# Mathematics in Years 3 to 6

## Year 3

In Semester One, students extended their understanding of whole numbers to tens of 1000s. They investigated number patterns when counting by 2s, 3s, 5s, and 10s and demonstrated fluency in mental computation of addition, subtraction and multiplication using place value and number properties. They were able to create and solve number story problems of the above operations using real life situations. In Measurement, students interpreted timetables and calendars relevant to school and community. They measured, ordered and compared objects using familiar metric units of length, mass and capacity. They have investigated time to the minute on both analogue and digital clocks. In Statistics and Probability, students continued to build the language of chance in every day situations by conducting chance experiments. Additionally, they collected data, organised and interpreted it into categories and created relevant displays.

By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays.

Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.

## Year 4

In Semester One, students had worked on a variety of mental strategies such as partitioning, rearranging and regrouping numbers for addition, subtraction, multiplication and division. They had investigated number sequences involving multiples of single digit numbers and strategies in solving word problems. Students learnt how to multiply up to 3 digit numbers by 2 digit numbers. In place value, students recognised that the place value system can be extended to tenths, hundredths and thousandths. In Measurement and Geometry, students learnt to use scaled instruments to measure and compare lengths, masses and capacities. They have also learnt to convert between units of time. Students also compared and described regular and irregular shapes and the properties of 2D and 3D shapes. In Statistics and Probabilities, students were able to interpret data from venn diagrams and graphs.

By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.

Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.

## Year 5

During Semester One, students had worked in areas of Number and Algebra, Measurement and Geometry, and Statistics and Probability. In Number and Algebra, students had used a variety of strategies to estimate results. They have been practicing mental strategies for addition, subtraction, multiplication and division. They have also been immersed in word problems and solving tasks that require the use of all four operations. In Measurement and Geometry, students have been using units of measurement for length, mass and volume. They were exposed to equivalence of measurements using decimal representations and learned how to convert between units by identifying the size of units. In Statistics and Probability, students used what they know about fractions, decimals and percentages.

By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets.

Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They 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 measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.

## Year 6

In Semester One, students had worked in areas of Number and Algebra, Measurement and Geometry, and Statistics and Probability. In Number and Algebra, students had used a variety of strategies to predict, find, and check results. They have been practising mental strategies for addition, subtraction, multiplication and division. Students can recognise the properties of prime, composite, square and triangular numbers. They can describe the use of integers in everyday contexts and can locate integers on a number line. Students can make connections between the powers of 10 and the multiplication and division of decimals. They can add, subtract and multiply decimals and divide decimals where the result is rational and write correct number sentences using brackets and order of operations. Students can locate an ordered pair in any one of the four quadrants on the Cartesian plane. In Measurement and Geometry, students have been using units of measurement for length, perimeter, mass, volume and capacity. They can connect decimal representations to the metric system and can choose appropriate units of measurement to perform a calculation. Students can make connections between capacity and volume and they can solve problems involving length and area. They can interpret timetables. In Statistics and Probability, students listed the probabilities of everyday events. They learned how to describe possible everyday events and ordered their chances of occurring. They constructed suitable data displays, with and without the use of digital technologies, from given or collected data. Students can also list and communicate probabilities using simple fractions, decimals and percentages.

By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate probabilities using simple fractions, decimals and percentages.