Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

understanding that some numbers have special properties and that these properties can be used to solve problems

representing composite numbers as a product of their prime factors and using this form to simplify calculations by cancelling common primes

understanding that if a number is divisible by a composite number then it is also divisible by the prime factors of that number (for example 216 is divisible by 8 because the number represented by the last three digits is divisible by 8, and hence 216 is also divisible by 2 and 4)

Literacy , Numeracy

Number and Algebra

Number and place value (F-8)

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

applying strategies already developed for solving problems involving small numbers to those involving large numbers

applying a range of strategies to solve realistic problems and commenting on the efficiency of different strategies

Critical and creative thinking , ICT, Literacy , Numeracy

Number and Algebra

Number and place value (F-8)

Investigate everyday situations that use positive and negative whole numbers and zero. Locate and represent these numbers on a number line (ACMNA124)

understanding that whole numbers can be positive and negative and continue indefinitely in both directions

investigating everyday situations that use positive and negative integers, such as temperatures, to understand how the positive numbers (whole numbers, fractions, decimals and percentages) can be extended to include negative numbers

using number lines to position and order positive and negative integers around zero

solving everyday additive problems involving positive and negative integers without developing formal rules for the operations (for example using a number line and counting to find the resulting outside temperature if it is 5°C at 7pm and drops by 8°C overnight)

Critical and creative thinking , Literacy , Numeracy

Number and Algebra

Fractions and Decimals (1-6)

Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

demonstrating equivalence between fractions using drawings and models

Critical and creative thinking , Literacy

Number and Algebra

Fractions and Decimals (1-6)

Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)

understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions

solving realistic additive (addition and subtraction) problems involving fractions to develop understanding of equivalent fractions and the use of fractions as operators

modelling and solving additive problems involving fractions by using methods such as jumps on a number line, or by making diagrams of fractions as parts of shapes

Critical and creative thinking , Literacy , Numeracy

Number and Algebra

Fractions and Decimals (1-6)

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

Critical and creative thinking , ICT, Literacy , Numeracy

Number and Algebra

Fractions and Decimals (1-6)

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

extending whole-number strategies to explore and develop meaningful written strategies for addition and subtraction of decimal numbers to thousandths

exploring and practising efficient methods for solving problems requiring operations on decimals, to gain fluency with calculating with decimals and with recognising appropriate operations

Critical and creative thinking , ICT, Numeracy

Number and Algebra

Fractions and Decimals (1-6)

Multiply decimals by whole numbers and perform divisions that result in terminating decimals, with and without digital technologies (ACMNA129)

interpreting and representing the remainder in division calculations, including non-integral remainders, appropriate to the context (for example understanding that the result of 6.5 ÷ 4 is sensibly expressed as 1.625km if the context involves dividing a 6.5km running course into four equal legs; $1.63 if it represents the price of one item where four sell for $6.50)

Critical and creative thinking , ICT, Numeracy

Number and Algebra

Fractions and Decimals (1-6)

Multiply and divide decimals by powers of 10 (ACMNA130)

understanding and using the fact that equivalent division calculations result if both numbers are multiplied or divided by the same amount (for example 34.87 ÷ 7 is equivalent to 3487 ÷ 700)

using and explaining the use of multiplication and division by powers of 10 to multiply decimal numbers mentally (for example 1.4 × 0.6 can be calculated by multiplying 14 by 6 and dividing the result by 100)

Numeracy

Number and Algebra

Fractions and Decimals (1-6)

Make connections between equivalent fractions, decimals and percentages (ACMNA131)

connecting fractions, decimals and percentages as different representations of the same number, moving fluently between representations and choosing the appropriate one for the problem being solved

Critical and creative thinking , Numeracy

Number and Algebra

Money and financial Maths (1-10)

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

using authentic information to calculate prices on sale goods

Critical and creative thinking , ICT, Literacy , Numeracy

Number and Algebra

Patterns and algebra (F-10)

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)

identifying and generalising number patterns as the beginning of algebraic thinking

investigating additive and multiplicative patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern, looking for patterns in the way the numbers increase/decrease

Critical and creative thinking , Literacy , Numeracy

Number and Algebra

Patterns and algebra (F-10)

Explore the use of brackets and order of operations to write number sentences (ACMNA134)

appreciating the need for rules to complete multiple operations within the same number sentence

Literacy , Numeracy

Measurement and Geometry

Using units of measurement (F-10)

Connect decimal representations to the metric system (ACMMG135)

recognising the equivalence of measurements such as 1.25 metres and 125 centimetres

Literacy , Numeracy

Measurement and Geometry

Using units of measurement (F-10)

