# Mathematics 7–10 units and assessments

Sample units and assessments to support teachers of Years 7–10 implementing the Mathematics K–10 Syllabus (2022).

## Syllabus

The Mathematics K–10 syllabus (2022) 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).

## Stage 4

These units and assessments for Year 7 represent 'one way' of designing teaching and learning experiences.

#### 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 (DOCX 283 KB).

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 (DOCX 283 KB).

- Stage 4 – question bank (DOCX 658 KB)
- Stage 4 – annotated sample responses (DOCX 862 KB)
- Stage 4 – sample class test (DOCX 586 KB)

#### Assessment 3

This portfolio style of assessment is designed to assess the outcomes from Unit 3 – representing numbers, Unit 4 – additive strategies and Unit 5 – multiplicative strategies of the Department of Education's sample Stage 4 Year 7 scope and sequence (DOCX 283 KB).

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 decisions. Students will explore different ways of representing data and make decisions 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 zero

#### 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 – make it clear

An 11-lesson unit for Year 7 with resources.

This program of learning addresses content from the focus areas of Angle relationships and Properties of geometrical figures. The lessons and sequences in this program of learning are designed to allow students to explore triangles and quadrilaterals, developing the language, knowledge and understanding to be able to classify these 2-dimensional shapes according to their geometrical properties and apply this to meaningfully make connections across topics and concepts.

#### Introduction

Triangles and quadrilaterals (DOCX 4.2 MB)

#### Lesson 1 – strike a pose

#### Lesson 2 – is that a triangle?

#### Lesson 3 – I see triangles

#### Lesson 4 – throwing light on the exteriors

#### Lesson 5 – unravelling tessellations

#### Lesson 6 – sides and angles united

#### Lesson 7 – diamonds of geometry

#### Lesson 8 – two of a kind

#### Lesson 9 – tackling trapeziums

#### Lesson 10 – let's go fly a kite

#### Lesson 11 – quadrilateral quest

This program of learning addresses content from the focus areas of fractions, decimals and percentages, algebraic techniques, equations, length and area.

The lessons and sequences in this program of learning are designed to allow students to explore the spatial properties of 2-dimensional figures, focusing specifically on length and area, as well as the usefulness of related numerical and algebraic tools.

#### Introduction

Length and area – unit of work (DOCX 364 KB)

#### Lesson 1 – getting around

#### Lesson 2 – express yourself

#### Lesson 3 – boundary battle

#### Lesson 4 – uncovering shape secrets

#### Lesson 5 – perimeter pals

#### Lesson 6 – enough room for us all

#### Lesson 7 – are all areas created equal

#### Lesson 8 – which quadrat

#### Lesson 9 – which way is up

#### Lesson 10 – escher llations

#### Lesson 11 – a slant on solar energy

#### Lesson 12 – too clever by half

#### Lesson 13 – quickly counting kites

#### Lesson 14 – property trap

#### Lesson 15 – growing pains

#### Lesson 16 – it's a sign

These units and assessments for Year 8 represent 'one way' of designing teaching and learning experiences.

This program of learning addresses content from the focus areas of Data classification and visualisation and Data analysis. The lessons and sequences in this program of learning are designed to allow students to explore how to analyse frequency distribution graphs using measures of centre and spread, and shape and skew of a graph.

#### Introduction

Shape and skew – unit of work (DOCX 5.89 MB)

#### Lesson 1 – broccoli soup

#### Lesson 2 – goal-free soccer

#### Lesson 3 – the big sick

#### Lesson 4 – shooting hoops

#### Lesson 5 – footy fit

#### Lesson 6 – picture perfect

#### Lesson 7 – pass it on graph style

#### Lesson 8 – wisdom of the crowd

#### Lesson 9 – the best centre

#### Lesson 10 – random samples

#### Lesson 11 – survival of the fittest

## Stage 5

These units and assessments for Year 9 represent 'one way' of designing teaching and learning experiences.

#### 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 (DOCX 258 KB).

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 (DOCX 258 KB).

- Stage 5 – question bank (DOCX 797 KB)
- Stage 5 – annotated sample responses (DOCX 2.2 MB)
- Stage 5 – sample class test (DOCX 322 KB)

#### Assessment 3

This presentation style assessment is designed to assess the outcomes from Unit 5 – financial mathematics and Unit 6 – constant rates of change of the Department of Education's sample stage year 9 scope and sequence (DOCX 258 KB).

Stage 5 – How can we provide for tomorrows healthcare? (DOCX 440.2 KB)

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 cool?

How do animals keep cool? (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 – sphere's 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)

#### Lesson 6 – percentage of my earnings

#### Lesson 7 – is that fair?

#### Lesson 8 – the secrets to keeping more money

#### Lesson 9 – how can I get my money back

#### Lesson 10 – watch money grow

#### Lesson 11 – now or later

A 14-lesson unit for Year 9 with resources.

