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Mathematics K–12

Mathematics 3–6 units

Sample units to support implementation of the Mathematics K–10 Syllabus.

Unit features

Sample units are optional resources forming part of the curriculum reform support package in mathematics for primary teachers. As part of the Curriculum Partnership Schools project, primary school teachers across the state worked collaboratively with the Primary Curriculum team to develop mathematics 3–6 sample units.

These units are designed for teachers of 3–6 students and represent ‘one way’ of designing teaching and learning experiences.

The Mathematics K–10 Syllabus (2022) affords a refreshed approach to mathematics units. Sample units include value-added features that support this approach.

Timeframe for use

Each unit is 2 weeks in duration, aligned to department scope and sequences. Including the Daily number sense instructional sequence.

Sample units

  • make connections within and between mathematical concepts including making connections to real-life experiences
  • highlight and reinforce the role of working mathematically and student reasoning
  • include rich mathematical tasks, resources and opportunities for assessment and differentiation
  • address all syllabus outcomes for Stage 2 and Stage 3
  • comply with curriculum policy and registration requirements.

Before engaging with sample units, it is imperative to develop a deep understanding of the Mathematics K–10 Syllabus (2022) and the underpinning evidence base.

Professional learning

  • Department microlearning course NR40415 (elective professional development)
  • Introduction to Mathematics 3–6 Syllabus (NESA) – all NSW teachers have access to the course by logging into NESA Online Learning.

Resources

Mathematics K–10 (2022) Syllabus (Years 3–6) – information for school leaders

How to use sample units

Sample units are optional resources to support classroom teachers in designing high-quality teaching and learning experiences for students.

Like any resource, sample units must be reviewed for suitability prior to use. Teachers should exercise professional judgement when making these decisions. Teachers are strongly encouraged to adapt and modify sample units to reflect their whole-school approach to mathematics and to meet their students’ learning needs.

Note

Where staff cannot adapt or modify sample units, consider use of alternatives that:

  • have a strong evidence base
  • are better matched to local-level curriculum requirements
  • are more effective in meeting student needs.

All units are best viewed digitally as opposed to printed hard copies.

To move through sections of a unit, open the unit and view the navigation pane (Ctrl+F or select View > Navigation pane). In the navigation pane, select the Headings tab.

To go to a heading in a sample unit, select that heading in the navigation pane. This allows teachers to view headings without scrolling.

Each sample unit has been designed using the following structure:

  • Title – indicates key learning area, stage of learning and unit number.
  • Contents – key reference page to support navigation.
  • Unit description and duration – describes the focus of the unit and indicates suggested student prior learning experiences. All sample K-2 units are 2 weeks in duration.
  • Lesson overview and resources – a high-level summary of each lesson, including indicative times, resources, and syllabus focus areas and content groups.
  • Lessons 1 to 8 – every sample unit comprises 8 lessons. Each lesson includes
    • the core concepts
    • learning intentions and success criteria
    • activities (daily number sense, consolidation and meaningful practice)
    • discuss and connect the mathematics
    • indicative times to support weekly timetabling
    • prompts and anticipated student responses
    • assessment opportunities (What to look for? What to collect?)
    • differentiation ideas (Too hard? Too easy?)
    • where relevant, content points show links to the National Numeracy Learning Progression (Version 3) identified.
  • Resources – for whole class display or distribution to small groups/individual students.
  • Syllabus outcomes and content – syllabus intent is explicitly indicated through relevant focus areas, outcomes, content groups and content points.
  • References – provide links to third-party material, websites and further reading.

Sample units are provided as a starting point for teachers to contextualise learning for their students. Implementation of inclusive practices in planning, programming, and assessing supports learning for the full range of students and ensure all students can access and engage with the units.

In NSW classrooms there is a diverse range of students including:

  • Aboriginal and/or Torres Strait Islander students
  • students learning English as an additional language or dialect, including Aboriginal English speakers
  • high potential and gifted students
  • students with disability.

Some students may identify with more than one of these groups, or possibly all of them.

Advice for teachers on curriculum planning for every student in every classroom.

Teachers are also encouraged to enrol in ‘Curriculum planning for every student in every classroom’, available in MyPL, to explore curriculum planning strategies and resources to optimise learning for every student.

