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 3

Year 3 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 connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry
  • fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions
  • problem-solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns
  • reasoning includes using generalising from number properties and results of calculations, comparing angles and creating and interpreting variations in the results of data collections and data displays.

Year 3 Content Descriptions

Number and place value

Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051 - Scootle )
  • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
  • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
Recognise, model, represent and order numbers to at least 10 000 (ACMNA052 - Scootle )
  • placing four-digit numbers on a number line using an appropriate scale
  • reproducing numbers in words using their numerical representations and vice versa
Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053 - Scootle )
  • recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens and 10 000 ones
  • justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations
Recognise and explain the connection between addition and subtraction (ACMNA054 - Scootle )
  • demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences
Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055 - Scootle )
  • recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers
  • combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 + 19 = 57 + 20 – 1)
Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056 - Scootle )
  • establishing multiplication facts using number sequences
Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057 - Scootle )
  • writing simple word problems in numerical form and vice versa
  • using a calculator to check the solution and reasonableness of the answer

Fractions and decimals

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058 - Scootle )
  • partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with their sizes
  • locating unit fractions on a number line
  • recognising that in English the term ‘one third’ is used (order: numerator, denominator) but that in other languages this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator) for example Japanese
    • Asia and Australia’s Engagement with Asia

Money and financial mathematics

Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059 - Scootle )
  • recognising the relationship between dollars and cents, and that not all countries use these denominations and divisions (for example Japanese Yen)
    • Asia and Australia’s Engagement with Asia

Patterns and algebra

Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060 - Scootle )
  • identifying and writing the rules for number patterns
  • describing a rule for a number pattern, then creating the pattern

Using units of measurement

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061 - Scootle )
  • recognising the importance of using common units of measurement
  • recognising and using centimetres and metres, grams and kilograms, and millilitres and litres
Tell time to the minute and investigate the relationship between units of time (ACMMG062 - Scootle )
  • recognising there are 60 minutes in an hour and 60 seconds in a minute

Shape

Make models of three-dimensional objects and describe key features (ACMMG063 - Scootle )
  • exploring the creation of three-dimensional objects using origami, including prisms and pyramids
    • Asia and Australia’s Engagement with Asia

Location and transformation

Create and interpret simple grid maps to show position and pathways (ACMMG065 - Scootle )
  • creating a map of the classroom or playground
Identify symmetry in the environment (ACMMG066 - Scootle )
  • identifying symmetry in Aboriginal rock carvings or art
  • identifying symmetry in the natural and built environment

Geometric reasoning

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064 - Scootle )
  • opening doors partially and fully and comparing the size of the angles created
  • recognising that analogue clocks use the turning of arms to indicate time, and comparing the size of angles between the arms for familiar times

Chance

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067 - Scootle )
  • conducting repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials

Data representation and interpretation

Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068 - Scootle )
  • refining questions and planning investigations that involve collecting data, and carrying out the investigation (for example narrowing the focus of a question such as ‘which is the most popular breakfast cereal?’ to ‘which is the most popular breakfast cereal among Year 3 students in our class?’)
Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069 - Scootle )
  • exploring meaningful and increasingly efficient ways to record data, and representing and reporting the results of investigations
  • collecting data to investigate features in the natural environment
Interpret and compare data displays (ACMSP070 - Scootle )
  • comparing various student-generated data representations and describing their similarities and differences

Year 3 Achievement Standards

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 conduct simple data investigations for categorical variables.


Year 3 Work Sample Portfolios