# K–10Mathematics K–10 Syllabus

## Course overview

### Mathematics K–2 overview

Through the study of mathematics, students develop essential concepts and skills and apply them to deepen their understanding of the world. In Mathematics K–2, students:

- develop essential numeracy skills and mathematical fluency
- identify, describe and apply patterns and relationships
- develop their reasoning and problem-solving skills
- apply their knowledge and understanding in practical situations and make informed decisions.

### Support documents

**Mathematics K–2 Syllabus (formatted document)**

A full list of support documents is available via the Teaching and learning support tab.

- Working mathematically in Mathematics K–2 (Word, 8 pages, 1.04 MB)
- Reasoning in Mathematics K–2 (Word, 9 pages, 5.79 MB)
- Making connections in Mathematics K–2: Early Stage 1 (PDF, 1 page, 99.39 KB)
- Making connections in Mathematics K–2: Stage 1 (PDF, 1 page, 104.09 KB)
- About the English and Mathematics K–2 syllabuses (Word, 5 pages, 930.41 KB)
- Structural features of the NSW Curriculum (Word, 2 pages, 906.32 KB)

### Syllabus structure

The new structure illustrates the important role working mathematically plays across all areas of mathematics and reflects the need to strengthen connections between concepts in mathematics.

Outcomes and their related content are organised in:

- Number and algebra
- Measurement and space
- Statistics and probability.

The diagram shows the organisation of the outcomes and content for Mathematics K–2.

#### Balance of content

The amount of content associated with an outcome may not be indicative of the time required to engage with that outcome. Teachers determine instructional priorities and the time needed for students to achieve expected outcomes based on student needs and abilities.

Content groups are used to cluster related content associated with an outcome(s). These content groups are not intended to be hierarchical, they describe in more detail:

- how to interpret and use the outcomes
- the intended learning appropriate for the stage.

### Key features

#### Working at different stages

The content presented in a stage represents the typical knowledge, skills and understanding that students learn throughout the stage. It is acknowledged that students develop at different rates and in different ways. Not all content for a particular stage may be relevant to a student in that stage.

For example, some students will achieve Stage 1 outcomes during Year 1, while the majority will achieve them by the end of Year 2. Other students might not develop the same knowledge, skills and understanding until Year 3 or later.

The syllabus is written with the flexibility to enable students to work at different stages in different outcomes. For example, students in Early Stage 1 could be working on Stage 1 content in Number and Algebra, while working on Early Stage 1 content in Measurement and Geometry. Teachers are best placed to make decisions about when students need to work at, above or below stage level. This recognises that outcomes may be achieved by students at different times across Early Stage 1 and Stage 1.

#### Parts A and B

To assist programming in Mathematics K–2, the content in Stage 1 is presented in two parts: A and B, for example in ‘Representing whole numbers A’ and ‘Representing whole numbers B’. Part A typically focuses on early concept development and part B builds on these earlier concepts. This provides flexibility for planning teaching and learning and helps teachers better visualise the progression and growth of concepts within Stage 1.

The content across parts A and B relate to the same stage-based outcomes. Teachers can choose which content, from part A and/or part B, to address based on students’ prior learning, needs and abilities.

In Stage 1, part A does not apply to Year 1 only. For example, when teaching a Year 2 class the teacher may need to address or consolidate some concepts within part A prior to addressing concepts in part B.

#### Making connections through related content

Many connections exist between areas of mathematics. Mathematical concepts are often interrelated or interdependent. Where appropriate, examples have been included of related outcomes and content that could be addressed in parallel. The suggested connections are not an exhaustive list of the ways that mathematical concepts are related or could be taught.

- Making connections in Mathematics K–2: Early Stage 1 (PDF, 1 page, 99.39 KB)
- Making connections in Mathematics K–2: Stage 1 (PDF, 1 page, 104.09 KB)

#### Access content points

Access content points have been developed to support students with significant intellectual disability who are working towards Early Stage 1 outcomes.

For each of the Early Stage 1 outcomes, access content points are provided to indicate content that students with significant intellectual disability may access as they work towards the outcomes. Teachers will be able to use the access content points on their own, or in combination with the content for each outcome. If students are able to access outcomes in the syllabus they should not require the access content points.

This is the first time in NSW the K–6 curriculum has included specific content for students with significant intellectual disability.

### Subject-specific features

#### Working mathematically

The working mathematically processes present in this syllabus are:

- communicating
- understanding and fluency
- reasoning
- problem-solving.

To highlight how these processes are interrelated, in Mathematics K–2 there is one overarching working mathematically outcome. The outcome describes the thinking and doing of mathematics. In doing so, the outcome indicates the breadth of mathematical actions that teachers need to emphasise.

Working mathematically requires students to:

- explore and connect mathematical concepts [understanding/fluency]
- choose and apply efficient techniques to solve problems [fluency/problem-solving]
- communicate their thinking and reasoning coherently and clearly [communicating/reasoning].

Further information is available in Working mathematically in Mathematics K–2 (Word, 8 pages, 1.04 MB).

#### Reasoning in mathematics

Reasoning in mathematics has been described using a variety of terms to characterise how a conclusion has been reached. These include terms such as analysing, deducing, justifying, explaining, inferring and generalising. Within the NSW Mathematics K–2 Syllabus, reasoning involves thinking logically about relationships, both spatial and quantitative.

- Reasoning in Mathematics K–2 (Word, 9 pages, 5.79 MB)

#### Importance of number in the early years of school

Children’s earliest number skills form the foundation for later mathematics learning and predict later mathematics performance in both primary and secondary school (Duncan et al. 2007; Watts et al. 2014).

Patterning is also associated with numerical ability in young children (Wijns et al 2019). Indeed, spatial skills contribute to mathematics performance and are associated with success in Science, Technology, Engineering and Mathematics (STEM) domains (Gilligan et al. 2017). However, it is knowledge of numerical magnitude that is predictive of and causally related to other crucial aspects of mathematics, including overall mathematics achievement (Siegler 2016).