Convert between common metric units of length, mass and capacity (ACMMG136)

identifying and using the correct operations when converting units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres

recognising the significance of the prefixes in units of measurement

Numeracy

Measurement and Geometry

Using units of measurement (F-10)

Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137)

recognising and investigating familiar objects using concrete materials and digital technologies

Critical and creative thinking , Literacy , Numeracy

Measurement and Geometry

Using units of measurement (F-10)

Connect volume and capacity and their units of measurement (ACMMG138)

recognising that 1ml is equivalent to 1cm3

Critical and creative thinking , Numeracy

Measurement and Geometry

Using units of measurement (F-10)

Interpret and use timetables (ACMMG139)

planning a trip involving one or more modes of public transport

Literacy , Numeracy

Measurement and Geometry

Shape (F-7)

Construct simple prisms and pyramids (ACMMG140)

considering the history and significance of pyramids from a range of cultural perspectives including those structures found in China, Korea and Indonesia

constructing prisms and pyramids from nets, and skeletal models

Critical and creative thinking

Asia and Australia’s engagement with Asia

Measurement and Geometry

Location and transformation (F-7)

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)

understanding that translations, rotations and reflections can change the position and orientation of shapes and objects but not their geometric features or size

visualising, demonstrating and describing the effects of transformations, such as using computer technology to visualise, test and record the movement of two-dimensional shapes, or designing a school or brand logo using transformation of one or more shapes

Critical and creative thinking , ICT, Literacy , Numeracy

Measurement and Geometry

Location and transformation (F-7)

Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

understanding that the Cartesian plane provides a graphical or visual way of describing location, and can be used to represent relationships

Critical and creative thinking , Numeracy

Measurement and Geometry

Geometric reasoning (3-10)

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 (ACMMG141)

building on students' understanding of turn and rotation in mapping and rotational symmetry to measure, estimate and compare angles in degrees and classify angles according to their sizes

investigating the use of rotation and symmetry in the diagrammatic representations of kinship relationships of Central and Western Desert people

estimating, measuring and comparing angles, for example, by recognising the magnitude of angles including 30°, 45°, 90°, 180° and 270° to make reasonable estimates of angles up to a complete turn of 360°, or using a protractor to measure angles to the nearest degree

identifying that angles have arms and a vertex, and that size is the amount of turn required for one arm to coincide with the other; the size is measured in degrees with a protractor using the two alternate conventions for naming angles

identifying that the size of a right angle is 90° and defining acute, obtuse and reflex angles and rotation by relating them to right angles

Critical and creative thinking , ICT, Literacy , Numeracy

Aboriginal Torres Straight Is history and culture

Statistics and Probability

Chance (1-10)

Describe probabilities using fractions, decimals and percentages (ACMSP144)

investigating games of chance popular in different cultures and evaluating the relative benefits to the organisers and participants (for example Pachinko)

Literacy , Numeracy

Asia and Australia’s engagement with Asia

Statistics and Probability

Chance (1-10)

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

conducting repeated trials of chance experiments, identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials

Critical and creative thinking , ICT, Numeracy

Statistics and Probability

Chance (1-10)

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

predicting likely outcomes from a run of chance events and distinguishing these from surprising results

Critical and creative thinking , Numeracy

Statistics and Probability

Data representation / interpretation (F-10)

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

understanding that data can be represented in different ways, sometimes with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgments

exploring ways of presenting data and showing the results of investigations, including creating dot plots with many-to-one correspondence between data and symbols

comparing different student-generated diagrams, tables and graphs, and describing their similarities and differences and commenting on the usefulness of each representation for interpreting the data

Critical and creative thinking , Literacy , Numeracy

Statistics and Probability

Data representation / interpretation (F-10)

Interpret secondary data presented in digital media and elsewhere (ACMSP148)

developing an understanding of sampling and the ability to interpret secondary data in order to critique data-based claims made in the media, advertising and elsewhere

investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey

understanding the various influences on data collection and display, including who created the representation, who funded the data collection and whether the representation is part of an advertisement; in order to be alert to possible biases in data representations

identifying potentially misleading data representations in the media, such as graphs with ‘broken’ axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made, and pie charts in which the whole pie does not represent the entire population about which the claims are made

considering the need for sampling and recognising when a census of an entire population is not possible or not necessary, and identifying examples of sampling in the media

Critical and creative thinking , Literacy , Numeracy

## YEAR 6 MATHS

MATHEMATICS STRANDSMATH SUB-STRANDSELEMENTELABORATIONGENERAL CAPABILITIESCROSS-CURRICULA PRIORITIES