# Mathematics 7–10 units and assessments

Sample units and assessments to support teachers of Years 7–10 implementing the mathematics K-10 syllabus.

## Syllabus

The Mathematics K-10 syllabus (2023) is to be taught in Years 3 to 10 from 2024.

Detailed implementation information including key features and resources is available on the Mathematics syllabus development page (NESA).

The mathematics Year 7-10 units and assessments represent 'one way' of designing teaching and learning experiences

## Stage 4

### Assessment 1

This investigation style assessment is designed to assess the outcomes from Unit 1 – making predictions of the Department of Education’s sample stage 4 year 7 scope and sequence.

Stage 4 – Game on (DOCX 428.2 KB)

### Assessment 2

This summative assessment package is designed to assess the outcomes from Unit 3 – representing number of the Department of Education’s sample stage 4 year 7 scope and sequence.

A 12-lesson unit for Year 7 with resources

This program of learning addresses content from the focus areas of Fractions, decimals and percentages and Probability. The lessons and sequences in this program of learning are designed to allow students to explore the likelihood of chance events occurring, develop skills with fractions to describe and represent probabilities and make predictions about future events.

### Introduction

Making predictions (DOCX 162 KB)

### Lesson 1 – alphabet soup

### Lesson 2 – would you rather?

Would you rather? (DOCX 149 KB)

### Lesson 3 – rolling to 10

### Lesson 4 – sense of order

### Lesson 5 – same same, but different

### Lesson 6 – to be, or not to be

### Lesson 7 – rock, paper scissors

### Lesson 8 – myths and misconceptions

### Lesson 9 – fakes on trial

### Lesson 10 – what's the chance?

What's the chance? (DOCX 841 KB)

### Lesson 11 – predicting evens

### Lesson 12 – alphabet soup the sequel

A 12-lesson unit for Year 7 with resources

This program of learning addresses content from the focus areas of Data analysis and Data classification and visualisation. The lessons and sequences in this program of learning are designed to allow students to explore how we use data to assist in making decsions. Students will explore different ways of representing data which allow us make decision by analysing and interpreting the data.

### Introduction

Making decisions (DOCX 135 KB)

### Lesson 1 – greedy pig game

### Lesson 2 – what is normal?

### Lesson 3 – the 3 M’s

### Lesson 4 – what does Google know about me?

What does Google know about me? (DOCX 1.1 MB)

### Lesson 5 – slow reveal graphs

### Lesson 6 – proportion graphs

### Lesson 7 – breaking the code

### Lesson 8 – texting competition

### Lesson 9 – myth busters

### Lesson 10 – you should eat more chocolate

You should eat more chocolate (DOCX 89 KB)

### Lesson 11 – going to the movies

### Lesson 12 – how heavy is too heavy?

A 13-lesson unit for Year 7 with resources

This program of learning addresses content from the focus areas of Computation with integers, fractions, decimals and percentages and Linear relationships. The lessons and sequences in this program of learning are designed to allow students to explore quantity of numbers and the different ways of representing this quantity. They consider the equivalence between different representations of numbers and the structural elements of numbers that form quantity.

### Introduction

Representing numbers (DOCX 166.1 KB)

### Lesson 1 – highest common factor of integers

Highest common factor of integers (DOCX 456.9 KB)

### Lesson 2 – less than 0

### Lesson 3 – direction and magnitude

Direction and magnitude (DOCX 3.1 MB)

### Lesson 4 – zero pairs

### Lesson 5 – listen to the music

Listen to the music (DOCX 531.3 KB)

### Lesson 6 – recipe for success

### Lesson 7 – inventing units of measurment

### Lesson 8 – the nasty game

The nasty game (DOCX 365.5 KB)

### Lesson 9 – comparing using place value

### Lesson 10 – approximate measurements

### Lesson 11 – be rational

### Lesson 12 – fractions and decimals and percentages – oh my!

- Fractions and decimals and percentages – oh my! (DOCX 234.5 KB)
- Fractions and decimals and percentages – oh my! (PPTX 2.7 MB)

### Lesson 13 – describing locations

A 12-lesson unit for Year 7 with resources.

This program of learning addresses content from the focus areas of Computation with integers, Fractions, decimals and percentages, and Algebraic techniques. The lessons and sequences in this program of learning are designed to allow students to explore addition and subtraction of integers, fractions, and algebraic terms. A variety of visual representations are developed as tools that students can rely on within this unit and beyond.

