Physical, Personal and Social Learning
Discipline-based Learning
Interdisciplinary Learning
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of Mathematics.
At this level:
Understanding develops from becoming aware of their physical state and encountering, reacting and responding to the world around them and to some everyday events and routines
Fluency includes students learning to control their behaviour and internal state and developing a repertoire of reactions to everyday experiences and events
Problem Solving includes students attending to and exploring the world around them with as much independence as possible
Reasoning includes students coactively exploring and manipulating objects in their immediate environment and experiencing the language associated with Maths activities.
Number and Algebra
Students observe the use of number within their daily life. They begin to respond to numbers in everyday experiences. Students demonstrate awareness of counting by responding to number rhymes, songs, stories and finger games. They experience and respond to ‘one for you, one for me’, ‘gone’, ‘no more left’ and ‘give me more’. Students participate in making piles, groups or bundles of familiar everyday objects and respond to objects being put together and taken apart.
Measurement and Geometry
Students observe and explore objects within daily life. They react and respond to objects and experience measurement attributes in practical situations. Students explore objects of varying weights, lengths, capacities and materials. They show an awareness of time and daily routine by responding to a signal from the teacher, and items being brought out or removed. Students respond to a signal from a timer, used to indicate the end of an activity. Students explore and respond to objects of varying textures, colours, sizes and shapes. Students explore space by moving and changing position and location, and respond to changes in position.
Statistics and Probability
Students observe objects and events within their daily life. Students begin to display a similar and predictable reaction to regular events. They respond to major changes to regular games and activities associated with chance, surprise and predictability, such as hitting a switch to activate a toy.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding develops through participating in a variety of everyday activities that involve objects, events and number
Fluency includes following regular routines, and matching objects using a repertoire of responses
Problem Solving includes students attending to, exploring and sorting objects in the world around them
Reasoning includes manipulating and playing with objects to develop links between their immediate environment, everyday language and mathematical activity.
Number and Algebra
Students participate in everyday activities that involve numbers and counting, comparing groups of objects, and pattern activities. Students can rote count to three. Students identify ‘one’ and ‘lots’ of objects and show an understanding of ‘more’ in familiar situations. They manipulate objects and build a tall tower by using ‘more’ blocks and take blocks away from a tower to make the tower ‘less’ tall.
Measurement and Geometry
Students participate in everyday activities that explore measurement and use measurement attributes in practical situations. Students demonstrate beginning understanding of basic measurement concepts such as ‘long or short’, ‘heavy or light’,
They explore routine events and show an awareness of time and daily...
Number and Algebra
Students participate in everyday activities that involve numbers and counting, comparing groups of objects, and pattern activities. Students can rote count to three. Students identify ‘one’ and ‘lots’ of objects and show an understanding of ‘more’ in familiar situations. They manipulate objects and build a tall tower by using ‘more’ blocks and take blocks away from a tower to make the tower ‘less’ tall.
Measurement and Geometry
Students participate in everyday activities that explore measurement and use measurement attributes in practical situations. Students demonstrate beginning understanding of basic measurement concepts such as ‘long or short’, ‘heavy or light’,
They explore routine events and show an awareness of time and daily routines by responding to a routine signal from the teacher, such as, ‘It’s time to go outside and play’, ‘pack up’, or ‘unpack bag’
They demonstrate an awareness of object permanence by searching for objects that have been hidden and participate in class activities that explore three-dimensional objects. They can match identical familiar three-dimensional shapes that are ‘the same’. Students respond to specific instructions relating to manipulating the movement and location of self and objects.
Statistics and Probability
They participate in class activities that explore object, events and displaying information. They develop an awareness of chance by playing with materials or objects that involve cause and effect (actions that will happen) and playing games where the outcome is unpredictable, for example, peekaboo. Students respond to a simple pictorial representation of their activities related to a short time-frame.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes connecting names and quantities (of objects, events and numbers to five)
Fluency includes counting numbers in sequence, matching objects to replicate a pattern and predicting day and night events
Problem Solving includes matching groups and objects
Reasoning includes manipulating and playing with objects to develop links between their immediate environment, everyday language, mathematical activity and concepts.
Number and Algebra
Students connect number names and numerals with sets of up to five elements. They match individual objects with counting sequences up to and back from five. Students use concrete materials to solve problems that involve comparing, combining and separating sets, for example “How might I make this group more than the other group?” Students make ‘groups’, ‘lots’ and groups of ‘one’ and can indicate which collection has ‘more’ than the other. They can distribute objects to each person in a group until there are no objects left. Students order the first three elements of a set. Students can match one attribute of familiar objects, for example, colour, size or shape.
