Browse class notes, worksheets, summaries, videos and activities organised by number and algebra topic. To suggest a resource or report a broken link, please use the contact form.

Whole Numbers

Addition and Subtraction

–Y7 Whole Numbers – 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Whole Number addition and subtraction (~13-minute video) by Darren Smyth (https://maffsguru.com)

Multiplication and Division

–Y7 Whole Numbers – 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Whole number multiplication and division (~17 minute video) by Darren Smyth (https://maffsguru.com)

Rounding

–Y7 Whole Numbers – 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Estimating and Rounding (~14 minute video) by Darren Smyth (https://maffsguru.com)

Order of Operations

Introduction to order of operations ↗ — Khan Academy video

–Y7 Whole Numbers – 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) – Order of Operations(~13 minute video) by Darren Smyth (https://maffsguru.com) (MathsTeachersOnly.com)

Investigations and further practice

The laws of arithmetic and their use in algebra — AMSI — Year 7 teacher and student resources.

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Place value practice

Place Value — Maths Genie — Year 7 revision; UK-based booklet. Solutions.

Number Properties and Patterns

Y8 Integers – 21 pages of class notes and handwritten solutions (MathsTeachersOnly.com)
Number Properties (16-minute video) by Darren Smyth (https://maffsguru.com).
Prime Factorisation Four lessons explore prime factorisation and how it can be used to solve problems related to the properties of numbers shared by reSolve
T h e Fundamental Theorem of Arithmetic –Video(3:52)An introductory video from Khan Academy. Covers primes , composites, prime factorisation and a thorough explanation of the fundamental theorem of arithmetic.

Highest (or Greatest) Common Factor (HCF (or GCF)) and Lowest Common Multiple (LCM)

HCF &LCM notes and videos (https://www.onlinemathlearning.com)
HCF and LCM(~17 minute video) by Darren Smyth (https://maffsguru.com)
HCF and LCM methods (https://www.onlinemath4all.com)

Divisibility Tests

Divisibility Rules summary (https://www.mathsisfun.com) Divisibility Rules for numbers 2-12, 15, 18, 25 summary ( https://www.onlinemath4all.com/)

Prime decomposition

Prime & Composite Numbers Song: – lyrics included by Numberock
Prime Numbers (~7 minute video) by Darren Smyth (https://maffsguru.com)
Prime Decomposition (10-minute video) by Darren Smyth (https://maffsguru.com)

Squares and Square Roots

Squares and square roots (~13 minute video) by Darren Smyth (https://maffsguru.com)

Investigations and further practice

Factors and Multiples Puzzle — NRICH — Years 7–8; printable puzzle, student solutions and teacher guidance.

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Integers

Y8 Integers – 21 pages of class notes and handwritten solutions (MathsTeachersOnly.com)
Number lines- an online worksheet generator– Create worksheets with various scales on number lines, found at TheMathWorksheetsite.com
Integers – a playlist of 10 short videos on how to add, subtract, multiply and divide integers by Rex Boggs.
Negative Numbers (11-minute video) by Darren Smyth (https://maffsguru.com)

Addition and subtraction of integers

–Y8 Integers: Adding and Subtracting -Worksheet (MathsTeachersOnly.com) –Whole number addition and subtraction (~11 minute video) by Darren Smyth (https://maffsguru.com)

Multiplication and Division of Integers

Whole number multiplication and division (17 minute video) by Darren Smyth (https://maffsguru.com)

Investigations and further practice

Real-Life Negatives — Corbettmaths — Years 7–8; UK-based practice in temperature, elevations and directed numbers. Answers.

