Mathematics 7–10 units and assessments

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

These units are currently under review, and the updated version will be uploaded once the review is complete.

Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus (2022) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2025.

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 is now available on the Lesson Library (staff only).

This program of learning is now available on the Lesson Library (staff only).

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

Assessment 5

The following assessment is designed to assess the outcomes from Unit 9 – shape and skew of the Department of Education's sample Stage 4 Year 8 scope and sequence (DOCX 283 KB).

Assessment 6

The following assessment is designed to assess the outcomes from Unit 11 – geometrical relationships of the Department of Education's sample Stage 4 Year 8 scope and sequence (DOCX 283 KB).

Assessment 7

The following assessment is designed to assess the outcomes from Unit 12 – further multiplicative thinking and Unit 13 – ratios and rates of the Department of Education's sample Stage 4 Year 8 scope and sequence (DOCX 283 KB).

Year 8 – assessment – question bank (DOCX 5.7 MB)

Assessment 8

The following assessment is designed to assess the outcomes from Unit 14 – analysing patterns and Unit 16 – constructing cylinders of the Department of Education's sample Stage 4 Year 8 scope and sequence (DOCX 283 KB).

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

This program of learning is now available on the Lesson Library (staff only).

This program of learning is now available on the Lesson Library (staff only).

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 is now available on the Lesson Library (staff only).

This program of learning is now available on the Lesson Library (staff only).

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).

Assessment 7

The following assessment is designed to assess the outcomes from Unit 12 –investigating parabolas of the Department of Education's sample Stage 5 Year 10 scope and sequence (DOCX 266 KB)

Assessment 8

The following assessment is designed to assess the outcomes from Unit 13 –bivariate relationships 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 is now available on the Lesson Library (staff only).

This program of learning is now available on the Lesson Library (staff only).

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