Measurement and Geometry
Students explore measurement attributes in practical...
Number and Algebra
Students connect number names and numerals with sets of up to five elements. They match individual objects with counting sequences up to and back from five. Students use concrete materials to solve problems that involve comparing, combining and separating sets, for example “How might I make this group more than the other group?” Students make ‘groups’, ‘lots’ and groups of ‘one’ and can indicate which collection has ‘more’ than the other. They can distribute objects to each person in a group until there are no objects left. Students order the first three elements of a set. Students can match one attribute of familiar objects, for example, colour, size or shape.
Measurement and Geometry
Students explore measurement attributes in practical situations and use words to describe the characteristics of familiar objects such as full, empty, long, short, light and heavy. Students solve simple mathematical problems associated with longer and shorter lengths, for example, ‘How can I make this stick shorter?’ They explore events and identify day and night events. They can identify events that may or may not happen today. Students respond to a simple pictorial representation of activities related to their whole day. They match objects that are the same and sort familiar objects, and an understanding of the concept of ‘inside and outside’ by following instructions. They demonstrate an understanding of location and spatial awareness by following simple instructions related to simple spatial concepts, such as ‘under’, ‘on’, ‘beside’.
Statistics and Probability
Students participate in and contribute to the development of picture schedules, timetables and pictorial lists associated with familiar activities, such as listing the ingredients needed for a cooking session. They demonstrate an understanding of the concept of chance by participating in games of chance, and identifying events that may or may not happen today.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of the mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes connecting names, numerals and quantities of objects, events and numbers to 10)
Fluency includes counting number in sequence, continuing patterns, comparing objects, recognising events in the day
Problem Solving includes manipulating, comparing and sorting objects, such as which group (out of three) has more or less
Reasoning includes manipulating and playing with objects to develop links between their immediate environment, everyday language and mathematical activity.
Number and Algebra
Students connect number names and numerals with sets of up to 10 elements. They match individual objects with counting sequences up to and back from 10. They recognise and point to numerals in and around the classroom, for example, numbers on a clock face. Students use concrete materials to solve problems that involve comparing, combining and separating sets. They can indicate when groups of less than 10 objects are the same or different in number and that two collections have the ‘same’ quantity by matching items one to one. They can find the first and last object in a sequence and place objects into sets to make ‘more’ and take objects from a group to make ‘less’. Students order the first five elements of a set. They sort objects and shapes based...
Number and Algebra
Students connect number names and numerals with sets of up to 10 elements. They match individual objects with counting sequences up to and back from 10. They recognise and point to numerals in and around the classroom, for example, numbers on a clock face. Students use concrete materials to solve problems that involve comparing, combining and separating sets. They can indicate when groups of less than 10 objects are the same or different in number and that two collections have the ‘same’ quantity by matching items one to one. They can find the first and last object in a sequence and place objects into sets to make ‘more’ and take objects from a group to make ‘less’. Students order the first five elements of a set. They sort objects and shapes based on a given attribute and create simple repeating patterns of two elements or more by copying a pattern.
Measurement and Geometry
Students explore measurement attributes in practical situations and identify and describe the basic characteristics of a range of objects, for example, heights of students, cup measures in cooking. They can identify regular events within the school week. They can follow a class pictorial schedule and mark off each passing day on a calendar. Students demonstrate an understanding of two- and three-dimensional shapes by matching basic geometric objects to pictures of that object, identifying basic three-dimensional shapes in the classroom and sorting shapes into like groups. Students show an understanding of ‘location’ and spatial concepts by responding to instructions to position items.
Statistics and Probability
They explore events and follow a simple picture schedule, and use these to answer simple ‘yes’ or ‘no’ questions. They play a variety of chance games such as bingo or snakes and ladders and demonstrate an understanding that they will not always win.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes connecting names, numerals and quantities
Fluency includes readily counting numbers in sequences, continuing patterns, and comparing the lengths of objects
Problem Solving includes using materials to model authentic problems, sorting objects, using familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer
Reasoning includes explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparison of length
Number and Algebra
Students connect number names and numerals with sets of up to 20 elements, estimate the size of these sets, and use counting strategies to solve problems that involve comparing, combining and separating these sets. They match individual objects with counting sequences up to and back from 20. Students order the first 10 elements of a set.
Measurement and Geometry
Students identify measurement attributes in practical situations and compare lengths, masses and capacities of familiar objects. They order events, explain their duration, and match days of the week to familiar events. Students identify simple shapes in their environment and sort shapes by their common and distinctive features. They use simple statements and gestures to describe location.