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Fractions and Percentages

Representing and comparing quantities (original resource unavailable) -activities designed to develop students’ understanding of fractions, decimals, percentages and standard form. Teacher resources for these activities are also included. (NRICH Maths).
Fractions, decimals and percentages- a playlist of 9 short videos on how to to compare fractions and compare decimals, and to convert between fractions, decimals and percentages by Rex Boggs.
A free online interactive percentage game that involves planning a park with a range of different features such as grass, water, woodland, flowers and playgrounds. Students read what percentage of the park each feature should cover and try to make it happen. Then they are asked to achieve the same goal using decimals.
Y8 Fractions, Decimals and Percentages -13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Fractions

What are fractions?(17 minute video) by Darren Smyth (https://maffsguru.com)

Equivalent fractions

Equivalent and simplified fractions(13 minute video) by Darren Smyth (https://maffsguru.com)

Mixed Numbers

Mixed numbers (16 minute video) by Darren Smyth (https://maffsguru.com)

Fraction Walls

Fraction Wall manipulative by Jonathan Hall (https://mathsbot.com)

Adding fractions

Adding fractions with different denominators ↗ — Khan Academy video

Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here. Free worksheet “Fraction-Addition and Subtraction” -adding subtracting fractions found at Mathster.com. More free worksheets on many other topics can also be found here.

Subtracting fractions

Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here.

Multiplying fractions

Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here.

Dividing fractions

Division of fractions lesson ( https://www.mathsisfun.com/) Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here.

Percentages

Which coupon should I use? Dan Meyer’s Three-Act Maths task

Investigations and further practice

Matching Fractions, Decimals and Percentages — NRICH — Years 7–8; matching activity with printable card sets and teacher guidance.
Percentage Change — Corbettmaths — Years 8–10; UK-based percentage increase and decrease practice. Answers.

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Decimals

Operations with decimals

Multiplying decimals ↗ — Khan Academy video

Dividing by a multi-digit decimal ↗ — Khan Academy video

Adding and subtracting decimals (~10 minute video) by Darren Smyth (https://maffsguru.com)

Investigations and further practice

Ordering Decimals — Corbettmaths — Years 7–8; worksheet (PDF).
Rounding Decimal Places — Corbettmaths — Years 7–8; worksheet (PDF). Answers.

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Ratios and Rates

Investigations and further practice

Rates and Ratios — AMSI — Years 8–9; 20-page teacher guide (PDF).
Mixing Lemonade — NRICH — Years 7–8; compare mixtures using proportional reasoning, with teacher guidance and student solutions.
Ratio Inquiry — Inquiry Maths — Years 7–9; an inquiry prompt with classroom approaches and supporting resources.

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Financial Maths

Recursion and Financial Maths Review for VCE Further Maths (40 min video)-An overview of the key skills required for Recurrence & Financial Modelling, covering some examples from past VCAA papers.

Recursion and Financial Modelling Summary (pdf) for VCE Further Maths from the Maths dept of St Leonard’s College.

Investigations and further practice

Consumer Arithmetic — AMSI — Year 9 teacher guide (PDF); financial calculations and percentage applications.

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Indices

Index laws

Multiplying and dividing powers with integer indices ↗ — Khan Academy video

Scientific notation

Scientific notation examples ↗ — Khan Academy video

What is standard form? by Pythagoras and That (UK site)

Investigations and further practice

Negative and Fractional Indices — Corbettmaths — Years 9–10A; UK-based practice questions (PDF). Answers.
Surds — AMSI — Years 9–10; teacher guide (PDF) on irrational numbers and surd calculations.

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Sequences and Series

Arithmetic and geometric sequences

Introduction to arithmetic sequences ↗ — Khan Academy video

Introduction to geometric sequences ↗ — Khan Academy video

-A great activity for teaching arithmetic sequences- “Expressing Number Patterns” by Bob Lochel found at Amplify Classroom (formerly Desmos Classroom) –Sequences and Series – A pdf guide for teachers: Principal author: Peter Brown (http://amsi.org.au/ESA_ Senior_Years/seniors_years. html)

Investigations and further practice

Growing Surprises — NRICH — Years 7–9; investigate connections between linear and quadratic patterns.
nth Term — Corbettmaths — Years 8–10; UK-based sequence practice (PDF). Answers.

