplication to division. (U) Relate multiplication facts to division facts (U)

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies

Use a range of strategies for multiplication such as the area model and the partitioning of numbers.(U,F)

FRACTIONS AND DECIMALS (1-6)Model and represent unit fractionsincluding 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole

Understand and model unit fractions. Find and relate unit fractions of a group through sharing (such as shared between (÷) 3 is 1/3)

Count by ½’s, 1/3’s and 1`/4’s to 1. (F)

use of fractions with numerators other than one; for example, 34 of a

block of chocolateMONEY AND FINANCIAL MATHEMATICS (1-10)Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

use of money as a model for grouping and unpacking lots of 10s rounding of amounts of money up and down to the nearest dollar Partition money amounts using place value denominations ($100’s,

$10’s, $1’s) and also with other denomination partitions.(F) Calculate change using strategies such as counting up. (F) Solve addition and subtraction problems using money as a context

using strategies such as counting on for addition and counting up for subtraction. (F)

PATTERNS AND ALGEBRA (F-10)Describe, continue, and create number patterns resulting from performing addition or subtraction

Understand and apply skip counting number patterns in solving problems involving repeated addition and repeated subtraction (U,F)

Use a function machine and the inverse machine as a model to apply mathematical rules to numbers or shapes

finding and describing simple rules in words to solve problems using simple function machines to represent and apply a process or

the inverse process, such as increase or decrease the value of a number by a specified amount







USING UNITS OF MEASUREMENT (F-10)Compare the masses of objects, using balance scales.

Interpret digital and analogue representations of minutes, hours, days, weeks and years.

Explore the properties of prisms.

Interpret grid maps of their local environment.

Recognise angles in terms of turns in everyday situations.

Use metric units for length, area, mass and capacity.

Tell time to the nearest minute.

Make models of three-dimensional objects.

Create simple maps.

Match positions on maps with given information.

Identify symmetry in natural and constructed environments.

Use angle size as a measure of turn in real situations.

Measure, order and compare objects using familiar metric units of length, area, mass and capacity

Recognise the importance of using common units of measurement. (R) Recognise and use centimetres and metres, grams and kilograms, and

millilitres and litres. (F)

Tell time to the minute and investigate the relationship between units of time

Tell and write time to the minute. (F) Understand, use and order units of time. (U,F) Recognise there are 60 minutes in an hour and 60 seconds in a minute

(U)

SHAPE (F-7)Make models of three-dimensional objects and describe key features

Use nets to make three-dimensional objects and identify faces, edges and vertices. (P)

LOCATION AND TRANSFORMATION (F-7)Create and interpret simple grid maps to show position and pathways

Create simple maps. (P) Use simple maps such as theme park or zoo maps. (U)

Identify symmetry in the environment

Identify symmetrical patterns, pictures and shapes. (P)

Identify and describe slides and turns found in the natural and built environment

recognising and representing slides and turn used in brickwork around the school

recognising and representing slides and turn used in sporting activities

GEOMETRIC REASONING (3-10)Identify angles as measures of turn and compare angle sizes in everyday situations

Identify comparative sizes of angles in everyday situations including the hands on a clock. (R)






CHANCE (1-10)Place events from familiar contexts in order of how likely they are to happen.

Recognise variation in measurements and other data.

Make tallies and convert them into one-to-one picture graphs (pictographs) and bar charts.

Conduct chance experiments, list possible outcomes and recognise variations in results.

Carry out simple data investigations for categorical variables.

Interpret and compare data displays.

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results

Conduct repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials. (F,R)

DATA REPRESENTATION AND INTERPRETATION (F-10)Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording

Collect and record categorical data to answer an identified question. (R)

Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies

Identify efficient ways to record data, and representing and reporting the results of investigations including using digital technologies. (P)

Interpret and compare data displays

Compare and contrast between displays of data and make appropriate conclusions. (U)








Count and order numbers to and from tens of thousands.

Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9.

Use addition and subtraction facts to develop efficient mental strategies for computation.

Count by quarters, halves and thirds, including with mixed numbers.

Make connections between fractions and decimal notation.

Calculate change and round to the nearest five cents.

Solve word problems by using number sentences involving multiplication or division.

Use equivalent number sentences involving addition and subtraction to find unknown quantities.

Use the properties of odd and even numbers.

Continue number sequences involving multiples of single-digit numbers and unit fractions, and locate them on a number line.

Recall multiplication facts to 10 x 10 and related division facts.

Choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology.

Estimate answers accurately enough for the context.

Recognise common equivalent fractions in familiar contexts.

