Mathematics sample scope and sequences

A scope and sequence is an important step in the design of effective teaching and learning programs. It summarises what is to be taught and the sequence in which it will be taught (NESA).

Introduction

A range of examples of how schools can organise a mathematics scope and sequence and the elements that could be included.

The purpose of a scope and sequence is to provide an overview of intended learning for the year. Decision making about the scope and sequence should be guided by information about student learning in mathematics, including assessment. It is considered a working document that is flexible and should be modified to meet the needs of students and the local school context. Teachers should be looking for opportunities to develop and make connections within and between strands to support the development of deep knowledge and a conceptual understanding for students.

The sample scope and sequences incorporate advice from NSW Education Standards Authority (NESA) and include the following elements:

  • the scope of learning in relation to the syllabus outcomes to be addressed
  • the sequence of learning in relation to the syllabus outcomes to be addressed
  • duration of the learning
  • syllabus outcomes addressed through the learning and related outcomes (from other KLAs) if the teaching program are integrated
  • relevant information for particular learning areas or particular school requirements.

Each document is a ‘sample’ that schools may adapt to meet the needs of their students and local context.

Two approaches for flexible organisation

The sample scope and sequences have been designed using two connected approaches. They provide a range of flexible options and models for whole school organisation of mathematics. Each approach builds upon basic requirements and provides additional syllabus information to assist planning and programming.

The 2 approaches are:

  1. Stage-based
  2. Stage-based with connections highlighted within an across the strands

Each approach contains a full set of sample scope and sequences and blank templates for all stages (Early Stage 1 to Stage 3).

Advice on working mathematically

Students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning. The five inter-related components of working mathematically are communicating, problem-solving, reasoning, understanding and fluency. These components describe how content is explored or developed – the thinking and doing of mathematics.

Working mathematically has a separate set of outcomes for the components:

  • communicating
  • problem solving
  • reasoning.

Understanding and fluency components do not have an outcome. These components are embedded in the development of knowledge, skills and understanding.

Interpreting the scope and sequence documents

Each term is organised into two parts – early term (the first half of the term) and later term (the second half of the term). This is intentional and gives teachers flexibility to use rich experiences that connect learning within and across strands and to spend more time exploring knowledge, skills and dispositions to support the development of conceptual understanding.

All syllabus outcomes need to be taught, assessed and reported to parents in every stage of learning. Each outcome is addressed several times throughout the year. This ensures students have the opportunity to learn, develop and apply the knowledge, understanding and skills across multiple contexts for learning. Outcomes referenced are drawn from the Mathematics K-10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2012.

5-week scope and sequences by stage

Approach 1

Simplified stage based mathematics scope and sequences

Features

  • stage of learning
  • half-term (duration)
  • syllabus outcomes

These scope and sequences are most suitable for:

  • teachers who feel confident in creating learning experiences which develop and make connections within and across strands to support deep conceptual understanding for students
  • stage-based or year-based classes.

Scope and sequences highlighting some possible connections within and across strands

Approach 2 – Connections within and across strands

Features

  • stage of learning
  • half-term (duration)
  • syllabus outcomes
  • possible connections within strands
  • possible connections across strands
  • links to some learning experiences which illustrate what connections within and across strands can look like

Most suitable for:

  • teachers who are seeking examples and support to develop a connectionist orientation to their teaching of mathematics in order to support the development of deep knowledge and a conceptual understanding for students
  • stage-based or year-based classes.

The importance of making, and teaching through, connections

Askew et al. (1997) identified that highly effective teaching of mathematics and numeracy emphasises connections across mathematics whilst also building on students’ understandings and reasoning. This is characterised as a connectionist orientation.

In order to support teachers to develop and use their knowledge and awareness of conceptual connections within and across aspects of the primary mathematics syllabus, these scope and sequences detail some of the connections that can be found. Critically, these connections are not exhaustive. They are merely sparks for collaborative conversations, planning and teaching that will be most effective when they are contextualised, debated, refined and enhanced by teachers with their students.

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