Additive Relations

Use the principle of equality

Recognise equal differences and record them in number sentences

Use the equals sign to mean 'the same as', rather than to perform an operation

Apply the associative property of addition to forming multiples of 10

Recognise and explain the connection between addition and subtraction

Use number relation principles to solve related problems

Demonstrate how addition and subtraction are inverse operations

Use the complement principle of addition and subtraction

Explain and check solutions to problems, including by using the inverse operation

Select strategies flexibly to solve addition and subtraction problems of up to 3 digits

Apply known mental strategies that use partitioning to add and subtract, such as bridging the decades

Use the compensation strategy to add and subtract

Apply the levelling and constant difference strategies

Represent solutions to addition and subtraction problems, including word problems, using an empty number line or bar model

Compare and evaluate strategies used to solve addition and subtraction problems, reasoning which strategy may be most efficient

Represent money values in multiple ways

Recognise the relationship between dollars and cents

Represent equivalent amounts of money using different denominations

Perform calculations with money, including finding change

Multiplicative Relations

Generate and describe patterns

Model, describe and record patterns of multiples

Create and continue a variety of number patterns that increase or decrease by a constant amount

Recognise the significance of the final digit of a whole number in determining whether a given number is even or odd

Recognise the connection between even numbers and the multiplication facts for 2

Investigate the result of multiplying by one and zero

Use arrays to establish multiplication facts from multiples of 2 and 4, 5 and 10

Create and represent multiplicative structure, using the term multiples when connecting grouping to arrays

Use the array structure to coordinate the number of groups with the number in each group

Record the first 10 multiples formed by counting by twos, fours, fives and tens

Relate doubling to multiplication facts for multiples of 2

Recognise that doubling is multiplying by 2 and halving is dividing by 2

Recognise the relationship between one multiple and its double

Model square numbers and record in numerical and diagrammatic form

Recall multiplication facts of 2 and 4, 5 and 10 and related division facts

Recognise and use the symbols for multiplied by, divided by and equals

Link multiplication and division fact families using arrays

Generate multiplication fact families for multiples of 2 and 4, 5 and 10

Model and apply the commutative property of multiplication

Represent and solve problems involving multiplication fact families

Describe multiplication problems using for each and times as many

Find the total of partially covered arrays

Apply the inverse relationship of multiplication and division

Partitioned Fractions

Create fractional parts of a length using techniques other than repeated halving

Make thirds of a length

Create fifths of a length

Model and represent unit fractions, and their multiples, to a complete whole on a number line

Model fractions with fraction strips and diagrams for halves, quarters, eighths, thirds

Describe fraction families formed by dividing the whole into the same total number of equal parts as having the same denominator

Determine the complementary fractional part needed to complete one whole (halves, quarters, eighths, thirds)

Recreate the whole unit from a fractional part (halves, quarters, eighths, thirds)

Geometric Measure

Position: Interpret movement on a map

Orient a map to determine directions to travel

Use given directions to follow routes on land and Aboriginal maps without a grid reference system

Describe a route taken on a map using landmarks and directional language

Position: Locate positions on grid maps

Locate positions by coordinating horizontal and vertical references

Use the array (row and column) structure of grid maps to locate position, horizontal before vertical

Length: Measure and compare objects using metres, centimetres and millimetres

Measure and record lengths and distances using a combination of metres and centimetres

Estimate lengths and distances using known lengths as benchmarks, in metres and centimetres and check by measuring

Compare and order lengths and distances using metres and centimetres

Recognise the need for a formal unit smaller than the centimetre to measure length

Identify that there are 10 millimetres in one centimetre

Use the millimetre as a unit to measure lengths with a ruler

Record lengths using the abbreviation for millimetres (mm)

Angles: Identify angles as measures of turn

Identify angles with 2 arms in practical situations

Identify the arms and vertex of an angle

Recognise an angle as the amount of turning between 2 arms

Compare angles and explain that the length of the arms does not affect the size of the angle

Use the term right angle to describe a quarter-turn in a range of orientations

Two-dimensional spatial structure

2D shapes: Compare and describe features of two-dimensional shapes

Describe and compare two-dimensional shapes, including parallelograms, rectangles, rhombuses, squares, trapeziums and kites