Use comments to annotate a unit, including to show evidence of strategies to optimise learning for specific groups of students, or individual students. This could include strategies to enhance teaching and learning, such as differentiation or personalised adjustments.

To learn how to share comments read Share and collaborate with Word for the web. Staff can reply to a comment, adding further detail about the level, type and effectiveness of support provided to a student or group of students.

Stage 2 units

Forty sample units for Stage 2 will be available for download, released in a phased manner across 2023 and 2024. Individual units, lessons and resources can be used interchangeably to meet the needs of students.

A suggested term-by-term approach, aligned with the department’s scope and sequence, is outlined below, including associated ‘big ideas’ and syllabus focus areas.

Stage 2 – Year A

NSW students in Years 3 and 4 may be working towards Stage 2 outcomes from the Mathematics K–10 Syllabus (2022). Year A sample units are designed for early concept development of Stage 2 outcomes, regardless of students’ year level. Teachers should exercise professional judgement in determining the suitability of teaching and learning experiences in meeting the needs of their students.

Unit 1 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Multiplicative relations

Mathematics Stage 2 Year A Unit 1 (DOCX 2.6 MB)

Unit 2 – Addition and subtraction problems can be solved using a variety of strategies

  • Representing numbers using place value
  • Additive relations

Mathematics Stage 2 Year A Unit 2 (DOCX 3.6 MB)

Unit 3 – What needs to be measured determines the unit of measurement

  • Geometric measure
  • Two-dimensional spatial structure
  • Non-spatial measure

Mathematics Stage 2 Year A Unit 3 (DOCX 2 MB)

Unit 4 – Fractions represent multiple ideas and can be represented in different ways

  • Partitioned fractions
  • Multiplicative relations
  • Geometric measure

Mathematics Stage 2 Year A Unit 4 (DOCX 2.6 MB)

Unit 5 – Questions can be asked and answered by collecting and interpreting data

  • Represents numbers using place value
  • Data

Mathematics Stage 2 Year A Unit 5 (DOCX 1.6 MB)

Unit 6 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Additive relations

Mathematics Stage 2 Year A Unit 6 (DOCX 6.25 MB)

Unit 7 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Representing numbers using place value
  • Multiplicative relations

Mathematics Stage 2 Year A Unit 7 (DOCX 7.1 MB)

Unit 8 – Visual representations help to understand aspects of the world (chance and position)

  • Geometric measure: position
  • Chance
  • Partitioned fractions

Mathematics Stage 2 Year A Unit 8 (DOCX 9.4 KB)

Unit 9 – What needs to be measured determines the unit of measurement

  • Representing numbers using place value
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics Stage 2 Year A Unit 9 (DOCX 4 KB)

Unit 10 – Angles are the primary structural component of many shapes

  • Partitioned fractions
  • Geometric measure: angles
  • Non-spatial measure: time

Mathematics Stage 2 Year A Unit 10 (DOCX 5.9 KB)

Unit 11 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Multiplicative relations

Mathematics Stage 2 Year A Unit 11 (DOCX 8 MB)

Unit 12 – Understanding relationships between the properties of 2D shapes helps visualise and organise spaces in the world

  • Multiplicative relations
  • Two-dimensional spatial structure

Mathematics Stage 2 Year A Unit 12 (DOCX 3.5 MB)

Unit 13 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

Multiplicative relations

Mathematics Stage 2 Year A Unit 13 (DOCX 7.89 MB)

Unit 14 – What needs to be measured determines the unit of measurement

  • Geometric measure
  • Non-spatial measure: Mass

Mathematics Stage 2 Year A Unit 14 (DOCX 7.8 MB)

Unit 15 – Addition and subtraction problems can be solved using a variety of strategies

  • Representing numbers using place value
  • Additive relations

Mathematics Stage 2 Year A Unit 15 (DOCX 7.68 MB)

Unit 16 – Fractions represent multiple ideas and can be represented in different ways

  • Multiplicative relations
  • Partitioned fractions

Mathematics Stage 2 Year A Unit 16 (DOCX 2.8 MB)

Unit 17 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Multiplicative relations
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics Stage 2 Year A Unit 17 (DOCX 4.25 MB)

Unit 18 – Questions can be asked and answered by interpreting data

  • Data
  • Chance

Mathematics Stage 2 Year A Unit 18 (DOCX 5.64 MB)