Locate familiar fractions on a number line.

Make connections between fractions and decimal notations up to two decimal places.

Solve simple purchasing problems with and without the use of digital technology.

Describe number patterns resulting from multiplication.

Identify unknown quantities in number sentences.

Investigate and use the properties of odd and even numbers

Explain why a number is odd or even. (U) Relate the properties of odd or even to authentic contexts. (R)

Recognise, represent and order numbers to at least tens of thousands

Read, write and order numbers up to and back from 10 000’s. (F)

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

Rename larger numbers using place value and using other non-place value partitions. (F)

Partition larger numbers into place value parts to use to assist calculations (Partial sums, Partial products). (R,F)

Apply a range of mental strategies to solve and/or estimate the result of calculations. (F)

Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9

Understand the number patterns for the multiples of 3 - 9 and use in assisting with determining multiplication facts. (U)

Recall multiplication facts up to 10 × 10 and related division facts

Know multiplication facts to 10x10. (F) Be able to relate all four fact family number facts for multiplication and division

to any multiplication or division number sentence. (U)Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder

use of written number sentences such as 20 ÷ 4 = 5 to summarise sharing (partition) and ‘how many?’ (quotition) processes

representation of multiplication as a rectangular array and as the area of a rectangle

use of fact families (5 × 7 = 35, 35 ÷ 7 = 5) to solve division problems estimate the results of computations and recognise whether these are likely to

be over-estimates or under-estimates. Use a range of techniques for multiplication such as the area model, repeated

addition and the partitioning of numbers.(F) Use a range of techniques for division such as the area model, repeated

subtraction and the partitioning of numbers.(F) Recognise the multiplication and division are inverse operations (U)

FRACTIONS AND DECIMALS (1-6)Investigate equivalent fractions used in contexts

Understand the relationship between ½, 2/4 and 4/8 in authentic contexts and other equivalent fractions. (U)

development and use of fraction notation and recognition of equivalent fractions

such as 12 = 48 , including the ordering of fractions using physical models

Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line

Count by ½’s, 1/3’s and 1`/4’s with and without a number line. (F) develop fraction notation and compare simple common fractions such as

34 > 23 using physical models.

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation

Understand the place value system into the hundredths using real life contexts such as money. (U,R)

use of place value (as the idea that ‘ten of these is one of those’) to determine the size and order of decimals to hundredths

Relate fractions as another way of representing division. Relate fractions to decimals through fractions of 100 (1 metre, $1.00, 100 piece

block of chocolate). (R)MONEY AND FINANCIAL MATHEMATICS (1-10)Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

Solve addition and subtraction problems using money as a context using strategies such as counting on for addition and counting up for subtraction. (F)

addition and subtraction of amounts of money including calculation of change from $10

PATTERNS AND ALGEBRA (F-10)Explore and describe number patterns resulting from performing multiplication

Understand and apply the multiplication (skip counting) number patterns in solving multiplication and resulting products. (U,F)

Solve word problems by using number sentences involving multiplication or division where there is no remainder

Apply a variety of strategies for multiplication and division including mental strategies for problem solving. (F)

Use equivalent number sentences involving addition and subtraction to find unknown quantities

Rearrange subtraction number sentences into addition and vice versa to solve for unknown quantities. (F)

Use partitioning to find missing numbers/digits in a number sentence eg.56+?=136 or 53+8?=136 (U,F)

Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions

constructing and applying an algorithm for multiplication of two-digit numbers partitioning and ordering a set of Australian coins by denomination








Use scaled instruments to measure length, angle, area and mass.

Use am and pm notation.

Identify time between two events.

Identify and describe symmetry, asymmetry and pattern in natural and made objects.

Use scaled instruments to measure length, angle, area, mass, capacity and temperature of shapes and objects.

Convert between units of time.

Solve problems involving time duration.

Compare areas of regular and irregular shapes, using informal units.

Interpret information contained in maps.

Create symmetrical simple and composite shapes and patterns, with and without the use of digital technology.

Classify angles in relation to a right angle.