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Number and Proof

Introduction to two-column algebra and geometry proofs free downloads (Introducing Two-Column Geometry Proofs: A Different Approach -post by mathgiraffe.com)

Direct proof

Two pages of notes including examples and exercises contributed to the Mathcentre Community Project by Katy Dobson, University of Leeds (http://www.mathcentre.ac.uk/students/topics/proofs/direct/)

Proof by induction

Two pages of notes including examples and exercises contributed to the Mathcentre Community Project by Katy Dobson, University of Leeds (http://www.mathcentre.ac.uk/students/topics/proofs/proof-by-induction/) Two pages of further examples contributed to the Mathcentre Community Project by Katy Dobson, University of Leeds (http://www.mathcentre.ac.uk/students/topics/proofs/proof-by-induction/)

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Algebraic Expressions

–Y9 Algebra 24- pages of fill-in class notes with handwritten solutions (MathsTeachersOnly.com) –Y10 Quadratic Equations -15 pages of fill-in class notes with handwritten solutions (MathsTeachersOnly.com) –Y10_10A Quadratics: One-page summary for factorising quadratic expressions and solving quadratic equations (MathsTeachersOnly.com) -A hands-on activity on how to teach collecting like terms using reversible (white/red) unit squares and strips-Ppt (13 slides) –Quadratic Factorisation and Expansion worksheet -18 practice questions (MathsTeachersOnly.com)

The language of algebra

–Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Substituting and evaluating

–Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Equivalent expressions

–Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Like terms

Introduction to collecting like terms ↗ — Khan Academy video

–Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Adding and subtracting terms

–Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Multiplying and dividing terms

–Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Expanding expressions

–Binomial expansions A worksheet of 12 practice questions on binomial expansions including answers (MathsTeachersOnly.com) –Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Year 9 Algebra: Harder Expansions – 3-page fill-in worksheet with harder expansion problems involving binomial and trinomial factors. Solutions included

Expanding binomial products

–Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Expanding perfect squares

–Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Factorising expressions by taking out common factors

–Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) –Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Factorising using the difference of perfect squares

–Factorising using DOPS– see the first 3:48 mins of the 8:19 min Vimeo video “Factorising quadratics” by Bryn Humberstone –Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Factorising by grouping

–Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Factorising quadratic trinomials of the form x2+bx+c

-Factorising using the cross-method- see “Factorising quadratics” by Bryn Humberstone (after 3:49 min) (Vimeo video 8:19 mins) –Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Factorising quadratic trinomials of the form ax2+bx+c

-see “Factorising quadratics” by Bryn Humberstone (after 3:49 min mark) (Vimeo video 8:19 mins) –Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Factorising quadratic trinomials by completing the square

–Completing the Square-Geometrically– a 4-page worksheet with handwritten solutions providing a geometrical explanation of ‘completing the square’ (MathsTeachersOnly.com) –Factorising quadratics by completing the square -video (9:46min) by Bryn Humberstone –Factorising by Completing the Square (~19 minute video) by Darren Smyth (https://maffsguru.com)

Simplifying algebraic fractions

–Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Refer to Dan Meyer’s blog for a way to introduce simplifying algebraic fractions. –Y10_10A Algebraic Fractions Worksheet– A one-page worksheet of 6 practice questions, including answers, involving adding, subtracting, multiplying and dividing algebraic fractions.(MathsTeachersOnly.com)

Multiplying and dividing algebraic fractions

–Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Adding and subtracting algebraic fractions

–Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Solving equations with algebraic fractions

–Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Investigations and further practice

Polynomials — AMSI TIMES — Years 9–10A; teacher guide (PDF).
Polynomials — AMSI Senior Years — Years 11–12; a separate 43-page senior teacher guide (PDF).

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Solving Linear Equations and Inequations

Two-step equations and inequalities

Introduction to two-step equations ↗ — Khan Academy video

Solving two-step inequalities ↗ — Khan Academy video

Linear equations resources which include problems, games and articles found at NRICH. An article on the method of determining the coefficients for complex equations of chemical reactions found at NRICH

Formulas and relationships

Formulas module by AMSI. A list of formulae are also listed at the end of this TIMES module.

