– P–6 Pre-primary Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Number and algebra Number and place value Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point 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 Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences Investigate the conditions required for a number to be odd or even and identify odd and even numbers Investigate and use the properties of odd and even numbers Identify and describe factors and multiples of whole numbers and use them to solve problems Identify and describe properties of prime, composite, square and triangular numbers Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line Recognise, model, represent and order numbers to at least 1000 Recognise, model, represent and order numbers to at least 10 000 Recognise, represent and order numbers to at least tens of thousands Use estimation and rounding to check the reasonableness of answers to calculations Subitise small collections of objects Count collections to 100 by partitioning numbers using place value Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems Compare, order and make correspondences between collections, initially to 20, and explain reasoning Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts Explore the connection between addition and subtraction Recognise and explain the connection between addition and subtraction Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 Investigate everyday situations that use integers. Locate and represent these numbers on a number line – P–6 Pre-primary Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Number and place value Represent practical situations to model addition and sharing Solve simple addition and subtraction problems using a range of efficient mental and written strategies Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation Recognise and represent multiplication as repeated addition, groups and arrays Recall multiplication facts of two, three, five and ten and related division facts Recall multiplication facts up to 10 × 10 and related division facts Recognise and represent division as grouping into equal sets and solve simple problems using these representations Solve problems involving division by a one digit number, including those that result in a remainder Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder Use efficient mental and written strategies and apply appropriate digital technologies to solve problems Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers Fractions and decimals Recognise and describe one-half as one of two equal parts of a whole Recognise and interpret common uses of halves, quarters and eighths of shapes and collections Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole Investigate equivalent fractions used in contexts Compare and order common unit fractions and locate and represent them on a number line Compare fractions with related denominators and locate and represent them on a number line – P–6 Pre-primary Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Pre-primary Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Money and financial mathematics Recognise, describe and order Australian coins according to their value Count and order small collections of Australian coins and notes according to their value Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies Create simple financial plans Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies Patterns and algebra Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings Investigate and describe number patterns formed by skip-counting and patterns with objects Describe patterns with numbers and identify missing elements Describe, continue, and create number patterns resulting from performing addition or subtraction Explore and describe number patterns resulting from performing multiplication Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence Solve problems by using number sentences for addition or subtraction Solve word problems by using number sentences involving multiplication or division where there is no remainder Explore the use of brackets and order of operations to write number sentences Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division Linear and non-linear relationships This sequence starts at Year 7 – P–6 Pre-primary Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Measurement and geometry Using units of measurement Use direct and indirect comparisons to decide which is longer, heavier or holds more, and Measure and compare the lengths and capacities of pairs of objects using uniform informal units Compare and order several shapes and objects based on length, area, volume and Measure, order and compare objects using familiar metric units of length, mass and Use scaled instruments to measure and compare lengths, masses, capacities and Choose appropriate units of measurement for length, area, volume, capacity and mass Connect decimal representations to the metric system
common shapes, with and without the use of digital technologies Location and transformation Describe position and movement Give and follow directions to familiar locations Interpret simple maps of familiar locations and identify the relative positions of key features Create and interpret simple grid maps to show position and pathways Use simple scales, legends and directions to interpret information contained in basic maps Use a grid reference system to describe locations. Describe routes using landmarks and directional language Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies Investigate the effect of one-step slides and flips with and without digital technologies Identify and describe half and quarter turns Identify symmetry in the environment Create symmetrical patterns, pictures and shapes with and without digital technologies Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries Introduce the Cartesian coordinate system using all four quadrants Apply the enlargement transformation to familiar two-dimensional shapes and explore the properties of the resulting image compared with the original Geometric reasoning This sequence starts at Year 3 Identify angles as measures of turn and compare angle sizes in everyday situations Compare angles and classify them as equal to, greater than, or less than, a right angle Estimate, measure and compare angles using degrees. Construct angles using a protractor 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 – P–6 Pre-primary Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Pythagoras and trigonometry This sequence starts at Year 9 Statistics and probability Chance Identify outcomes of familiar events involving chance and describe them using everyday Identify practical activities and everyday events that involve chance. Describe Conduct chance experiments, identify and describe possible outcomes and recognise Describe possible everyday events and order their chances of occurring List outcomes of chance experiments involving equally likely outcomes and represent Describe probabilities using fractions, decimals and percentages
language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ variation in results probabilities of those outcomes using fractions Identify everyday events where one cannot happen if the other happens Recognise that probabilities range from 0 to 1 Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies Identify events where the chance of one will not be affected by the occurrence of the other Compare observed frequencies across experiments with expected frequencies Data representation and interpretation Answer yes/no questions to collect information and make simple inferences Choose simple questions and gather responses and make simple inferences Identify a question of interest based on one categorical variable. Gather data relevant to the question Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording Select and trial methods for data collection, including survey questions and recording sheets Pose questions and collect categorical or numerical data by observation or survey Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays Collect, check and classify data 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 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 Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies Interpret secondary data presented in digital media and elsewhere – P–6 Pre-primary Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Data representation and interpretation Create displays of data using lists, table and picture graphs and interpret them Interpret and compare data displays Evaluate the effectiveness of different displays in illustrating data features including variability Describe and interpret different data sets in context
factorise monic quadratic expressions using a variety of strategies – 7–10 Year 7 Year 8 Year 9 Year 10 Year 10A Patterns and algebra Substitute values into formulas to determine an unknown Linear and non-linear relationships Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point Plot linear relationships on the Cartesian plane with and without the use of digital technologies Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software Solve problems involving linear equations, including those derived from formulas Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations Solve simple linear equations Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software Solve linear inequalities and graph their solutions on a number line Solve simple exponential equations Investigate, interpret and analyse graphs from authentic data Sketch linear graphs using the coordinates of two points and solve linear equations Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations Solve problems involving parallel and perpendicular lines Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate Solve linear equations involving simple algebraic fractions Solve simple quadratic equations using a range of strategies