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures

Read and interpreting scales on a range of measuring instruments. (U)

Compare objects using familiar metric units of area and volume

Comparing areas using centimetre grid paper and volume using centicubes and litres in authentic contexts. (R)

Compare a variety of measuring units ie. Imperial/metric (R) Convert between units of time Convert between units of time including hours to minutes and weeks to

days and vise versa. (F)Use am and pm notation and solve simple time problems

Apply am and pm appropriately. (R) Calculate elapsed time problems using counting on strategies. (F)

SHAPE (F-7)Compare the areas of regular and irregular shapes by informal means

Comparing areas using informal means such as centimeter grid paper or tiles. (R)

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

Identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes. (R)

Explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects

describing the similarities and differences between two-dimensional shapes and three-dimensional objects

recognising two-dimensional shapes that are the faces for three-dimensional objects such as prisms, pyramids and platonic solids (including tetrahedrons, cubes and dodecahedrons)

LOCATION AND TRANSFORMATION (F-7)Use simple scales, legends and directions to interpret information contained in basic maps

Understand and use scales and directions in maps. (U) Interpret information from a variety of maps (U,R)

Create symmetrical patterns, pictures and shapes with and without digital technologies

Create symmetrical patterns, pictures and shapes. (P)

GEOMETRIC REASONING (3-10)Compare angles and classify them as equal to, greater than or less than a right angle

Apply Acute, Right and Obtuse correctly to angles in everyday situations. (F)






CHANCE (1-10)Compare one event to the other as being less, equally or more likely to happen, and justify their reasoning.

List the probabilities of everyday events. Describe possible everyday

events and order their chances of occurring

Discuss and apply probabilities to everyday situations ranging from Impossible (0) to Certain(1). (R)

Order lists of familiar events from least to most likely (R)

Identify everyday events where Apply an understanding of mutually exclusive events such as tossing a


one cannot happen if the other happens

coin once, which can result in either heads or tails, but not both. (R)Identify everyday events where if one event occurs, the other event cannot occur.

Define data sources, and plan and trial methods of data collection and recording.

Use a variety of methods of data presentation.

Identify questions or issues involving categorical variables.

Identify dependent and independent events.

Construct data displays from given or collected data, with and without the use of digital technology.

Describe different methods for data collection and representation, and evaluate their effectiveness.

Identify events where the chance of one will not be affected by the occurrence of the other

Apply an understanding of independent events such as the outcome in rolling a die cannot affect the outcome in tossing a coin. (R)

DATA REPRESENTATION AND INTERPRETATION (F-10)Select and trial methods for data collection, including survey questions and recording sheets

Choose an effective way to collect and record data for a given investigation. (P)

Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values

Choose appropriate representations for different types of data for interpretation, especially using digital technologies. (P)

Read, interpret and make data displays, where one object represents a greater value (U,R)

Evaluate the effectiveness of different displays in illustrating data features including variability

Compare and contrast different displays of data and make appropriate conclusions. (U)

Make judgements about data displays and determine if they are effective or misleading (U,R)






NUMBER AND PLACE VALUE (F-8)Identify and describe factors and multiples.

Estimate to check the reasonableness of answers and approximate

Identify and describe factors and multiples of whole numbers and use them to solve problems

Identify factors and multiples of whole numbers. (F) Know the difference between factors and multiples. (U) Identify the patterns involved in identifying factors and multiples. (R) Using simple divisibility tests (F)

Use estimation and rounding to check the reasonableness of answers to calculations

Apply a range of mental strategies to estimate the result of calculations and know the usefulness of this. (F)


Solve problems involving multiplication of large numbers by one- or two-digit numbers, using efficient mental and written methods and digital technology.

Use number properties for efficient mental calculation.

Extend fluency with the number system to beyond tens of thousandths.

Represent and order decimals.

Create a simple financial plan.

Use equivalent number sentences involving multiplication and division to find unknown quantities.

answers by rounding.

Solve simple problems involving the four operations using a range of strategies including digital technology.

Add and subtract fractions with the same denominator.

Order decimals and unit fractions and locate them on a number line.

Explain plans for simple budgets.

Continue patterns by adding or subtracting fractions and decimals.

Find unknown quantities in number sentences.

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies

Use a range of techniques for multiplication such as the area model and the partitioning of numbers.(F)

Apply and explain the distributive law and represent arrays to model multiplication. (F,R)

Solve problems involving division by a one digit number, including those that result in a remainder

Solve real life division problems that result in a remainder. (F)

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems

Use a range of written and mental calculation strategies to solve division problems. (F)

Interpret the resulting remainder in real contexts. (R)

Recognise, represent and order numbers to at least hundreds of thousands

reproducing six-digit numbers in words using their numerical representations, and vice versa

FRACTIONS AND DECIMALS (1-6)Compare and order common unit fractions and locate and represent them on a number line

Understand, model and order unit fractions. (U)

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator

Model and therefore add and subtract fractions with similar denominators, such as using the area model, numberlines, diagrams for adding and subtracting fractions. (U,R,F)