Unit 19 – Angles are the primary structural component of many shapes

  • Geometric measure: Angles
  • Two-dimensional spatial structure
  • Non-spatial measure: Time

Mathematics Stage 2 Year A Unit 19 (DOCX 7.6 MB)

Unit 20 – Our number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Additive relations
  • Multiplicative relations
  • Geometric measure: Position

Mathematics Stage 2 Year A Unit 20 (DOCX 4.57 MB)

Stage 2 – Year B

NSW students in Years 3 and 4 may be working towards Stage 2 outcomes from the Mathematics K–10 Syllabus (2022). Year B sample units are designed for later concept development of Stage 2 outcomes, regardless of students’ year level.

Teachers should exercise professional judgement in determining the suitability of teaching and learning experiences in meeting the needs of their students.

Unit 21 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Multiplicative relations

Mathematics Stage 2 Year B Unit 21 (DOCX 1.9 MB)

Unit 22 – Addition and subtraction problems can be solved using a variety of strategies

  • Representing numbers using place value
  • Additive relations

Mathematics Stage 2 Year B Unit 22 (DOCX 3.9 MB)

Unit 23 – What needs to be measured determines the unit of measurement

  • Geometric measure
  • Two-dimensional spatial structure
  • Non-spatial measure

Mathematics Stage 2 Year B Unit 23 (DOCX 3.4 MB)

Unit 24 – Fractions represent multiple ideas and can be represented in different ways

  • Partitioned fractions
  • Represents numbers using place value
  • Multiplicative relations
  • Geometric measure

Mathematics Stage 2 Year B Unit 24 (DOCX 1.9 MB)

Unit 25 – Questions can be asked and answered by collecting and interpreting data

  • Represents numbers using place value
  • Data

Mathematics Stage 2 Year B Unit 25 (DOCX 3.4 MB)

Unit 26 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Additive relations

Mathematics Stage 2 Year B Unit 26 (DOCX 19.07 MB)

Unit 27 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Representing numbers using place value
  • Multiplicative relations

Mathematics Stage 2 Year B Unit 27 (DOCX 4.2 MB)

Unit 28 – Visual representations help understand aspects of our world (chance and position)

  • Geometric measure: position
  • Chance
  • Two-dimensional spatial structure
  • Data

Mathematics Stage 2 Year B Unit 28 (DOCX 5.3 MB)

Unit 29 – What needs to be measured determines the unit of measurement

  • Representing numbers using place value
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics Stage 2 Year B Unit 29 (DOCX 11.1 MB)

Unit 30 – Angles are the primary structural component of many shapes

  • Geometric measure: angles
  • Non-spatial measure: time
  • Partitioned fractions

Mathematics Stage 2 Year B Unit 30 (DOCX 3.8 MB)

Unit 31 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Multiplicative relations

Mathematics Stage 2 Year B Unit 31 (DOCX 9.5)

Unit 32 – Understanding relationships between the properties of 2D shapes helps visualise and organise spaces in the world

  • Multiplicative relations
  • Two-dimensional spatial structure

Mathematics Stage 2 Year B Unit 32 (DOCX 7.84 MB)

Unit 33 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Representing numbers using place value
  • Multiplicative relations

Mathematics Stage 2 Year B Unit 33 (DOCX 7.28 MB)

Unit 34 – What needs to be measured determines the unit of measurement

  • Representing numbers using place value
  • Geometric measure
  • Non-spatial measure: Mass

Mathematics Stage 2 Year B Unit 34 (DOCX 6.38 MB)

Unit 35 – Addition and subtraction problems can be solved using a variety of strategies

  • Representing numbers using place value
  • Additive relations

Mathematics Stage 2 Year B Unit 35 (DOCX 7.62 MB)

Unit 36 – Fractions represent multiple ideas and can be represented in different ways

  • Representing numbers using place value
  • Multiplicative relations
  • Partitioned fractions

Mathematics Stage 2 Year B Unit 36 (DOCX 2.61 MB)

Unit 37 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Multiplicative relations
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics Stage 2 Year B Unit 37 (DOCX 3.34 MB)

Unit 38 – Questions can be asked and answered by collecting and interpreting data

