# 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.

### 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.

### 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.

### 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.

### PDF documents

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

## Year 1

### Year 1 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 names, numerals and quantities, and partitioning numbers in various ways
• fluency includes readily counting number in sequences forwards and backwards, locating numbers on a line and naming the days of the week
• problem-solving includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer
• reasoning includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data and explaining patterns that have been created.

### Year 1 Content Descriptions

#### Number and place value

Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012 - Scootle )
• using the popular Korean counting game (sam-yuk-gu) for skip counting
• developing fluency with forwards and backwards counting in meaningful contexts such as circle games
Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013 - Scootle )
• modelling numbers with a range of material and images
• identifying numbers that are represented on a number line and placing numbers on a prepared number line
Count collections to 100 by partitioning numbers using place value (ACMNA014 - Scootle )
• understanding partitioning of numbers and the importance of grouping in tens
• understanding two-digit numbers as comprised of tens and ones/units
Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015 - Scootle )
• developing a range of mental strategies for addition and subtraction problems

#### Fractions and decimals

Recognise and describe one-half as one of two equal parts of a whole. (ACMNA016 - Scootle )
• sharing a collection of readily available materials into two equal portions
• splitting an object into two equal pieces and describing how the pieces are equal

#### Money and financial mathematics

Recognise, describe and order Australian coins according to their value (ACMNA017 - Scootle )
• showing that coins are different in other countries by comparing Asian coins to Australian coins
• understanding that the value of Australian coins is not related to size
• describing the features of coins that make it possible to identify them

#### Patterns and algebra

Investigate and describe number patterns formed by skip-counting and patterns with objects (ACMNA018 - Scootle )
• using place-value patterns beyond the teens to generalise the number sequence and predict the next number
• investigating patterns in the number system, such as the occurrence of a particular digit in the numbers to 100

#### Using units of measurement

Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019 - Scootle )
• understanding that in order to compare objects, the unit of measurement must be the same size
Tell time to the half-hour (ACMMG020 - Scootle )
• reading time on analogue and digital clocks and observing the characteristics of half-hour times
Describe duration using months, weeks, days and hours (ACMMG021 - Scootle )
• describing the duration of familiar situations such as ‘how long is it until we next come to school?’

#### Shape

Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features (ACMMG022 - Scootle )
• focusing on geometric features and describing shapes and objects using everyday words such as 'corners', 'edges' and 'faces'

#### Location and transformation

Give and follow directions to familiar locations (ACMMG023 - Scootle )
• understanding that people need to give and follow directions to and from a place, and that this involves turns, direction and distance
• understanding the meaning and importance of words such as ‘clockwise’, ‘anticlockwise’, ‘forward’ and ‘under’ when giving and following directions
• interpreting and following directions around familiar locations

#### Chance

Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024 - Scootle )
• justifying that some events are certain or impossible

#### Data representation and interpretation

Choose simple questions and gather responses and make simple inferences (ACMSP262 - Scootle )
• determining which questions will gather appropriate responses for a simple investigation
Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays (ACMSP263 - Scootle )
• understanding one-to-one correspondence
• describing displays by identifying categories with the greatest or least number of objects

### Year 1 Achievement Standards

By the end of Year 1, students describe number sequences resulting from skip counting by 2s, 5s and 10s. They identify representations of one half. They recognise Australian coins according to their value. Students explain time durations. They describe two-dimensional shapes and three-dimensional objects. Students describe data displays.

Students count to and from 100 and locate numbers on a number line. They carry out simple additions and subtractions using counting strategies. They partition numbers using place value. They continue simple patterns involving numbers and objects. Students order objects based on lengths and capacities using informal units. They tell time to the half-hour. They use the language of direction to move from place to place. Students classify outcomes of simple familiar events. They collect data by asking questions, draw simple data displays and make simple inferences.