Recognise that the place value system can be extended beyond hundredths

Understand the place value system into the thousandths and smaller, including in real life situations such as mass and volume. (R)

Compare, order and represent decimals

Know how to represent decimals in different ways, such as words, numbers, fractions and models and compare relative sizes of decimals. ((U)

MONEY AND FINANCIAL MATHEMATICS (1-10)Create simple financial plans Develop financial plans for suitable relevant real life situations. (P)

PATTERNS AND ALGEBRA (F-10)Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction

Find, continue and create number patterns using fractions, decimals and whole numbers. (R)

Use equivalent number sentences involving multiplication and division to find unknown quantities

Make relevant fact family number sentences for multiplication and division with known and unknown multipliers and quotients. (F)

Follow a mathematical algorithm involving branching and repetition (iteration)

simulating a simple random walk manipulating sets of numbers using a given rule, for example, if a

number is even halve it; if a number is odd, subtract 1 then halve it







USING UNITS OF MEASUREMENT (F-10)Investigate units of measurement from historical and cultural contexts.

Convert between units of metric and other standard non-metric systems of measurement.

Use square centimetres, square metres, square kilometres and hectares as units of area.

Estimate areas by counting squares.

Describe routes using landmarks.

Compare maps with aerial photographs or representations created by digital technology.

Estimate angles between 0 and 360 degrees in both clockwise and anticlockwise directions.

Use appropriate units of measurement for length, area, volume, capacity and mass.

Calculate perimeter and area of rectangles.

Calculate volume and capacity of regular prisms

Convert between 12 and 24-hour time.

Connect three-dimensional objects with their two-dimensional representations.

Use a grid reference system to locate landmarks.

Describe transformations of two-dimensional shapes.

Identify line and rotational symmetry.

Estimate angles, and use protractors and digital technology to construct and measure angles.

Choose appropriate units of measurement for length, area, volume, capacity and mass

Choose, use and describe appropriate units of measurement for length, area, volume, capacity and mass. (U,R)

Calculate the perimeter and area of rectangles and the volume and capacity of prisms using familiar metric units

Use a variety of strategies in calculating the area and perimeter of rectangles. (F,R)

exploring efficient ways of calculating the perimeters of rectangles such as adding the length and width together and doubling the result

exploring efficient ways of finding the areas of rectangles measuring volume and capacity by counting the number of cubes

(cubic centimetres) exploring efficient ways of finding the volume and capacity of

rectangular prisms and cubesCompare 12- and 24-hour time systems and convert between them

Compare 12- and 24-hour time systems and convert between them. (F)

SHAPE (F-7)Connect three-dimensional objects with their nets and other two-dimensional representations

Make and use nets of a variety of 3D shapes. (R) Use 2D representations of 3D shapes. (R) Investigate and recognise the different nets of a 3D object

LOCATION AND TRANSFORMATION (F-7)Use a grid reference system to describe locations. Describe routes using landmarks and directional language

Understand and use common grids in everyday situations such as maps. (U)

Describe routes using the language of direction. (U) Compare aerial views and maps with grid references (F)

Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries

Identify and describe the lines and rotational symmetries of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies. (P)

Identify the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies. (R)

Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original

Enlarge 2D figures using manual and digital technologies. (F)

GEOMETRIC REASONING (3-10)Estimate, measure and compare angles using degrees. Construct angles using a protractor

Identify and measure the angles in a figure. (F) Estimate and compare angles in a figure. (R) Measure and construct angles using both 180° and 360° protractors

(F) Recognise that angles have arms and a vertex, and that size is the

amount of turn required for one arm to coincide with the other (F,U)



http://www.australiancurriculum.edu.au/Glossary?a=bab552e6-1437-4684-8c54-9e4600a2533d&t=Capacity

http://www.australiancurriculum.edu.au/Glossary?a=bab552e6-1437-4684-8c54-9e4600a2533d&t=Volume





CHANCE (1-10)

Recognise that probabilities range from 0 to 1, and place events in order on a number line from 0 to 1 based on their probability.

Construct column graphs and picture graphs where one picture can represent many data values from given or collected data, with and without the use of digital technology.

List outcomes of chance experiments with equally likely outcomes.

Assign probabilities as a number from 0 to 1.

Pose questions to gather data.

Construct various displays appropriate for the data, with and without the use of digital technology.

Compare and interpret different data sets.

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions

Understand the likelihood of winning simple games of chance by considering the number of possible outcomes. (U)

Represent the likelihood of winning simple games of chance in fractional form. (F)

Recognise that probabilities range from 0 to 1

Discuss and apply probabilities to everyday situations ranging from 0 to 1. (R)

Understand that the sum of all simple chance experiments equal 1.

