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).

Year 7 – 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).

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).

Year 7– Portfolio (DOCX 6.2 MB)

Assessment 4

This Pirozzo grid style assessment is designed to assess the outcomes from Unit 6 – triangles and quadrilaterals and Unit 7 – length and area 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.

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.

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.

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

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

Lesson 9 – which numbers go here?

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)

Lesson 18 – inverse journeys – multiplying

Lesson 19 – make it clear

Make it clear (DOCX 131 KB)

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

Two of a kind (DOCX 5.9 MB)

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

Getting around (DOCX 522 KB)

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

Escher llations (DOCX 567 KB)

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

This program of learning addresses content from the focus area of Volume. The lessons and sequences in this program of learning are designed to allow students to describe, represent and calculate the volume of prisms. As well as convert between metric units of volume and capacity to solve problems involving right prisms.

Introduction

Constructing prisms – unit (DOCX 341 KB)

Lesson 1 – different views

Lesson 2 – cross-sections

Cross-sections (DOCX 659 KB)

Lesson 3 – multiple cubes

Lesson 4 – a loaf of bread

Lesson 5 – finding volumes

Lesson 6 – volume and capacity

Lesson 7 – fish in captivity

Lesson 8 – fuel

    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 (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

    Survival of the fittest (DOCX 4.27 MB)

    This program of learning addresses content from the focus areas of Equations and Right-angled triangles (Pythagoras’ theorem). The lessons and sequences in this program of learning are designed to allow students to explore solving quadratic equations, justifying whether a triangle is a right-angled triangle, and finding the lengths of unknown sides in right-angled triangles.

    Introduction

    Investigating triangles – unit of work (DOCX 343 KB)

    Lesson 1 – ways of working (equations)

    Lesson 2 – quadratic equations

    Lesson 3 – Pythagoras' theorem

    Lesson 4 – almost exactly

    Lesson 5 – hole in one

    Lesson 6 – what's square

    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 angles between lines, including those in transversals on sets of parallel lines and those within known shapes.

    Introduction

    Geometrical relationships (DOCX 340 KB)

    Lesson 1 – draw it out

    Lesson 2 – supplementing seesaws

    Lesson 3 – the cake thief

    Lesson 4 – complements to you

    Lesson 5 – the corresponding connection

    Lesson 6 – alternate views

    Lesson 7 – come inside

    Lesson 8 – all in this together

    This program of learning addresses content from the focus areas of Fractions, decimals and percentages, indices and algebraic techniques. The lessons and sequences in this program of learning are designed to allow students to explore problems involving percentages, including GST, factorisation, and expansion of algebraic expressions and use index notation to establish the index laws.

    This program of learning addresses content from the focus area of ratios and rates. The lessons and sequences in this program of learning are designed to allow students to explore recognising, simplifying, and solving problems that involve ratios and rates, as well as interpreting and constructing distance–time graphs.

    This program of learning addresses content from the focus area of analysing patterns. The lessons and sequences in this program of learning are designed to allow students to explore plotting and identifying points on the Cartesian plane, graphing linear relationships on the Cartesian plane and solving linear equations using graphical techniques.

    Introduction

    Analysing patterns – unit (DOCX 337 KB)

    Lesson 1 – plotting points

    Lesson 2 – describing geometrical patterns

    Lesson 3 – describing linear relationships

    Lesson 4 – linear equations

    Lesson 5 – solving equations

    Lesson 6 – comparing straight-line graphs

    Lesson 7 – point of intersection

    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).

    Year 9 – 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).

    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 5 year 9 scope and sequence (DOCX 258 KB).

    Year 9 – How can we provide for tomorrows healthcare? (DOCX 440.2 KB)

    Assessment 4

    This investigation-style assessment is designed to assess the outcomes from Unit 7 – making predictions and Unit 8 – making decisions of the Department of Education's sample stage 5 year 9 scope and sequence (DOCX 258 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.

    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

    Distances (DOCX 647 MB)

    Lesson 11 – midpoints

    Midpoints (DOCX 510 KB)

    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

    Gradients in the Cartesian plane (DOCX 298 KB)

    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.

    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.

    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.

    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.

    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

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

    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

    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.

    Assessment 5

    The following task is a sample test designed to complement the Stage 5 department unit of learning ‘Unit 9 – surveying’ of the Department of Education’s sample Stage 5 Year 10 scope and sequence (DOCX 266 KB).

    Assessment 6

    The following task is a sample test designed to complement the Stage 5 department unit of learning ‘Unit 11 – applying exponentials’ of the Department of Education’s sample Stage 5 Year 10 scope and sequence (DOCX 266 KB).

    This program of learning addresses content from the focus areas of Trigonometry B and C, Non-linear relationships C and Properties of geometrical figures A. The lessons and sequences in this program of learning are designed to allow students to explore mapping and navigation of the world using right-angled and non-right angled trigonometry, circles and similar figures.