  • Data
  • Chance

Mathematics Stage 2 Year B Unit 38 (DOCX 2.3 MB)

Unit 39 – Angles are the primary structural component of many shapes

  • Geometric measure: Angles
  • Two-dimesnsional spatial structure
  • Non-spatial measure: Time

Mathematics Stage 2 Year B Unit 39 (DOCX 4.1 MB)

Unit 40 – Our number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Additive relations
  • Multiplicative relations
  • Geometric measure: Position

Mathematics Stage 2 Year B Unit 40 (DOCX 5.5 MB)

Stage 3 units

Forty sample units for Stage 3 will be available for download, released in a phased manner across 2023 and 2024. Individual units, lessons and resources can be used interchangeably to meet the needs of students.

A suggested term-by-term approach, aligned with the department’s scope and sequence, is outlined below, including associated ‘big ideas’ and syllabus focus areas.

Stage 3 – Year A

NSW students in Years 5 and 6 may be working towards Stage 3 outcomes from the Mathematics K–10 Syllabus (2022). Year A sample units are designed for early concept development of Stage 3 outcomes, regardless of students’ year level. Teachers should exercise professional judgement in determining the suitability of teaching and learning experiences in meeting the needs of their students.

Unit 1 – The number system extends infinitely to very large and very small numbers

  • Represents numbers
  • Multiplicative relations

Mathematics Stage 3 Year A Unit 1 (DOCX 1.9 MB)

Unit 2 – Addition and subtraction problems can be solved using a variety of strategies

  • Represents numbers
  • Additive relations

Mathematics Stage 3 Year A Unit 2 (DOCX 7.81 MB)

Unit 3 – What needs to be measured determines the unit of measurement

  • Geometric measure
  • Two-dimensional spatial structure
  • Non-spatial measure

Mathematics Stage 3 Year A Unit 3 (DOCX 3.53 MB)

Unit 4 – Fractions represent multiple ideas and can be represented in different ways

  • Representing quantity fractions
  • Additive relations

Mathematics Stage 3 Year A Unit 4 (DOCX 2.2 MB)

Unit 5 – Questions can be asked and answered by collecting and interpreting data

  • Represents numbers
  • Data

Mathematics Stage 3 Year A Unit 5 (DOCX 3.4 MB)

Unit 6 – The number system extends infinitely to very large and very small numbers

  • Representing numbers
  • Additive relations

Mathematics Stage 3 Year A Unit 6 (DOCX 10.21 MB)

Unit 7 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Represents numbers
  • Multiplicative relations

Mathematics Stage 3 Year A Unit 7 (DOCX 2.8 MB)

Unit 8 – Visual representations help to understand aspects of the world (chance and position)

  • Geometric measure: position
  • Chance
  • Represents quantity fractions

Mathematics Stage 3 Year A Unit 8 (DOCX 5.6 MB)

Unit 9 – What needs to be measured determines the unit of measurement

  • Represents numbers
  • Three-dimensional spatial structure

Mathematics Stage 3 Year A Unit 9 (DOCX 8.07 MB)

Unit 10 – Angles are the primary structural component of many shapes

  • Representing quantity fractions
  • Geometric measure: angles
  • Non-spatial measure: time

Mathematics Stage 3 Year A Unit 10 (DOCX 8.66 MB)

Unit 11 – The number system extends infinitely to very large and very small numbers

  • Represents numbers
  • Multiplicative relations

Mathematics Stage 3 Year A Unit 11 (DOCX 6.2 MB)

Unit 12 – Understanding relationships between the properties of 2D shapes helps visualise and organise spaces in the world

  • Two-dimensional spatial structure
  • Multiplicative relations

Mathematics Stage 3 Year A Unit 12 (DOCX 5.55 MB)

Unit 13 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

Multiplicative relations

Mathematics Stage 3 Year A Unit 13 (DOCX 6.89 MB)

Unit 14 – What needs to be measured determines the unit of measurement

  • Represents numbers
  • Geometric measure
  • Non-spatial measure: Mass

Mathematics Stage 3 Year A Unit 14 (DOCX 8.71 MB)

Unit 15 – Addition and subtraction problems can be solved using a variety of strategies

  • Represents number (Stage 3)
  • Additive relations

Mathematics Stage 3 Year A Unit 15 (DOCX 11.09 MB)