### Introduction

Additive thinking (DOCX 161 KB)

### Lesson 1 – banking troubles

Banking troubles (DOCX 395 KB)

### Lesson 2 – bonuses and penalties

### Lesson 3 – addition of integers using vectors

### Lesson 4 – subtraction of integers using vectors

- Subtraction of integers using vectors (DOCX 240 KB)
- Subtraction of integers using vectors (PPTX 694 KB)

### Lesson 5 – same same

### Lesson 6 – why fractions with different denominators don’t align

Why fractions with different denominators don’t align (DOCX 106 KB)

### Lesson 7 – seeing double

### Lesson 8 – how to deal with different denominators

- How to deal with different denominators (DOCX 184 KB)
- How to deal with different denominators (PPTX 868 KB)

### Lesson 9 – which numbers go here?

- Which numbers go here? (DOCX 328 KB)
- Grid algebra ‘1 to 24 grid (no negatives)’ (ZIP 5.9 KB)
- Grid algebra ‘Introducing letters’ (ZIP 1.4 KB)

### Lesson 10 – inverse journeys

### Lesson 11 – stepping through unknowns

### Lesson 12 – laying the foundations of algebra

A 19-lesson unit for Year 7 with resources.

This program of learning addresses content from the focus areas of Computation with integers, Fractions, decimals and percentages, Algebraic techniques and Indices. The lessons and sequences in this program of learning are designed to allow students to explore the multiplication and division of integers, fractions, and algebraic terms. A variety of visual representations are developed as tools students can rely on within this unit and beyond.

### Introduction

Multiplicative thinking (DOCX 169 KB)

### Lesson 1 – negative groups of negatives

### Lesson 2 – sharing, grouping and negating

### Lesson 3 – area models and divisibility tests

### Lesson 4 – the ants go marching

### Lesson 5 – a big problem with small numbers

### Lesson 6 – the magical factor trees

### Lesson 7 – that's about right

### Lesson 8 – a quick guess

### Lesson 9 – cooking for one

### Lesson 10 – a shopping plan

### Lesson 11 – when it's fair to compare the pair

### Lesson 12 – a fair share

### Lesson 13 – the order of things

### Lesson 14 – four fours

### Lesson 15 – groups of mysteries

### Lesson 16 – dividing into the unknown

### Lesson 17 – which number goes here? – (multiplying and dividing)

- Which number goes here – multiplying – dividing (DOCX 419 KB)
- Multiplying and dividing with letters (ZIP 3 KB)
- Grid algebra ‘1 to 30 grid – (no negatives)' (ZIP 7 KB)

### Lesson 18 – inverse journeys – multiplying

### Lesson 19 – a fair share

## Stage 5

### Assessment 1

This investigation style assessment is designed to assess the outcomes from Unit 1 – Geometrical Representations of the Department of Education’s sample stage 5 year 9 scope and sequence.

Stage 5 – How accessible is your school? (DOCX 428.2 KB)

### Assessment 2

This summative assessment package is designed to assess the outcomes from Unit 2 – Working with triangles and Unit 3 – prisms and cylinders of the Department of Education’s sample stage 5 year 9 scope and sequence.

An 11-lesson unit for Year 9 with resources

The lessons and sequences in this program of learning are designed to allow students to understand and use geometrical representations, applying concepts including proportion, scale factors, similarity and connections (networks) to represent real-life objects, spaces, situations and concepts.

### Introduction

Geometrical representations (DOCX 155 KB)

### Lesson 1 – whales and chihuahuas

### Lesson 2 – scaled copies

### Lesson 3 – similar figures in art

### Lesson 4 – how many angles?

### Lesson 5 – corresponding sides and angles

### Lesson 6 – scale factor

### Lesson 7 – scale factor in similar triangles

### Lesson 8 – movie magic

### Lesson 9 – maps and scale

### Lesson 10 – comparing representations

### Lesson 11 – scale factor and area

A 16-lesson unit for Year 9 with resources

This program of learning addresses content from the focus areas Trigonometry A, Linear relationships A, Numbers of any magnitude, as well as Path focus areas Linear relationships C, and Indices C. The lessons and sequences in this program of learning are designed to allow students to use the properties of right-angled triangles to solve a range of geometrical, measurement and real-world problems.