DATA REPRESENTATION AND INTERPRETATION (F-10)Pose questions and collect categorical or numerical data by observation or survey

Pose questions regarding and collect and interpret both numerical and categorical data. (R,P)

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies

Choose and justify appropriate representations for different types of data for interpretation, especially using digital technologies. (R)

Describe and interpret different data sets in context

Compare and contrast different sets of data and make appropriate decisions and conclusions. (U)



Essential Teachings with Proficiencies Progression Score 5.5A student progressing towards Level 6 may, for example:


NUMBER AND PLACE VALUE (F-8)Represent composite numbers as a product of their prime factors.

Recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers.

Identify and describe properties of prime, composite, square and triangular numbers

Identify and describe properties of prime, composite, square and triangular numbers. (F)

Use these properties to create patterns and solve problems. (R) representation of square numbers using a power of 2; for


http://www.australiancurriculum.edu.au/Glossary?a=bab552e6-1437-4684-8c54-9e4600a2533d&t=Square

example, 9 = 32 creation of sets of multiples of numbers and their representation

in index form; for example, 3, 9, 27 written as 31, 32, 33 respectively

Identify the highest common factor (greatest common divisor) and lowest common multiple of two whole numbers.

Use ordered pairs of whole numbers to represent coordinates of points and locate these points on simple grids and in the first quadrant on the Cartesian plane.

Continue and create sequences involving whole numbers, fractions and decimals, according to a given rule.

Explore the use of brackets and order of operations to write and evaluate number sentences.

Solve problems that involve all four operations with whole numbers.

Describe the use of integers in everyday contexts.

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.

Locate fractions and integers on a number line.

Solve problems involving the addition and subtraction of related fractions.

Calculate a simple fraction of a quantity.

Add, subtract and multiply decimals, and divide decimals where the result is rational.

Make connections between the powers of 10 and the multiplication and division of decimals.

Connect fractions, decimals and percentages as different representations of the same number.

Calculate common percentage discounts on sale items, with and without the use of digital technology.

Specify rules used to generate sequences involving whole numbers, fractions and decimals.

Write number sentences using brackets and order of operations.

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations

Select between and use a variety of written, mental and digital calculation strategies involving the four operations to solve a variety of everyday problems. (F)

multiplication by increasing and decreasing by a factor of two; for example, 24 × 16 = 48 × 8= 96 × 4 = 192 × 2 = 384 × 1 = 384

Comment on the efficiency of different strategies (U) applying strategies already developed for solving problems

involving small numbers to those involving large numbers applying a range of strategies to solve realistic problems and

commenting on the efficiency of different strategies forming simple single digit estimates with consideration of order

of magnitude of the resultInvestigate everyday situations that use integers. Locate and represent these numbers on a number line

Become familiar with and use the range of integers. (F) Use a number line to solve addition and subtraction problems

using positive and negative integers. (F) Apply integers in everyday situations. (F)

FRACTIONS AND DECIMALS (1-6)Compare fractions with related denominators and locate and represent them on a number line

Understand, model and order fractions with related denominators. (U)

Solve problems involving addition and subtraction of fractions with the same or related denominators

Model and therefore add and subtract fractions with related denominators, such as using the area model for adding and subtracting fractions. (U,F)

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies

Find fractional quantities where a group is the whole. (F)

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers

Apply a variety of strategies to add and subtract decimals. (F) Estimate the solution to addition and subtraction problems

involving decimals. (R) Explore and practise efficient methods for solving problems

requiring operations on decimals, to gain fluency with calculating with decimals and with recognising appropriate operations

Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies

Understand and use as variety of strategies to multiply and divide problems involving decimals in everyday situations (U,F)

recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication by fractions or decimals)

Multiply and divide decimals by powers of 10

Understand how multiplying and dividing decimals by powers of ten affects the initial decimal. (U)

Make connections between equivalent fractions, decimals and percentages

Know how to represent decimals in different ways, such as words, numbers, fractions and models and compare relative sizes of decimals. (R)

recognition of equivalent rates expressed as percentages, fractions and decimals

MONEY AND FINANCIAL MATHEMATICS (1-10)Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies

Use the understanding of percentages to calculate the sale price of items in everyday situations. (U,F)

PATTERNS AND ALGEBRA (F-10)Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence

Find, continue and create number patterns using fractions, decimals and whole numbers. (R)

Find and describe the rule used to create a pattern. (R)

Explore the use of brackets and order of operations to write number sentences

Understand and apply the rules for completing multiple operations within the same number sentence including brackets (BODMAS,BOMDAS,PEMDAS,etc.) (F)

Design algorithms involving branching and iteration to solve specific classes of mathematical problems

implementing algorithms such as the Euclidean division algorithm devising flowcharts to represent algorithms for a common

processes such as adding two fractions



Essential Teachings with Proficiencies Progression Score 5.5A student progressing towards Level 6 may, for example:



Convert between common metric units.