Unit 16 – Fractions represent multiple ideas and can be represented in different ways

  • Represents numbers
  • Additive relations
  • Representing quantity fractions

Mathematics Stage 3 Year A Unit 16 (DOCX 1.76 MB)

Unit 17 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Multiplicative relations
  • Geometric measure: Length
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics Stage 3 Year A Unit 17 (DOCX 1.48 MB)

Unit 18 – Questions can be asked and answered by interpreting data

  • Represents numbers
  • Data
  • Chance

Mathematics Stage 3 Year A Unit 18 (DOCX 4.9 MB)

Unit 19 – Angles are the primary structural component of many shapes

  • Geometric measure: Angles
  • Two-dimensional spatial structure
  • Non-spatial measure: Time

Mathematics Stage 3 Year A Unit 19 (DOCX 7 MB)

Unit 20 – Our number system extends infinitely to very large and very small numbers

  • Represents numbers
  • Additive relations
  • Multiplicative relations
  • Geometric measure: Position

Mathematics Stage 3 Year A Unit 20 (DOCX 3.73 MB)

Stage 3 – Year B

NSW students in Years 5 and 6 may be working towards Stage 3 outcomes from the Mathematics K–10 Syllabus (2022). Year B sample units are designed for later concept development of Stage 3 outcomes, regardless of students’ year level. Teachers should exercise professional judgement in determining the suitability of teaching and learning experiences in meeting the needs of their students.

Unit 21 – The number system extends infinitely to very large and very small numbers

  • Represents numbers
  • Multiplicative relations

Mathematics Stage 3 Year B Unit 21 (DOCX 4.8 MB)

Unit 22 – Addition and subtraction problems can be solved using a variety of strategies

  • Represents numbers
  • Additive relations

Mathematics Stage 3 Year B Unit 22 (DOCX 2.7 MB)

Unit 23 – What needs to be measured determines the unit of measurement

  • Geometric measure
  • Two-dimensional spatial structure
  • Non-spatial measure

Mathematics Stage 3 Year B Unit 23 (DOCX 2.4 MB)

Unit 24 – Fractions represent multiple ideas and can be represented in different ways

  • Representing quantity fractions
  • Additive relations

Mathematics Stage 3 Year B Unit 24 (DOCX 1.3 MB)

Unit 25 – Questions can be asked and answered by collecting and interpreting data

  • Represents numbers
  • Data

Mathematics Stage 3 Year B Unit 25 (DOCX 5.2 MB)

Unit 26 – The number system extends infinitely to very large and very small numbers

  • Representing numbers
  • Additive relations

Mathematics Stage 3 Year B Unit 26 (DOCX 13.62 MB)

Unit 27 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Represents numbers
  • Additive relations
  • Multiplicative relations

Mathematics Stage 3 Year B Unit 27 (DOCX 3.3 MB)

Unit 28 – Visual representations help understand aspects of our world (chance and position)

  • Geometric measure: position
  • Chance
  • Representing quantity fractions
  • Two-dimensional spatial structure

Mathematics Stage 3 Year B Unit 28 (DOCX 7.76 MB)

Unit 29 – What needs to be measured determines the unit of measurement

  • Represents numbers
  • Three-dimensional spatial structure

Mathematics Stage 3 Year B Unit 29 (DOCX 10.06 MB)

Unit 30 – Angles are the primary structural component of many shapes

  • Representing quantity fractions
  • Geometric measure: angles
  • Non-spatial measure: time

Mathematics Stage 3 Year B Unit 30 (DOCX 6.49 MB)

Unit 31 – The number system extends infinitely to very large and very small numbers

  • Represents numbers
  • Multiplicative relations

Mathematics Stage 3 Year B Unit 31 (DOCX 2.8 MB)

Unit 32 – Understanding relationships between the properties of 2D shapes helps visualise and organise spaces in the world

  • Multiplicative relations
  • Two-dimensional spatial structure

Mathematics Stage 3 Year B Unit 32 (DOCX 3.5 MB)

Unit 33 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

Multiplicative relations

Mathematics Stage 3 Year B Unit 33 (DOCX 5.86 MB)

Unit 34 – What needs to be measured determines the unit of measurement

  • Additive relations
  • Geometric measure
  • Non-spatial measure: Mass

Mathematics Stage 3 Year B Unit 34 (DOCX 6.75 MB)