Statistics and Probability
Students sort familiar categorical data into sets and use these to answer yes/no questions and make simple true/false statements about the data.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level: Understanding includes connecting names, numerals and quantities, and partitioning numbers in various ways
Fluency includes counting number in sequences readily forward and backwards, locating numbers on a line, and naming the days of the week
Problem Solving includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, and using familiar counting sequences to solve unfamiliar problems and discusing the reasonableness of the answer
Reasoning includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data, and explaining patterns that have been created
Number and Algebra
Students count to and from 100 and locate these numbers on a number line. They partition numbers using place value and carry out simple additions and subtractions, using counting strategies. Students recognise Australian coins according to their value. They identify representations of one half. Students describe number sequences resulting from skip counting by 2s, 5s and 10s. They continue simple patterns involving numbers and objects with and without the use of digital technology.
Measurement and Geometry
Students use informal units of measurement to order objects based on length and capacity. They tell time to the half-hour and explain time durations. Students describe two-dimensional shapes and three-dimensional objects. They use the language of distance and direction to move from place to place.
Statistics and Probability
Students describe data displays. They ask questions to collect data and draw simple data displays. Students classify outcomes of simple familiar events.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry,
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes connecting number calculations with counting sequences, partitioning and combining numbers flexibly, identifying and describing the relationship between addition and subtraction and between multiplication and division
Fluency includes counting numbers in sequences readily, using informal units iteratively to compare measurements, using the language of chance to describe outcomes of familiar chance events and describing and comparing time durations
Problem Solving includes formulating problems from authentic situations, making models and using number sentences that represent problem situations, and matching transformations with their original shape
Reasoning includes using known facts to derive strategies for unfamiliar calculations, comparing and contrasting related models of operations, and creating and interpreting simple representations of data
Number and Algebra
Students count to and from, and order numbers up to 1000. They perform simple addition and subtraction calculations, using a range of strategies. They find the total value of simple collections of Australian notes and coins. Students represent multiplication and division by grouping into sets and divide collections and shapes into halves, quarters and eighths. They recognise increasing and decreasing number sequences involving 2s, 3s, 5s and 10s, identify the missing element in a number sequence, and use digital technology to produce sequences by constant addition.
Measurement and Geometry
Students order shapes and objects, using informal units for a range of measures. They tell time to the quarter hour and use a calendar to identify the date, days, weeks and months included in seasons and other events. Students draw two-dimensional shapes, specify their features and explain the effects of one-step transformations. They recognise the features of three-dimensional objects. They interpret simple maps of familiar locations.
Statistics and Probability
Students collect data from relevant questions to create lists, tables and picture graphs with and without the use of digital technology. They interpret data in context. Students describe outcomes of familiar events using everyday language.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry
Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions
Problem Solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns
Reasoning includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of data collections and data displays
Number and Algebra
Students count and order numbers to and from 10 000. They recognise the connection between addition and subtraction, and solve problems using efficient strategies for multiplication with and without the use of digital technology. Students recall addition and multiplication facts for single-digit numbers. They represent money values in various ways and correctly count out change from financial transactions. Students model and represent unit fractions for halves, thirds, quarters, fifths and eighths, and multiples of these up to one. They classify numbers as either odd or even, continue number patterns involving addition or subtraction, and explore simple number sequences based on multiples.
Measurement and Geometry
Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students identify symmetry in natural and constructed environments. They use angle size as a measure of turn in real situations and make models of three-dimensional objects. Students match positions on maps with given information and create simple maps.
Statistics and Probability
Students carry out simple data investigations for categorical variables. They interpret and compare data displays. Students conduct chance experiments, list possible outcomes and recognise variations in results.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times, and describing properties of symmetrical shapes
Fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations, and collecting and recording data
Problem Solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations, and using properties of numbers to continue patterns
Reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays
Number and Algebra
Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students solve simple purchasing problems with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in familiar contexts and make connections between fractions and decimal notations up to two decimal places. Students identify unknown quantities in number sentences. They use the properties of odd and even numbers and describe number patterns resulting from multiplication. Students continue number sequences involving multiples...
Number and Algebra
Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students solve simple purchasing problems with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in familiar contexts and make connections between fractions and decimal notations up to two decimal places. Students identify unknown quantities in number sentences. They use the properties of odd and even numbers and describe number patterns resulting from multiplication. Students continue number sequences involving multiples of single-digit numbers and unit fractions, and locate them on a number line.
