Additive Relations

Choose and use efficient strategies to solve addition and subtraction problems

Solve multistep word problems, including problems that require more than one operation

Compare, evaluate and communicate strategies used to solve addition and subtraction problems

Applies known strategies to add and subtract decimals

Model the addition and subtraction of decimals up to 3 decimal places using appropriate representations

Solve word problems involving the addition and subtraction of decimals up to 3 decimal places

Justify why the strategy used to solve addition and subtraction word problems is appropriate.

Multiplicative Relations

Select and apply strategies to solve problems involving multiplication and division with whole numbers

Select and use efficient strategies to multiply whole numbers of up to 4 digits by one- and 2-digit numbers

Solve word problems involving rates using multiplication and division

Determine why different division questions have the same answer

Multiply and divide decimals by powers of 10

Use mental strategies to multiply benchmark decimals by single-digit numbers

Compare the relative place value of digits to multiply and divide a decimal by powers of 10

Estimate the product of a decimal and a whole number to determine the magnitude of a calculator answer

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

Complete number sentences that involve more than one operation by calculating missing numbers

Identify and use inverse operations to assist with the solution of number sentences

Recognise that division can be recorded using fractions

Represent and describe number patterns formed by multiples

Use a given geometric pattern involving multiples to create a table of values

Describe a pattern formed by multiples in words, in terms of multiplication rather than addition

Determine a rule describing the relationship between the bottom number and the top number in a table

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

Recognise the need to agree on the order in which to perform operations

Use grouping symbols () in number sentences to indicate operations that must be performed first

Investigate the order of operations using real-life contexts

Solve problems involving grouping symbols

Representing Quantity Fractions

Recognise that a fraction can represent a division

Identify how the relationship between the number being divided and the divisor is represented in a fraction

Compare common fractions with related denominators

Order common fractions with related denominators using diagrams and number lines

Subdivide the area of a rectangle by both length and width to represent the multiplicative relationship between common fractions

Compare and represent fractions with denominators of 2, 4 and 8; 3 and 6; 5 and 10 of a whole shape (area model) and a collection of objects (discrete model)

Create equivalent fractions for half in quarters, eighths, sixths and tenths by re-dividing the whole, using diagrams and number lines

Record equivalent fractions using diagrams, words and fraction notation

Build up to the whole from a given fractional part

Generate the whole quantity from non-unit fractional parts such as quarters, eighths, thirds, sixths, fifths and tenths

Use equivalence to add and subtract fractional quantities

Solve word problems involving adding or subtracting fractional quantities with related denominators

Represent fractional quantities with the same or related denominators to add and subtract fractions

Find fractional quantities of whole numbers (halves, quarters, fifths and tenths)

Calculate quarters and fifths of whole numbers that are multiples of the denominator, using a tape diagram

Solve word problems involving a fraction of a quantity

Find 1/2, 1/4, 1/5 and 1/10 of collections, expressing remainders as decimals

Geometric Measure

Position: Use the 4 quadrants of the coordinate plane

Plot and label points, given coordinates, in all 4 quadrants of the number plane

Identify and record the coordinates of given points on the number plane in all 4 quadrants

Describe changes to coordinates when a point is translated or reflected across an axis

Length: Connect decimal representations to the metric system

Recognise the equivalence of whole-number and decimal representations of measurements of length

Interpret decimal notation for lengths and distances

Record lengths and distances using decimal notation

Length: Convert between common metric units of length

Use decimal place value system to convert between metres and kilometres

Convert measurements to the same unit to compare lengths and distances

Explain and use the relationship between the size of a unit and the number of units needed

Length: Solve problems involving the comparison of lengths using appropriate units

Investigate and compare perimeters of rectangles with the same area

Determine the number of different rectangles that can be formed using whole-number dimensions for a given area

Solve a variety of problems involving length and perimeter, including problems involving different units of length

Angles: Investigate angles on a straight line and angles at a point

Recognise right angles, angles on a straight line and angles at a point embedded in diagrams

Identify the vertex and arms of angles formed by intersecting lines

Angles: Investigate the relationships formed by the intersection of straight lines

Identify angle types formed by the intersection of straight lines, including right angles (90°), angles on a straight line (add to 180°) and angles at a point that form an angle of revolution (add to 360°)

Recognise that perpendicular lines intersect at right angles (90°)

Investigate adjacent angles that form a right angle and establish that they add to 90°

