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 2 – representing numbers, Unit 3 – additive strategies and Unit 4 – 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
A 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
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
An 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)