Measurement and Geometry
Students compare areas of regular and irregular shapes, using informal units. They solve problems involving time duration. Students use scaled instruments to measure length, angle, area, mass, capacity and temperature of shapes and objects. They convert between units of time. Students create symmetrical simple and composite shapes and patterns, with and without the use of digital technology. They classify angles in relation to a right angle. Students interpret information contained in maps.
Statistics and Probability
Students describe different methods for data collection and representation, and evaluate their effectiveness. They construct data displays from given or collected data, with and without the use of digital technology. Students list the probabilities of everyday events. They identify dependent and independent events.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry
Fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles
Problem Solving includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans
Reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets
Number and Algebra
Students solve simple problems involving the four operations using a range of strategies including digital technology. They estimate to check the reasonableness of answers and approximate answers by rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students order decimals and unit fractions and locate them on a number line. Students add and subtract fractions with the same denominator. They find unknown quantities in number sentences and continue patterns by adding or subtracting fractions and decimals.
Measurement and Geometry
Students use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24-hour time. Students use a grid reference system to locate landmarks. They estimate angles, and use protractors and digital technology to construct and measure angles. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry.
Statistics and Probability
Students pose questions to gather data and construct various displays appropriate for the data, with and without the use of digital technology. They compare and interpret different data sets. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities as a number from 0 to 1.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations
Fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units, and interpreting timetables
Problem Solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays, and finding the size of unknown angles
Reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another, explaining why the actual results of chanceexperiments may differ from expected results
Number and Algebra
Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. They solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts. Students locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology. They make connections between the powers of 10 and the multiplication and division of decimals. Students add, subtract and multiply decimals...
Number and Algebra
Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. They solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts. Students locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology. They make connections between the powers of 10 and the multiplication and division of decimals. Students add, subtract and multiply decimals and divide decimals where the result is rational. Students write number sentences using brackets and order of operations, and specify rules used to generate sequences involving whole numbers, fractions and decimals. They 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.
Measurement and Geometry
Students relate decimals to the metric system and choose appropriate units of measurement to perform a calculation. They solve problems involving length and area, and make connections between capacity and volume. Students interpret a variety of everyday timetables. They solve problems using the properties of angles and investigate simple combinations of transformations in the plane, with and without the use of digital technology. Students construct simple prisms and pyramids.
Statistics and Probability
Students interpret and compare a variety of data displays, including displays for two categorical variables. They analyse and evaluate data from secondary sources. Students compare observed and expected frequencies of events, including those where outcomes of trials are generated with the use of digital technology. They specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes describing patterns in uses of indices with whole numbers, recognising equivalences between fractions, decimals, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions
Fluency includes calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms
Problem Solving includes formulating and solving authentic problems using numbers and measurements,working with transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments
Reasoning includes applying the number laws to calculations, applying known geometric facts to draw conclusions about shapes, applying an understanding of ratio and interpreting data displays
Number and Algebra
Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all four operations with fractions, decimals, percentages and their equivalences, and express fractions in their simplest form. Students compare the cost of items to make financial decisions, with and without the use of digital technology. They make simple estimates to judge the reasonableness of results. Students use variables to represent arbitrary numbers and connect the laws and properties of number to algebra and substitute numbers into algebraic expressions. They assign ordered pairs to given points on the Cartesian plane...
Number and Algebra
Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all four operations with fractions, decimals, percentages and their equivalences, and express fractions in their simplest form. Students compare the cost of items to make financial decisions, with and without the use of digital technology. They make simple estimates to judge the reasonableness of results. Students use variables to represent arbitrary numbers and connect the laws and properties of number to algebra and substitute numbers into algebraic expressions. They assign ordered pairs to given points on the Cartesian plane and interpret and analyse graphs of relations from real data. Students develop simple linear models for situations, make predictions based on these models, solve related equations and check their solutions.
Measurement and Geometry
Students use formulas for the area and perimeter of rectangles. They classify triangles and quadrilaterals and represent transformations of these shapes on the Cartesian plane, with and without the use of digital technology. Students name the types of angles formed by a transversal crossing parallel lines and solve simple numerical problems involving these lines and angles. They describe different views of three-dimensional objects, and use models, sketches and digital technology to represent these views. Students calculate volumes of rectangular prisms.