Unit 35 – Addition and subtraction problems can be solved using a variety of strategies

  • Represents numbers
  • Additive relations
  • Non-spatial measure: Time

Mathematics Stage 3 Year B Unit 35 (DOCX 11.78 MB)

Unit 36 – Fractions represent multiple ideas and can be represented in different ways

  • Represents number
  • Representing quantity fractions
  • Chance

Mathematics Stage 3 Year B Unit 36 (DOCX 2.24 MB)

Unit 37 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Multiplicative relations
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics Stage 3 Year B Unit 37 (DOCX 3.32 MB)

Unit 38 – Questions can be asked and answered by interpreting data

  • Data
  • Chance

Mathematics Stage 3 Year B Unit 38 (DOCX 5.4 MB)

Unit 39 – Angles are the primary structural component of many shapes

  • Geometric measure: Angles
  • Two-dimensional spatial structure
  • Non-spatial measure: Time

Mathematics Stage 3 Year B Unit 39 (DOCX 13.1 MB)

Unit 40 – Our number system extends infinitely to very large and very small numbers

  • Representing numbers using place value
  • Additive relations
  • Multiplicative relations
  • Geometric measure: Position

Mathematics Stage 3 Year B Unit 40 (DOCX 1.9 MB)

3–6 multi-age units

Across 2023 and 2024, forty sample units will be available for download that may assist teachers with multi-age classes. Individual units, lessons, activities and resources can be taught in any order, at any time in meeting student learning needs.

A suggested term-by-term approach, aligned with the department’s scope and sequence, is outlined below, including associated ‘big ideas’ and syllabus focus areas. This approach covers all Stage 2 and Stage 3 syllabus outcomes across the two years.

Multi-age – Year A

Year A sample units are designed for early concept development of Stage 2 and Stage 3 outcomes, regardless of students’ year level. Teachers should exercise professional judgement in determining the suitability of teaching and learning experiences in meeting the needs of their students.

Unit 1 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Multiplicative relations

Mathematics 3–6 multi-age Year A Unit 1 (DOCX 2 MB)

Unit 2 – Addition and subtraction problems can be solved using a variety of strategies

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Additive relations

Mathematics 3–6 multi-age Year A Unit 2 (DOCX 4.5 MB)

Unit 3 – What needs to be measured determines the unit of measurement

  • Geometric measure
  • Two-dimensional spatial structure
  • Non-spatial measure

Mathematics 3–6 multi-age Year A Unit 3 (DOCX 4.1 MB)

Unit 4 – Fractions represent multiple ideas and can be represented in different ways

  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)
  • Multiplicative relations (Stage 2 only)
  • Geometric measure (Stage 2 only)
  • Additive relations (Stage 3 only)

Mathematics 3–6 multi-age Year A Unit 4 (DOCX 4MB)

Unit 5 – Questions can be asked and answered by collecting and interpreting data

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Data

Mathematics 3–6 multi-age Year A Unit 5 (DOCX 4.5 MB)

Unit 6 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Additive relations

Mathematics 3–6 multi-age Year A Unit 6 (DOCX 5 MB)

Unit 7 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Multiplicative relations

Mathematics 3–6 multi-age Year A Unit 7 (DOCX 11.2 MB)

Unit 8 – Visual representations help to understand aspects of our world (chance and position)

  • Geometric measure: position
  • Chance
  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)

Mathematics 3–6 multi-age Year A Unit 8 (DOCX 14.5 MB)

Unit 9 – What needs to be measured determines the unit of measurement

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Two-dimensional spatial structure (Stage 2 only)
  • Three-dimensional spatial structure

Mathematics 3–6 multi-age Year A Unit 9 (DOCX 7.9 MB)

Unit 10 – Angles are the primary structural component of many shapes

  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)
  • Geometric measure: angles
  • Non-spatial measure: time

Mathematics 3–6 multi-age Year A Unit 10 (DOCX 14.2 MB)

Unit 11 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Multiplicative relations

Mathematics 3–6 multi-age Year A Unit 11 (DOCX 10.1 MB)

Unit 12 – Understanding relationships between the properties of 2D shapes helps visualise and organise spaces in the world

  • Multiplicative relations
  • Two-dimensional spatial structure

Mathematics 3–6 multi-age Year A Unit 12 (DOCX 5 MB)

Unit 13 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

Multiplicative relations

Mathematics 3–6 multi-age Year A Unit 13 (DOCX 11.31 MB)

Unit 14 – What needs to be measured determines the unit of measurement

  • Represents numbers (Stage 3)
  • Geometric measure
  • Non-spatial measure: Mass

Mathematics 3–6 multi-age Year A Unit 14 (DOCX 11.02 MB)

Unit 15 – Addition and subtraction problems can be solved using a variety of strategies.