### Introduction

Working with triangles (DOCX 162 KB)

### Lesson 1 – 45-degree angles

### Lesson 2 – larger and smaller angles

### Lesson 3 – the tangent ratio

### Lesson 4 – the sine and cosine ratios

### Lesson 5 – I lost my calculator

I lost my calculator (DOCX 102 KB)

### Lesson 6 – finding missing sides

### Lesson 7 – significant distances

### Lesson 8 – mapping the classroom

Mapping the classroom (DOCX 7.1 MB)

### Lesson 9 – surd is the word

Surd is the word (DOCX 125 KB)

### Lesson 10 – distances

### Lesson 11 – midpoints

### Lesson 12 – trigonometry for navigation

Trigonometry for navigation (DOCX 1.2 MB)

### Lesson 13 – how far around is one degree?

### Lesson 14 – how steep is too steep?

### Lesson 15 – slopes as gradients

Slopes as gradients (DOCX 1.9 MB)

### Lesson 16 – gradients in the Cartesian plane

An 18-lesson unit for Year 9 with resources

This program of learning addresses content from the focus areas of Area and surface area A, Volume A, Algebraic techniques A, Equations A, Numbers of any magnitude, as well as Path focus areas Area and surface area B, Volume B and Equations C. The lessons and sequences in this program of learning are designed to allow students to tie together the big ideas across algebra, number and geometry and measurement and will build on student knowledge and understanding of area to develop and apply formulas for the surface area of prisms and cylinders.

### Introduction

Prisms and cylinders (DOCX 167 KB)

### Lesson 1 – visualising nets

### Lesson 2 – leftover challenge

Leftover challenge (DOCX 186 KB)

### Lesson 3 – cube houses

### Lesson 4 – beyond the surface

Beyond the surface (DOCX 327 KB)

### Lesson 5 – A4 cylinders

### Lesson 6 – margin for errors

### Lesson 7 – under pressure

### Lesson 8 – how do animals keep cools

How do animals keep cools (DOCX 2.4 MB)

### Lesson 9 – deep dive

### Lesson 10 – exploring unknowns

### Lesson 11 – the secrets of pyramids

The secrets of pyramids (DOCX 1.1 MB)

### Lesson 12 – spheres the thing

### Lesson 13 – cup or cone

### Lesson 14 – concrete dreams

### Lesson 15 – perfect packaging

Perfect packaging (DOCX 294 KB)

### Lesson 16 – tank it to the limit

Tank it to the limit (DOCX 1.2 MB)

### Lesson 17 – icing on the cake

Icing on the cake (DOCX 96 KB)

### Lesson 18 – to the beat of your own drum

A 9-lesson unit for Year 9 with resources

This program of learning addresses content from the Core focus areas of Indices A and Numbers of any magnitude as well as Path focus areas of Indices B and Indices C. The lessons and sequences in this program of learning are designed to allow students to explore the index laws and apply them both numerically and algebraically.

### Introduction

### Lesson 1 – invaluable indices

### Lesson 2 – mathematical shorthand

### Lesson 3 – how many trips to the moon?

How many trips to the moon? (DOCX 124 KB)

### Lesson 4 – growing with power

Growing with power (DOCX 194 KB)

### Lesson 5 – let's power down

### Lesson 6 – reflecting on practice

Reflecting on practice (DOCX 874 KB)

### Lesson 7 – mathematical shorthand continued

### Lesson 8 – half-life

### Lesson 9 – that's ab-surd!

An 11-lesson unit for Year 9 with resources

This program of learning addresses content from the focus areas of Financial mathematics A and Equations A. The lessons and sequences in this program of learning are designed to allow students to explore number and algebra skills and build students’ knowledge and understanding of earning and spending money by relating the concepts to a real world context.

### Introduction

Financial mathematics (DOCX 148 KB)

### Lesson 1 – how much will I earn

### Lesson 2 – what should I do when I am older

What should I do when I am older (DOCX 102 KB)

### Lesson 3 – how much will it cost

- How much will it cost? (DOCX 2.33 MB)
- How much will it cost? (PPTX 662 KB)
- How much will it cost? (XLSX 42 KB)

### Lesson 4 – what more pay!

### Lesson 5 – I need more money

I need more money (DOCX 516 KB)