Statistics and Probability
Students identify issues involving the collection of discrete and continuous data from primary and secondary sources. They construct stem-and-leaf plots and dot-plots. Students identify or calculate mean, mode, median and range for data sets, using digital technology for larger data sets. They describe the relationship between the median and mean in data displays. Students determine the sample space for simple experiments with equally likely outcomes, and assign probabilities outcomes.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations their graphs, explaining the purpose of statistical measures, and explaining measurements of perimeter and area
Fluency includes calculating accurately with simple decimals, indices and integers, recognising equivalence of common decimals and fractions including recurring decimals, factorising and simplifying basic algebraic expressions, and evaluating perimeters, areas of common shapes and their volumes and three dimensional objects
Problem Solving includes formulating, and modelling practical situations involving ratios, profit and loss, areas and perimeters of common shapes, and using two-way tables and Venn diagrams to calculate probabilities
Reasoning includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations
Number and Algebra
Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions. Students solve linear equations and graph linear relationships on the Cartesian plane.
Measurement and Geometry
Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the...
Number and Algebra
Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions. Students solve linear equations and graph linear relationships on the Cartesian plane.
Measurement and Geometry
Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms. They make sense of time duration in real applications, including the use of 24-hour time. Students identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. They use tools, including digital technology, to construct congruent shapes.
Statistics and Probability
Students explain issues related to the collection of sample data and discuss the effect of outliers on means and medians of the data. They use various approaches, including the use of digital technology, to generate simple random samples from a population. Students model situations with Venn diagrams and two-way tables and explain the use of 'not', 'and' and 'or'. Students choose appropriate language to describe events and experiments. They determine complementary events and calculate the sum of probabilities.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes describing the relationship between graphs and equations, simplifying a range of algebraic expressions, explaining the use of relative frequencies to estimate probabilities, and the use of the trigonometric ratios for right-angle triangles
Fluency includes applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments and developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms
Problem Solving includes formulating, and modelling practical situations involving surface areas and volumes of right prisms, applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry, and collecting data from secondary sources to investigate an issue
Reasoning includes following mathematical arguments, evaluating media reports and using statistical knowledge to clarify situations, developing strategies in investigating similarity and sketching linear graphs
Number and Algebra
Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without...
Number and Algebra
Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without the use of digital technology.
Measurement and Geometry
Students solve measurement problems involving perimeter and area of composite shapes, surface area and volume of rectangular prisms and cylinders, with and without the use of digital technology. They relate three-dimensional objects to two-dimensional representations. Students explain similarity of triangles, interpret ratios and scale factors in similar figures, and apply Pythagoras's theorem and trigonometry to solve problems involving angles and lengths in right-angled triangles.
Statistics and Probability
Students compare techniques for collecting data from primary and secondary sources, and identify questions and issues involving different data types. They construct histograms and back-to-back stem-and-leaf plots with and without the use of digital technology. Students identify mean and median in skewed, symmetric and bi-modal displays and use these to describe and interpret the distribution of the data. They calculate relative frequencies to estimate probabilities. Students list outcomes for two-step experiments and assign probabilities for those outcomes and related events.
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry...
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics.
At this level:
Understanding includes applying the four operations to algebraic fractions, finding unknowns in formulas after substitution, making the connection between equations of relations and their graphs, comparing simple and compound interest in financial contexts and determining probabilities of two and three step experiments
Fluency includes factorising and expanding algebraic expressions, using a range of strategies to solve equations and using calculations to investigate ing the shape of data sets
Problem Solving includes calculating the surface area and volume of a diverse range of prisms to solve practical problems, finding unknown lengths and angles using applications of trigonometry, using algebraic and graphical techniques to find solutions to simultaneous equations and inequalities, and investigating independence of events
Reasoning includes formulating geometric proofs involving congruence and similarity, interpreting and evaluating media statements and interpreting and comparing data sets
Number and Algebra
Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students substitute into formulas, find unknown values, manipulate linear algebraic expressions, expand binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital technology. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them to model situations and solve practical problems.
Measurement and Geometry
Students solve and explain surface area and volume problems relating to composite...
Number and Algebra
Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students substitute into formulas, find unknown values, manipulate linear algebraic expressions, expand binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital technology. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them to model situations and solve practical problems.
Measurement and Geometry
Students solve and explain surface area and volume problems relating to composite solids. They use parallel and perpendicular lines, angle and triangle properties, similarity, trigonometry and congruence to solve practical problems and develop proofs involving lengths, angles and areas in plane shapes. They use digital technology to construct and manipulate geometric shapes and objects, and explore symmetry and pattern in two dimensions.
Statistics and Probability
Students compare univariate data sets by referring to summary statistics and the shape of their displays. They describe bivariate data where the independent variable is time and use scatter-plots generated by digital technology to investigate relationships between two continuous variables. Students evaluate the use of statistics in the media. They list outcomes for multi-step chance experiments involving independent and dependent events, and assign probabilities for these experiments.