  • Representing numbers using place value (Stage 2)
  • Represents number (Stage 3)
  • Additive relations

Mathematics 3–6 multi-age Year A Unit 15 (DOCX 14.97 MB)

Unit 16 – Fractions represent multiple ideas and can be represented in different ways

  • Represents numbers (Stage 3 only)
  • Additive relations (Stage 3 only)
  • Multiplicative relations
  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)

Mathematics 3–6 Multi-age Year A Unit 16 (DOCX 4.44 MB)

Unit 17 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Multiplicative relations
  • Geometric measure (Stage 3 only)
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics 3–6 Multi-age Year A Unit 17 (DOCX 11.4 MB)

Unit 18 – Questions can be asked and answered by collecting and interpreting data

  • Represents numbers (Stage 3 only)
  • Data
  • Chance

Mathematics 3–6 Multi-age Year A Unit 18 (DOCX 9.7 MB)

Unit 19– Angles are the primary structural component of many shapes

  • Geometric measure: Angles
  • Two-dimensional spatial structure
  • Non-spatial measure: Time

Mathematics 3–6 Multi-age Year A Unit 19 (DOCX 5.14 MB)

Unit 20 – Our number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2)
  • Represents numbers (Stage 3)
  • Additive relations
  • Multiplicative relations
  • Geometric measure: Position

Mathematics 3–6 Multi-age Year A Unit 20 (DOCX 7.3 MB)

Multi-age – Year B

Year B sample units are designed for later concept development of Stage 2 and Stage 3 outcomes, regardless of students’ year level. Teachers should exercise professional judgement in determining the suitability of teaching and learning experiences in meeting the needs of their students

Unit 1 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Multiplicative relations

Mathematics 3–6 multi-age Year B Unit 1 (DOCX 2.7 MB)

Unit 2 – Addition and subtraction problems can be solved using a variety of strategies

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Additive relations

Mathematics 3–6 multi-age Year B Unit 2 (DOCX 4.8 MB)

Unit 3 – What needs to be measured determines the unit of measurement

  • Geometric measure
  • Two-dimensional spatial structure
  • Non-spatial measure

Mathematics 3–6 multi-age Year B Unit 3 (DOCX 3.9 MB)

Unit 4 – Fractions represent multiple ideas and can be represented in different ways

  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)
  • Represents numbers using place value (Stage 2 only)
  • Multiplicative relations (Stage 2 only)
  • Additive relations (Stage 3 only)
  • Geometric measure

Mathematics 3–6 multi-age Year B Unit 4 (DOCX 2.5 MB)

Unit 5 –Questions can be asked and answered by collecting and interpreting data

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Data

Mathematics 3–6 multi-age Year B Unit 5 (DOCX 11.3 MB)

Unit 6 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Additive relations

Mathematics 3–6 multi-age Year B Unit 6 (DOCX 3.8 MB)

Unit 7 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Additive relations (Stage 3 only)
  • Multiplicative relations

Mathematics 3–6 multi-age Year B Unit 7 (DOCX 4.6 MB)

Unit 8 – Visual representations help understand aspects of our world (chance and position)

  • Geometric measure: position
  • Chance
  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)
  • Two-dimensional spatial structure (Stage 2 only)
  • Data (Stage 2 only)

Mathematics 3–6 multi-age Year B Unit 8 (DOCX 11.1 MB)

Unit 9 – What needs to be measured determines the unit of measurement

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Three-dimensional spatial structure

Mathematics 3–6 multi-age Year B Unit 9 (DOCX 8.3 MB)

Unit 10 – Angles are the primary structural component of many shapes

  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)
  • Geometric measure: angles
  • Non-spatial measure: time