Investigate adjacent angles on a straight line and establish that they add to 180°

Investigate angles at a point and establish that they form an angle of revolution and add to 360°

Two-dimensional spatial structure

2D shapes: Dissect two-dimensional shapes and rearrange them using translations, reflections and rotations

Use the terms translate, reflect and rotate to describe transformations of two-dimensional shapes

Dissect and rearrange one shape to make another

Recognise that translations, reflections or rotations change the position and orientation but not the size of shapes

Area: Find the area of composite figures

Find different ways to calculate the area of a composite L-shape figure

Area: Calculate the area of a parallelogram using subdivision and rearrangement

Show how to transform a parallelogram into a rectangle to find its area

Record, using words, a method for finding the area of any parallelogram

Area: Determine the area of a triangle

Investigate the area of a triangle by comparing it to the area of a parallelogram with the same base length and height

Establish the relationship between the area of a triangle and the area of a parallelogram formed by duplicating and rotating the triangle

Record, using words, a method for finding the area of any triangle

Three-dimensional spatial structure

3D objects: Construct prisms and pyramids

Create skeletal models of prisms and pyramids

Construct three-dimensional models of prisms and pyramids, given drawings of different views

Volume: Use cubic metres for measurement of volume

Recognise the need for a formal unit larger than the cubic centimetre

Construct and use the cubic metre as a unit to measure larger volumes

Estimate and measure volumes in cubic metres

Volume: Recognise the multiplicative structure for finding volume

Describe the length, width and height of a rectangular prism as the dimensions of the prism

Describe arrangements of cubic-centimetre blocks in terms of layers

Establish the relationship between the number of cubes in one layer and the number of layers to find the volume of a rectangular prism

Volume: Find the volumes of rectangular prisms in cubic centimetres and cubic metres

Construct rectangular prisms using cubic-centimetre blocks and determine the volumes

Explain that objects with the same volume may be different shapes

Record, using words, the method for finding the volumes of rectangular prisms

Recognise that rectangular prisms with the same volume may have different dimensions

Calculate volumes of rectangular prisms in cubic centimetres (cm3) and cubic metres (m3)

Non-spatial Measure

Mass: Convert between common metric units of mass

Convert between kilograms and grams and between kilograms and tonnes

Solve problems involving different units of mass

Time: Solve problems involving duration, using 12- and 24-hour time

Use start and finish times to calculate the elapsed time of events

Add and subtract time mentally using bridging strategies

Round answers to time calculations to the nearest minute or hour

Represent commonly used time intervals as decimals

Solve a variety of problems involving duration, including where times are expressed in 12-hour and 24-hour notation

Data

Interpret and compare a range of data displays

Interpret side-by-side column graphs for 2 categorical variables

Interpret data on a timeline using the given scale

Interpret and compare different displays in terms of the shape of the distribution, including the range and the most frequent value (mode)

Interpret data presented in digital media and elsewhere

Interpret data representations found in digital media and in factual texts

Identify sources of possible bias in representations of data in the media

Identify misleading representations of data in the media

Chance

Compare observed frequencies of outcomes with expected results

Use the term frequency to describe the number of times a particular outcome occurs in a chance experiment

Distinguish between the frequency of an outcome (the number of times it occurs) and the probability of an outcome in a chance experiment

Compare the expected frequencies of outcomes of chance experiments with observed frequencies, including where the outcomes are not equally likely

Discuss the fairness of simple games involving chance and the idea of randomness

Explain why observed frequencies of outcomes in chance experiments may differ from expected frequencies, and how this relates to randomness

Create random generators and describe probabilities using fractions

Create random generators to follow specified probabilities or proportions

Record the outcomes for chance experiments where the outcomes are not equally likely to occur and assign probabilities to the outcomes using fractions (denominators of 2, 3, 4, 5, 6, 8 and 10)

Use knowledge of benchmark fractions, decimals and percentages to assign probabilities to the likelihood of outcomes

Conduct chance experiments with both small and large numbers of trials

Assign expected probabilities to outcomes in chance experiments with random generators, including digital simulators, and compare the expected probabilities with the observed probabilities after both small and large numbers of trials

Determine and discuss the differences between the expected probabilities and the observed probabilities after both small and large numbers of trials

Determine the likely make up of a large collection of objects, by sampling objects and returning them to the collection before the next sample (sampling with replacement)