Recognise metric prefixes.

Relate decimals to the metric system.

Choose appropriate units of measurement to perform a calculation.

Connect decimal representations to the metric system

Understand the connection between the Base 10 System of numbers and the Decimal system of measurement. (U)

Convert between common metric units of length, mass and capacity

Convert between different decimal units. (F) Recognise the significance of the prefixes in units of measurement (U)

Solve problems involving the comparison of lengths and

Be able to use different units of measurement in appropriate contexts to solve everyday problems involving length and area. (P)


areas using appropriate units

Access print and digital timetables, answer simple questions using a timetable and create simple personal timetables.

Describe acute, obtuse and reflex angles in terms of their relationship to multiples of a right angle.

Investigate compass points, angles on a straight line, angles at a point, and vertically opposite angles.

Solve problems involving time, length and area.

Make connections between capacity and volume.

Interpret a variety of everyday timetables.

Construct simple prisms and pyramids.

Investigate simple combinations of transformations in the plane, with and without the use of digital technology.

Solve problems using the properties of angles.

Connect volume and capacity and their units of measurement

Use volume and capacity in everyday situations. (F)

Interpret and use timetables Use common timetables such as public transport. (F)

Measure, calculate and compare elapsed time

recognising that some units of time are better suited for some tasks than others, for example, seconds rather than minutes to measure the duration of a short event

using a stopwatch to measure and compare the duration of a series of events, for example, how long does it take to jump a skipping rope 100 times

using the starting and finishing times to calculate and compare elapsed time, for example, the time taken to walk to school compared to the time taken to ride to school

SHAPE (F-7)Construct simple prisms and pyramids

Use a variety of materials to construct and deconstruct prisms and pyramids. (P)

LOCATION AND TRANSFORMATION (F-7)Investigate combinations of translations, reflections and rotations, with and without the use of digital technologiesInvestigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies

identify the effects of a combination of transformations by flipping, sliding and turning two-dimensional shapes. (R)

understanding which attributes of a shape remain the same or change under the effects of transformations such as size, shape or orientation

creating tessellations with simple shapes or simple composite shapes

Introduce the Cartesian coordinate system using all four quadrants

Use and relate the Cartesian Plane to everyday situations. (U) Identify the four quadrants of a Cartesian plane and plot points into all

four quadrants. (F)GEOMETRIC REASONING (3-10)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

Identify, define and measure right, acute, obtuse, straight and reflex angles. (F)

Identify vertically opposite angles and use to determine unknown angles such as intersecting roads. (U,R)




Essential Teachings with Proficiencies (examples to illustrate the content)

Progression Score 5.5A student progressing towards Level 6 may, for example:


CHANCE (1-10)Represent probabilities as simple ratios and fractions.

Conduct chance experiments with both small and large numbers of trials, using digital technology.

Recognise that probability can be interpreted as an expected frequency.

Evaluate the effectiveness of different displays in illustrating data features, including variability.

Pose questions and collect categorical or numerical data by observation or survey.

Distinguish between a sample and a population.

Specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages.

Compare observed and expected frequencies of events, including those where outcomes of trials are generated with the use of digital technology.

Interpret and compare a variety of data displays, including displays for two categorical variables.

Analyse and evaluate data from secondary sources.

Describe probabilities using fractions, decimals and percentages

Understand use and convert between probabilities using fractions, decimals and percentages. (U,F)

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies

Conduct trials of chance and identify the variation between trials. (U,F)

Understand why larger numbers of trials result in more accurate probabilities. (U)

Compare observed frequencies across experiments with expected frequencies

Compare observed and expected probabilities. (R)

DATA REPRESENTATION AND INTERPRETATION (F-10)Construct, interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables

Select and use a range of appropriate data representations for comparison between sets of similar data. (U,F)

Interpret secondary data presented in digital media and elsewhere

Discuss and interpret data found in everyday situations. (R)

Identifying potentially misleading data representations in the media, such as graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made, and pie charts in which the whole pie does not represent the entire population about which the claims are made (F,U,PS)

Pose and refine questions to collect categorical or numerical data by observation or survey

narrowing or broadening a question to be posed for an observation or survey, for example, ‘which of these ice cream flavours – vanilla or chocolate?’ to ‘do you like ice cream, if yes what is your favourite flavour?’