Identify and describe polygons that have parallel sides and those that do not

Identify quadrilaterals that have all sides equal in length

Identify right angles in shapes

Group quadrilaterals using one or more attributes

2D shapes: Transform shapes by reflecting, translating and rotating

Identify lines of symmetry in pictures, artefacts, designs and the environment

Draw lines of symmetry on given shapes and identify quadrilaterals that do not have lines of symmetry

Create and record tessellating designs by reflecting, translating and rotating triangles

Apply and describe amounts of rotation including half-turns, quarter-turns and three-quarter-turns when creating designs

Area: Use square centimetres to measure and estimate the areas of rectangles

Create the array structure of area using squares (1 cm × 1 cm) in rows and columns

Recognise that area can be measured in square centimetres

Discuss strategies to estimate area in square centimetres

Explain how the grid structure of rows and columns helps to find the area

Estimate and measure the areas of squares and rectangles (within the range of 100 square centimetres)

Record area in square centimetres using numerals and words

Use efficient strategies for counting large numbers of square centimetres

Area: Use square metres to measure and estimate the areas of rectangles

Recognise the need for a formal unit larger than the square centimetre to measure area

Construct a square metre and use it to measure the areas of large squares and rectangles

Recognise that an area of one square metre need not be a square

Record areas in square metres using numerals and words

Estimate the areas of squares and rectangles in square metres

Three-dimensional spatial structure

3D objects: Make models of three-dimensional objects to compare and describe key features

Identify the differences between prisms (including cubes), pyramids and cylinders

Construct models of prisms, pyramids and cylinders using physical or virtual manipulatives, identifying their features

Deconstruct everyday packages that are prisms (including cubes) to create nets

Investigate the variety of nets that can be used to create a particular prism

Volume: Measure and order containers using litres

Recognise the need for formal units to measure capacity (internal volume) accurately

Use the litre as a unit to measure capacities (internal volumes) to the nearest litre

Relate the litre to familiar everyday containers

Recognise that one-litre containers can be a variety of shapes

Record capacities (internal volumes) using the abbreviation for litres (L)

Estimate the capacity (internal volume) of a container in litres and check by measuring

Volume: Compare objects using familiar metric units of volume

Construct rectangular prisms using cubic-centimetre blocks and describe the volumes in terms of layers

Record volumes using numerals and words

Compare the volumes of 2 or more objects made from cubic-centimetre blocks

Non-spatial Measure

Mass: Compare objects using the kilogram

Recognise the need for a formal unit to measure mass

Identify familiar objects that have a mass of about one kilogram

Record masses using the abbreviation for kilograms (kg)

Find objects that have an estimated mass of more than, less than and about the same as one kilogram and check by comparing to a 1 kg mass

Time: Represent and read analog time

Use minutes to describe the duration of events

Identify 30 minutes as being a half-hour and 60 minutes as an hour

Connect the quarter-hour to 15 minutes

Recognise that the position of the numerals on an analog timepiece often represents 2 different values

Recognise that 5-minute intervals (corresponding to the hour markers) are used as benchmarks to read time on an analog clock

Read time as past the hour to half-past and then towards the hour

Read analog clocks to the minute

Data

Collect discrete data

Pose questions about a matter of interest to obtain information that can be recorded in categories

Collect data from identified sources

Predict and create a list of categories for efficient data collection in relation to a matter of interest

Organise and display data using tables and graphs

Create a list or table to organise the data

Construct column graphs (with scale intervals of 1) and dot plots using relevant software where appropriate

Mark equal spaces (intervals) on axes, name and label axes and choose appropriate titles for column graphs

Interpret and compare data

Describe and interpret information presented in tally tables and column graphs

Investigate how data is interpreted to make decisions

Represent the same dataset using more than one type of display and compare the displays

Chance

Identify possible outcomes from chance experiments

Use the term outcome to describe any possible result of a chance experiment

Record all possible outcomes in a chance experiment where the outcomes are equally likely

Record all possible combinations in a chance situation where the outcomes are equally likely

Predict the number of times each outcome might occur in a chance experiment involving a set number of trials

Conduct experiments and compare the predicted and actual results where the outcomes are equally likely