Mathematics 3–6 multi-age Year B Unit 10 (DOCX 9.4 MB)

Unit 11 – The number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2 only)
  • Represents numbers (Stage 3 only)
  • Multiplicative relations

Mathematics 3–6 multi-age Year B Unit 11 (DOCX 4.3 MB)

Unit 12 – Understanding relationships between the properties of 2D shapes helps visualise and organise spaces in the world

  • Multiplicative relations
  • Two-dimensional spatial structure

Mathematics 3–6 multi-age Year B Unit 12 (DOCX 13.57 MB)

Unit 13 – What needs to be measured determines the unit of measurement

  • Representing numbers using place value (Stage 2)
  • Multiplicative relations

Mathematics 3–6 multi-age Year B Unit 13 (DOCX 8.62 MB)

Unit 14 – What needs to be measured determines the unit of measurement

  • Additive relations
  • Geometric measure
  • Non-spatial measure: Mass

Mathematics 3–6 multi-age Year B Unit 14 (DOCX 7.62 MB)

Unit 15 – Addition and subtraction problems can be solved using a variety of strategies

  • Representing numbers using place value (Stage 2)
  • Represents numbers (Stage 3)
  • Additive relations
  • Non-spatial measure: Time

Mathematics 3–6 multi-age Year B Unit 15 (DOCX 14.5 MB)

Unit 16 – Fractions represent multiple ideas and can be represented in different ways

  • Representing numbers using place value (Stage 2 only)
  • Multiplicative relations
  • Partitioned fractions (Stage 2 only)
  • Representing quantity fractions (Stage 3 only)
  • Chance (Stage 3 only)

Mathematics 3–6 Multi-age Year B Unit 16 (DOCX 4.27 MB)

Unit 17 – Multiplicative thinking involves flexible use of multiplication and division concepts, strategies and representations

  • Multiplicative relations
  • Geometric measure: Length (Stage 3 only)
  • Two-dimensional spatial structure
  • Three-dimensional spatial structure

Mathematics 3–6 Multi-age Year B Unit 17 (DOCX 7.49 MB)

Unit 18 – Questions can be asked and answered by collecting and interpreting data

  • Data
  • Chance

Mathematics 3–6 Multi-age Year B Unit 18 (DOCX 4.1 MB)

Unit 19 – Angles are the primary structural component of many shapes

  • Geometric measure: Angles
  • Two-dimensional spatial structure
  • Non-spatial measure: Time

Mathematics 3–6 Multi-age Year B Unit 19 (DOCX 8.15 MB)

Unit 20 – Our number system extends infinitely to very large and very small numbers

  • Representing numbers using place value (Stage 2)
  • Represents numbers (Stage 3)
  • Additive relations
  • Multiplicative relations
  • Geometric measure: Position

Mathematics 3–6 Multi-age Year B Unit 20 (DOCX 6.9 MB)

Quality assurance

Sample units have undergone a rigorous quality assurance process as part of our commitment to improving school support. The process ensures that all sample units provided to schools are relevant, of high quality, and underpinned by evidence-based practice.

Alignment to School Excellence Framework 

These resources support the School Excellence Framework and clearly align to the following domains and themes:

Learning domain 

  • Curriculum: Curriculum provision, Teaching and learning programs 

  • Assessment: Whole school monitoring of student learning 

  • Student performance measures: NAPLAN 

Teaching domain 

  • Effective classroom practice: Lesson planning, Explicit teaching 

  • Learning and development: Collaborative practice and feedback; Expertise and innovation 

Leading domain 

  • Educational leadership: Instructional leadership 

Alignment to system priorities and/or needs 

These resources reflect the following existing frameworks: 

Consultation 

Resources have been developed with NSW school-based writing teams as part of the department's Curriculum Partnership Schools project. Subject matter experts from Curriculum Early Years and Primary Learners endorsed documents to ensure accuracy of content.

Evidence base 

The evidence base for these resources is: 

Contact 

Email questions, comments and feedback about these resources to mathematicsk6@det.nsw.edu.au.

Category:

  • Teaching and learning

Topics:

  • All primary schools
  • Classroom teachers
  • Mathematics
  • Teaching and learning
  • Year 3
  • Year 4
  • Year 5
  • Year 6

Business Unit:

  • Curriculum and Reform
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