ELABORATIONS(examples to illustrate the content)





Investigate index notation and represent whole numbers as products of powers of prime numbers.

Find equivalent fractions and use them to order fractions.

Locate fractions and mixed numbers on a number line.

Solve problems involving addition and subtraction of fractions, including those with unrelated denominators.

Investigate and calculate 'best buys' and solve problems involving simple ratios, with and without the use of digital technology.

Make the connections between whole numbers and index notation and the relationship between perfect squares and square roots.

Solve problems involving the order, addition and subtraction of integers.

Express fractions in their simplest form.

Solve problems involving all four operations with fractions, decimals, percentages and their equivalences.

Make simple estimates to judge the reasonableness of results.

Compare the cost of items to make financial decisions, with and without the use of digital technology.

Investigate index notation and represent whole numbers as products of powers of prime numbers

defining and comparing prime and composite numbers and explaining the difference between them

applying knowledge of factors to strategies for expressing whole numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees

solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of whole numbers by comparing their prime factorisation

Investigate and use square roots of perfect square numbers

investigating square numbers such as 25 and 36 and developing square-root notation

investigating between which two whole numbers a square root liesApply the associative, commutative and distributive laws to aid mental and written computation

understanding that arithmetic laws are powerful ways of describing and simplifying calculations

Compare, order, add and subtract integers

Nil

REAL NUMBERS (7-10)Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line

exploring equivalence among families of fractions by using a fraction wall or a number line (for example by using a fraction wall to show that 2/3 is the same as 4/6 and 6/9)

Solve problems involving addition and subtraction of fractions, including those with unrelated denominators

exploring and developing efficient strategies to solve additive problems involving fractions (for example by using fraction walls or rectangular arrays with dimensions equal to the denominators)

Multiply and divide fractions and decimals using efficient written strategies and digital technologies

investigating multiplication of fractions and decimals, using strategies including patterning and multiplication as repeated addition, with both concrete materials and digital technologies, and identifying the processes for division as the inverse of multiplication

Express one quantity as a fraction of another, with and without the use of digital technologies

using authentic examples for the quantities to be expressed and understanding the reasons for the calculations

Round decimals to a specified number of decimal places

using rounding to estimate the results of calculations with whole numbers and decimals, and understanding the conventions for rounding

Connect fractions, decimals and percentages and carry out simple conversions

justifying choices of written, mental or calculator strategies for solving specific problems including those involving large numbers

understanding that quantities can be represented by different number types and calculated using various operations, and that choices need to be made about each

calculating the percentage of the total local municipal area set aside for parkland, manufacturing, retail and residential dwellings to compare land use

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies

using authentic problems to express quantities as percentages of other amounts

Recognise and solve problems involving simple ratios

understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem

MONEY AND FINANCIAL MATHEMATICS (1-10)Investigate and calculate 'best buys', with and without digital technologies

applying the unitary method to identify ‘best buys’ situations, such as comparing the cost per 100g

Continued…


Number and Algebra Level 7 Continued…

PATTERNS AND ALGEBRA (F-10)

Use substitution to check solutions.

Use a variety of methods to solve linear equations with whole number solutions.

Use variables to represent arbitrary numbers.

Substitute numbers into algebraic expressions.

Connect the laws and properties of number to algebra.

Assign ordered pairs to given points on the Cartesian plane.

Develop simple linear models for situations, make predictions based on these models, solve related equations and check their solutions.

Interpret and analyse graphs of relations from real data.

Introduce the concept of variables as a way of representing numbers using letters

understanding that arithmetic laws are powerful ways of describing and simplifying calculations and that using these laws leads to the generality of algebra

Create algebraic expressions and evaluate them by substituting a given value for each variable

using authentic formulas to perform substitutions

Extend and apply the laws and properties of arithmetic to algebraic terms and expressions

identifying order of operations in contextualised problems, preserving the order by inserting brackets in numerical expressions, then recognising how order is preserved by convention

moving fluently between algebraic and word representations as descriptions of the same situation

LINEAR AND NON-LINEAR RELATIONSHIPS (7-10)Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point

plotting points from a table of integer values and recognising simple patterns, such as points that lie on a straight line

Solve simple linear equations solving equations using concrete materials, such as the balance model, and explain the need to do the same thing to each side of the equation using substitution to check solutions

investigating a range of strategies to solve equations

Investigate, interpret and analyse graphs from authentic data

using travel graphs to investigate and compare the distance travelled to and from school

interpreting features of travel graphs such as the slope of lines and the meaning of horizontal lines

using graphs of evaporation rates to explore water storage




ELABORATIONS(examples to illustrate the content)



USING UNITS OF MEASUREMENT (F-10)Use formulas for the area and perimeter of a square.