This program of learning addresses content from the focus areas of Linear relationships A, Linear relationships B and Equations A, as well as Path focus areas Variation and rates of change A, Equations C and Linear Relationships C. The lessons and sequences in this program of learning are designed to allow students to explore the representations of linear relationships and how they are used to model situations and solve problems.

#### Introduction

Constant rates of change (DOCX 6.3 MB)

#### Lesson 1 – journey to linearity

Journey to linearity (DOCX 7.7 MB)

#### Lesson 2 – money matters

#### Lesson 3 – slope-a-palooza

#### Lesson 4 – how efficient is my car?

#### Lesson 5 – holiday money

#### Lesson 6 – yubercept

#### Lesson 7 – what’s the line?

#### Lesson 8 – line it up

#### Lesson 9 – cutting through lines

#### Lesson 10 – graphing general mayhem

#### Lesson 11 – it’s getting hot in here

#### Lesson 12 – tortoise and the hare

Tortoise and the hare (DOCX 7.8 MB)

#### Lesson 13 – simultaneous shopping

#### Lesson 14 – sums and differences

This program of learning addresses content from the focus area of Probability. The lessons and sequences in this program of learning are designed to allow students to explore multi-stage events and simulations to make predictions.

#### Introduction

Making predictions – unit of work (DOCX 348 KB)

#### Lesson 1 – prediction palette

#### Lesson 2 – the skunk game

#### Lesson 3 – random relay

#### Lesson 4 – toadal eclipse

#### Lesson 5 – Monty Hall

#### Lesson 6 – demystifying the birthday paradox

- Demystifying the birthday paradox (DOCX 338 KB)
- Demystifying the birthday paradox presentation (PPTX 1227 KB)

#### Lesson 7 – what’s on the packet is in the packet

- What’s on the packet is in the packet (DOCX 1985 KB)
- What’s on the packet is in the packet presentation (PPTX 10346 KB)

#### Lesson 8 – tables 2 ways

#### Lesson 9 – home ground advantage

This program of learning addresses content from the core focus area of Data analysis A. The lessons and sequences in this program of learning are designed to allow students to explore standard deviation, the 5-number summary and box plots to help make informed decisions about the data.

#### Introduction

Making decisions – unit of work (DOCX 4.38 MB)

#### Lesson 1 – revisiting the mean

Revisiting the mean (DOCX 9.83 MB)

#### Lesson 2 – average from the average

#### Lesson 3 – who gets to drive?

#### Lesson 4 – four equal groups

#### Lesson 5 – IQR and boxplots

#### Lesson 6 – balls and boxes

#### Lesson 7 – distracted drivers

- Distracted drivers (DOCX 4.39 MB)
- Distracted drivers spreadsheet part 1 (XLSM 48 KB)
- Distracted drivers spreadsheet part 2 (XLSM 57 KB)

#### Lesson 8 – temperature's rising

#### Lesson 9 – what is the data telling us

These units and assessments for Year 10 represent 'one way' of designing teaching and learning experiences.

This program of learning addresses content from the Path focus areas of Variation and rates of change A, Variation and rates of change B, Non-linear relationships C, and Logarithms. The lessons and sequences in this program of learning are designed to allow students to explore applications of mathematics in science. Students will explore rates of change, non-linear relationships, and logarithms in real world contexts.

This Year 10 unit is designed to be an elective unit to extend students that have completed the Core content within Stage 5. All lessons incorporate Path content and assume students are confident with related Core content.

#### Introduction

Maths in science elective – unit of learning (DOCX 355 KB)

#### Lesson 1 – graphing stories

Graphing stories (DOCX 4.93 MB)

Graphing stories presentation (PPTX 1.3 MB)

#### Lesson 2 – graph-ity falls

Graph-ity falls (DOCX 5.14 MB)

Graph-ity falls presentation (PPTX 1.86 MB)

#### Lesson 3 – direct variation

Direct variation (DOCX 7.8 MB)

Direct variation presentation (PPTX 1.8 MB)

#### Lesson 4 – inverse variation

Inverse variation (DOCX 6.98 MB)

Inverse variation presentation (PPTX 2 MB)

#### Lesson 5 – para-solar

Para-solar presentation (PPTX 2.61 MB)

#### Lesson 6 – in a galaxy far, far away

In a galaxy far, far away (DOCX 5.85 MB)

#### Lesson 7 – breeding like rabbits

Breeding like rabbits (DOCX 7.29 MB)

#### Lesson 8 – why vampires don’t exist

Why vampires don’t exist (DOCX 8.26 MB)

Why vampires don’t exist presentation (PPTX 1.51 MB)

#### Lesson 9 – where’s the pHun in that?

Where’s the pHun in that? (DOCX 7.3 MB)

Where’s the pHun in that? presentation (PPTX 1.48 MB)

#### Lesson 10 – logging those sounds

Logging those sounds (DOCX 6.73 MB)

Logging those sounds presentation (PPTX 2.53 MB)

#### Lesson 11 – one small step IS one giant leap

One small step IS one giant leap (DOCX 5.86 MB)

One small step IS one giant leap presentation (PPTX 3.22 MB)