Investigations and further practice

Changing the Subject — Corbettmaths — Years 8–10A; UK-based algebra practice (PDF). Answers.
Simultaneous Equations — Corbettmaths — Years 9–10; UK-based practice questions (PDF). Answers.
Inequalities — Corbettmaths — Years 8–10; UK-based practice questions (PDF). Answers.

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Solving Quadratic Equations and Inequations

-101 uses of a quadratic equation: Part 1 and Part II by Plus Magazine (plus.maths.org)

Solving quadratic equations by factorising

–Year 10 Quadratic Equations – 15-pages fill-in class including hand-written solutions. (MathsTeachersOnly.com)

Solving quadratic equations by completing the square

Year 10 Quadratic Equations – 15-pages fill-in class including hand-written solutions. (MathsTeachersOnly.com) –Solving quadratics by completing the square ~12 min video by Darren Smyth –Completing the Square-Geometrically– a 4-page worksheet with handwritten solutions providing a geometrical explanation of ‘completing the square’.(MathsTeachersOnly.com)

Solving quadratic equations by applying the quadratic formula.

The quadratic formula ↗ — Khan Academy video

–Year 10 Quadratic Equations – 15-pages fill-in class including hand-written solutions.

Solving quadratic inequations

–Year 10 Quadratic Equations – 15-pages fill-in class including hand-written solutions. (MathsTeachersOnly.com) – Solving Quadratic Inequations-video(2:36) by Freda Armstrong from Maths Turning Point

See also ALGEBRAIC EXPRESSIONS tab for expanding and factorising quadratics

Investigations and further practice

Quadratic Equations — AMSI — Years 9–10A; teacher guide (PDF), complementing the original MathsTeachersOnly notes.

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Exponentials and Logarithms

Logarithm laws

Introduction to logarithm laws — part 1 ↗ — Khan Academy video

Introduction to logarithm laws — part 2 ↗ — Khan Academy video

–A summary of Log laws and traps to avoid can be downloaded from Maths Turning Point.

Exponentials and Logarithms

Introduction to logarithms ↗ — Khan Academy video

Exponential and logarithms (original resource unavailable) –sample class notes and exercises by David Treeby (https://www.t2maths.com.au)
Exponential and logarithms (original resource unavailable) –solutions to sample class notes and exercises by David Treeby (https://www.t2maths.com.au)

Investigations and further practice

Logarithms — mathcentre — Years 10A–12; notes, examples and exercises (PDF).

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Matrices

Summary Notes on Matrices pdf– A three-page summary covering all the concepts covered in the VCE Further Mathematics Matrices module (MathsTeachersOnly.com) Matrices -20 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) How to solve matrix equations using on a TI nspire CX CAS calculator (1:10 min video) produced by Carmen Popescu-Rose director and co-author of LegaC. How to do matrix operations using a TI-nspire CX CAS calculator (3:56 min video) produced by Carmen Popescu-Rose director and co-author of LegaC resources

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Complex Numbers

NCERT exemplar problems: select Class XI Mathematics, then Complex Numbers and Quadratic Equations. Complex numbers and quadratic equations: Chapter 5 solutions (NCERT-National Council of Educational Research and Training) A Visual, Intuitive Guide to Imaginary Numbers: Post by by Kalid Azad Intuitive Arithmetic With Complex Numbers: Post by by Kalid Azad Understanding Why Complex Multiplication Works: Post by by Kalid Azad

Investigations and further practice

Complex Rotations — NRICH — Years 11–12 extension; explore complex numbers and rotations.