    Introduction

    Surveying – unit of work (DOCX 358 KB)

    Lesson 1 – traverse survey

    Lesson 2 – approximating distance

    Lesson 3 – river crossing

    Lesson 4 – slope seekers

    Lesson 5 – the great pyramid

    Lesson 6 – getting my bearings

    Lesson 7 – lost in the clouds

    Lesson 8 – bearing it all

    Lesson 9 – going around in circles

    Lesson 10 – GPS positioning

    Lesson 11 – sine of the apostle

    Lesson 12 – tracking erosion

    Lesson 13 – cosine rules

    Lesson 14 – cos it's the angle

    Lesson 15 – radial survey

    This program of learning addresses content from the focus areas of Algebraic techniques A, Equations A, Algebraic techniques B, and Equations C. The lessons and sequences in this program of learning are designed to allow students to explore operating with algebraic expressions and equations.

    Introduction

    Expressions and equations – unit of work (DOCX 351 KB)

    Lesson 1 – the power of one

    Lesson 2 – multiplying multiple ways

    Lesson 3 – divide and conquer

    Lesson 4 – expand your mind

    Lesson 5 – factor it in

    Lesson 6 – age old question

    Lesson 7 – packing then unpacking

    Lesson 8 – does it matter where you start

    This program of learning addresses content from the focus areas of Financial Mathematics B and Non-linear relationships A, B and C. The lessons and sequences in this program of learning are designed to allow students to explore exponential functions in a variety of contexts, including compound interest and depreciation.

    Introduction

    Applying exponentials – unit (DOCX 353 KB)

    Lesson 1 – simple and compound interest

    Lesson 2 – bad investments

    Lesson 3 – Euler’s number

    Lesson 4 – invasive species

    Lesson 5 – exponential marbleslides

    Lesson 6 – free falling

    Free falling (DOCX 347 KB)

    Lesson 7 – population clock

    This program of learning addresses content from the focus areas of Algebraic techniques A, B and C, Non-linear relationships A, B and C and Equations B and C. The lessons and sequences in this program of learning are designed to allow students to explore expanding, factorising and solving quadratics, as well as graphing parabolas.

    Introduction

    Investigating parabolas – unit (DOCX 353 KB)

    Lesson 1 – what’s that graph

    Lesson 2 – features of a parabola

    Lesson 3 – modelling quadratics

    Lesson 4 – area for expansion

    Lesson 5 – difference of two squares

    Lesson 6 – parabola marbleslides

    Parabola marbleslides (DOCX 337 KB)

    Lesson 7 – factorising monic quadratics

    Lesson 8 – factorising non-monics

    Lesson 9 – solving quadratic equations

    Lesson 10 – sketching parabolas

    Lesson 11 – completing the square

    Lesson 12 – can't factorise, no problem

    Lesson 13 – discriminating with the discriminant

    Lesson 14 – problem solving quadratics

    This program of learning addresses content from the focus areas of Data Analysis B, Data Analysis C and Linear Relationships B. The lessons and sequences in this program of learning are designed to allow students to explore bivariate data and correlation.

    Introduction

    Bivariate relationships – unit (DOCX 344 KB)

    Lesson 1 –introduction to scatter plots

    Lesson 2 – flame vs time

    Lesson 3 – lines of best fit

    Lesson 4 – causation

    Lesson 5 – doll bungee

    Doll bungee (DOCX 4.5 MB)

    Lesson 6 – where are the bees?

    Lesson 7 – mobile phone battery

    Mobile phone battery (DOCX 335 KB)

    Lesson 8 – methods of sampling

    Methods of sampling (DOCX 1.7 MB)

    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 (DOCX 355 KB)

    Lesson 1 – graphing stories

    Graphing stories (DOCX 4.93 MB)

    Graphing stories slide deck (PPTX 1.3 MB)

    Lesson 2 – graph-ity falls

    Graph-ity falls (DOCX 5.14 MB)

    Graph-ity falls slide deck (PPTX 1.86 MB)

    Lesson 3 – direct variation

    Direct variation (DOCX 7.8 MB)

    Direct variation slide deck (PPTX 1.8 MB)

    Lesson 4 – inverse variation

    Inverse variation (DOCX 6.98 MB)

    Inverse variation slide deck (PPTX 2 MB)

    Lesson 5 – para-solar

    Para-solar (DOCX 7.84 MB)

    Para-solar slide deck (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 slide deck (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? slide deck (PPTX 1.48 MB)

    Lesson 10 – logging those sounds

    Logging those sounds (DOCX 6.73 MB)

    Logging those sounds slide deck (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 slide deck (PPTX 3.22 MB)

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