Mathematics

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Rationale

Learning mathematics creates opportunities for and enriches the lives of all Australians. The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in number and algebra, measurement and geometry, and statistics and probability.

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Aims

The Australian Curriculum: Mathematics aims to ensure that students:

are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens.

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Key ideas

In Mathematics, the key ideas are the proficiency strands of understanding, fluency, problem-solving and reasoning. The proficiency strands describe the actions in which students can engage when learning and using the content.

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Structure

The Australian Curriculum: Mathematics is organised around the interaction of three content strands and four proficiency strands.
The content strands are number and algebra, measurement and geometry, and statistics and probability. They describe what is to be taught and learnt.

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PDF documents

Resources and support materials for the Australian Curriculum: Mathematics are available as PDF documents. 
Mathematics: Sequence of content
Mathematics: Sequence of achievement

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Glossary

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Year 4

Year 4 Level Description

The proficiency strands understanding, fluency, problem-solving and reasoning are an integral part of mathematics content across the three content strands: number and algebra, measurement and geometry, and statistics and probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. The achievement standards reflect the content and encompass the proficiencies.

At this year level:

  • understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times and describing properties of symmetrical shapes
  • fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data
  • problem-solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns
  • reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.

Year 4 Content Descriptions

Number and place value

Investigate and use the properties of odd and even numbers (ACMNA071 - Scootle )
  • using the four operations with pairs of odd or even numbers or one odd and one even number, then using the relationships established to check the accuracy of calculations
Recognise, represent and order numbers to at least tens of thousands (ACMNA072 - Scootle )
  • reproducing five-digit numbers in words using their numerical representations, and vice versa
Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073 - Scootle )
  • recognising and demonstrating that the place-value pattern is built on the operations of multiplication or division of tens
Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074 - Scootle )
  • recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences
Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075 - Scootle )
  • using known multiplication facts to calculate related division facts
Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076 - Scootle )
  • using known facts and strategies, such as commutativity, doubling and halving for multiplication, and connecting division to multiplication when there is no remainder

Fractions and decimals

Investigate equivalent fractions used in contexts (ACMNA077 - Scootle )
  • exploring the relationship between families of fractions (halves, quarters and eighths or thirds and sixths) by folding a series of paper strips to construct a fraction wall
Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078 - Scootle )
  • converting mixed numbers to improper fractions and vice versa
  • investigating the use of fractions and sharing as a way of managing Country: for example taking no more than half the eggs from a nest to protect future bird populations
    • Aboriginal and Torres Strait Islander Histories and Cultures
    • Sustainability
Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079 - Scootle )
  • using division by 10 to extend the place-value system
  • using knowledge of fractions to establish equivalences between fractions and decimal notation

Money and financial mathematics

Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080 - Scootle )
  • recognising that not all countries use dollars and cents, eg India uses rupees.
    • Asia and Australia’s Engagement with Asia
  • carrying out calculations in another currency as well as in dollars and cents, and identifying both as decimal systems

Patterns and algebra

Explore and describe number patterns resulting from performing multiplication (ACMNA081 - Scootle )
  • identifying examples of number patterns in everyday life
Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082 - Scootle )
  • representing a word problem as a number sentence
  • writing a word problem using a given number sentence
Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction (ACMNA083 - Scootle )
  • writing number sentences to represent and answer questions such as: ‘When a number is added to 23 the answer is the same as 57 minus 19. What is the number?’
  • using partitioning to find unknown quantities in number sentences

Using units of measurement

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084 - Scootle )
  • reading and interpreting the graduated scales on a range of measuring instruments to the nearest graduation
Compare objects using familiar metric units of area and volume (ACMMG290 - Scootle )
  • comparing areas using grid paper
  • comparing volume using centicubes
  • recognising that metric units are not the only units used throughout the world, for example measuring the area of floor space using tatami mats (Japan), using squares for room and house area (Australia)
    • Asia and Australia’s Engagement with Asia
Convert between units of time (ACMMG085 - Scootle )
  • identifying and using the correct operation for converting units of time
Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086 - Scootle )
  • calculating the time spent at school during a normal school day
  • calculating the time required to travel between two locations
  • determining arrival time given departure time

Shape

Compare the areas of regular and irregular shapes by informal means (ACMMG087 - Scootle )
  • comparing areas using metric units, such as counting the number of square centimetres required to cover two areas by overlaying the areas with a grid of centimetre squares
Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088 - Scootle )
  • identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes
  • creating a two-dimensional shapes from verbal or written instructions

Location and transformation

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090 - Scootle )
  • identifying the scale used on maps of cities and rural areas in Australia and a city in Indonesia and describing the difference
    • Asia and Australia’s Engagement with Asia
  • using directions to find features on a map
Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091 - Scootle )
  • using stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and symmetry in Yolngu or Central and Western Desert art
    • Aboriginal and Torres Strait Islander Histories and Cultures
    • Asia and Australia’s Engagement with Asia

Geometric reasoning

Compare angles and classify them as equal to, greater than, or less than, a right angle (ACMMG089 - Scootle )
  • creating angles and comparing them to a right angle using digital technologies

Chance

Describe possible everyday events and order their chances of occurring (ACMSP092 - Scootle )
  • using lists of events familiar to students and ordering them from ‘least likely’ to ‘most likely’ to occur
Identify everyday events where one cannot happen if the other happens (ACMSP093 - Scootle )
  • using examples such as weather, which cannot be dry and wet at the same time
Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094 - Scootle )
  • explaining why the probability of a new baby being either a boy or a girl does not depend on the sex of the previous baby

Data representation and interpretation

Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095 - Scootle )
  • comparing the effectiveness of different methods of collecting data
  • choosing the most effective way to collect data for a given investigation
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 (ACMSP096 - Scootle )
  • exploring ways of presenting data and showing the results of investigations
  • investigating data displays using many-to-one correspondence
Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097 - Scootle )
  • interpreting data representations in the media and other forums in which symbols represent more than one data value
  • suggesting questions that can be answered by a given data display and using the display to answer questions

Year 4 Achievement Standards

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 and explain strategies for finding 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 4 Work Sample Portfolios