Calculate the surface area and volume of a cube.

Draw different views of prisms, and solids formed from combinations of prisms.

Construct parallel and perpendicular lines.

Demonstrate that the angle sum in a triangle is 180 degrees.

Identify squares, rectangles, rhombuses, parallelograms, kites and trapeziums based on their properties.

Use formulas for the area and perimeter of rectangles.

Calculate volumes of rectangular prisms.

Describe different views of three-dimensional objects, and use models, sketches and digital technology to represent these views.

Represent transformations of triangles and quadrilaterals on the Cartesian plane, with and without the use of digital technology.

Name the types of angles formed by a transversal crossing parallel line, and solve simple numerical problems involving these lines and angles.

Classify triangles and quadrilaterals.

Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving

building on the understanding of the area of rectangles to develop formulas for the area of triangles

establishing that the area of a triangle is half the area of an appropriate rectangle

using area formulas for rectangles and triangles to solve problems involving areas of surfaces

Calculate volumes of rectangular prisms

investigating volumes of cubes and rectangular prisms and establishing and using the formula V = l × b × h

understanding and using cubic units when interpreting and finding volumes of cubes and rectangular prisms

SHAPE (F-7)Draw different views of prisms and solids formed from combinations of prisms

using aerial views of buildings and other 3-D structures to visualise the structure of the building or prism

LOCATION AND TRANSFORMATION (F-7)Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries

describing patterns and investigating different ways to produce the same transformation such as using two successive reflections to provide the same result as a translation

experimenting with, creating and re-creating patterns using combinations of reflections and rotations using digital technologies

GEOMETRIC REASONING (3-10)Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal

defining and classifying pairs of angles as complementary, supplementary, adjacent and vertically opposite

Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning

constructing parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software

defining and identifying the relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal

Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral

using concrete materials and digital technologies to investigate the angle sum of a triangle and quadrilateral

Classify triangles according to their side and angle properties and describe quadrilaterals

identifying side and angle properties of scalene, isosceles, right-angled and obtuse-angled triangles

describing squares, rectangles, rhombuses, parallelograms, kites and trapeziums




Essential Teachings with Proficiencies (examples to illustrate the content)



CHANCE (1-10)

Interpret secondary data presented in digital media and elsewhere, including consideration of sampling, misleading displays, bias and purpose.

Create side-by-side column graphs.

Determine probabilities by symmetry and counting.

Recognise that summarising data by calculating measures of centre and spread can help make sense of the data.

Determine the median for different data sets.

Determine the sample space for simple experiments with equally likely outcomes, and assign probabilities outcomes.

Identify issues involving the collection of discrete and continuous data from primary and secondary sources.

Construct stem-and-leaf plots and dot-plots.

Identify or calculate mean, mode, median and range for data sets, using digital technology for larger data sets.

Describe the relationship between the median and mean in data displays.

Construct sample spaces for single-step experiments with equally likely outcomes

discussing the meaning of probability terminology (for example probability, sample space, favourable outcomes, trial, events and experiments)

distinguishing between equally likely outcomes and outcomes that are not equally likely

Assign probabilities to the outcomes of events and determine probabilities for events

expressing probabilities as decimals, fractionals and percentages

DATA REPRESENTATION AND INTERPRETATION (F-10)Identify and investigate issues involving numerical data collected from primary and secondary sources

obtaining secondary data from newspapers, the Internet and the Australian Bureau of Statistics

investigating secondary data relating to the distribution and use of non-renewable resources around the world

Construct and compare a range of data displays including stem-and-leaf plots and dot plots

understanding that some data representations are more appropriate than others for particular data sets, and answering questions about those data sets

using ordered stem-and-leaf plots to record and display numerical data collected in a class investigation, such as constructing a class plot of height in centimetres on a shared stem-and-leaf plot for which the stems 12, 13, 14, 15, 16 and 17 have been produced

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data

understanding that summarising data by calculating measures of centre and spread can help make sense of the data

Describe and interpret data displays using median, mean and range

using mean and median to compare data sets and explaining how outliers may affect the comparison

locating mean, median and range on graphs and connecting them to real life


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