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Graphs and Networks

Undirected Networks summary –St Leonard’s College Networks and Decision Mathematics summary –Vic Maths Notes Graphs and Networks Chapter by Pearson Global Schools

Graph theory basics

Graphs and Networks: two-page summary (Vic Maths Notes)

Adjacency matrices

Matrix representation: one-page summary (Vic Maths Notes)

Euler’s formula

Euler’s Formula for Planar Graphs: one-page summary (Vic Maths Notes)

Traversable graphs

Traversable Graphs: one-page summary (Vic Maths Notes)

Minimum spanning trees

The problem in Good Will Hunting (video ~4 mins) -A quick introduction to trees (Numberphile) Trees and spanning trees: one-page summary (Vic Maths Notes) Minimum Connector Problems: one-page summary (Vic Maths Notes)

Dijkstra’s Algorithm for Shortest Path

Shortest Path Problems: one-page summary (Vic Maths Notes)

Investigations and further practice

Can You Traverse It? — NRICH — Years 9–12; investigate traversable networks.
Hamilton’s Puzzle — NRICH — Years 9–12 extension; explore routes through a network.

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Revision and Practice

Choose material to suit your class. UK-based worksheets provide topic practice rather than Victorian examination preparation; answers are linked beside the relevant resource.

Years 7–8: Directed numbers, fractions and percentages, and decimal worksheets.
Years 9–10: indices and surds, sequences, and equations and inequalities.
Year 10A and senior: polynomial teacher guides, logarithms, and proof by induction.

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NUMBER AND ALGEBRA

Resources will be continually added for the topics listed here and can be accessed from the yellow tabs below.

1. Whole Numbers

WHOLE NUMBERS

SKILLS	DESCRIPTION (REFERENCE)
Addition and Subtraction	-Y7 Whole Numbers - 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Whole Number addition and subtraction (~13-minute video) by Darren Smyth (https://maffsguru.com)
Multiplication and Division	-Y7 Whole Numbers - 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Whole number multiplication and division (~17 minute video) by Darren Smyth (https://maffsguru.com)
Rounding	-Y7 Whole Numbers - 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Estimating and Rounding (~14 minute video) by Darren Smyth (https://maffsguru.com)
Order of Operations	-Y7 Whole Numbers - 13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) - Order of Operations (original resource unavailable)(~13 minute video) by Darren Smyth (https://maffsguru.com) (MathsTeachersOnly.com)

2. Number properties and patterns

NUMBER PROPERTIES AND PATTERNS

Y8 Integers - 21 pages of class notes and handwritten solutions (MathsTeachersOnly.com)
Number Properties (16-minute video) by Darren Smyth (https://maffsguru.com).
Prime Factorisation Four lessons explore prime factorisation and how it can be used to solve problems related to the properties of numbers shared by reSolve
T h e Fundamental Theorem of Arithmetic -Video(3:52)An introductory video from Khan Academy. Covers primes , composites, prime factorisation and a thorough explanation of the fundamental theorem of arithmetic.

Skills	DESCRIPTION (Reference)
Factors and Multiples
Highest (or Greatest) Common Factor (HCF (or GCF)) and Lowest Common Multiple (LCM)	HCF &LCM notes and videos (https://www.onlinemathlearning.com) HCF and LCM(~17 minute video) by Darren Smyth (https://maffsguru.com) HCF and LCM methods (https://www.onlinemath4all.com)
Divisibility Tests	Divisibility Rules summary (https://www.mathsisfun.com) Divisibility Rules for numbers 2-12, 15, 18, 25 summary ( https://www.onlinemath4all.com/)
Prime decomposition	Prime & Composite Numbers Song: - lyrics included by Numberock Prime Numbers (~7 minute video) by Darren Smyth (https://maffsguru.com) Prime Decomposition (10-minute video) by Darren Smyth (https://maffsguru.com)
Squares and Square Roots	Squares and square roots (~13 minute video) by Darren Smyth (https://maffsguru.com)
Number Patterns
Spatial Patterns
Table Patterns

3. Integers

INTEGERS

Y8 Integers - 21 pages of class notes and handwritten solutions (MathsTeachersOnly.com)
Number lines- an online worksheet generator- Create worksheets with various scales on number lines, found at TheMathWorksheetsite.com
Integers - a playlist of 10 short videos on how to add, subtract, multiply and divide integers by Rex Boggs.
Negative Numbers (11-minute video) by Darren Smyth (https://maffsguru.com)

Skills	DESCRIPTION (Reference)
Addition and subtraction of integers	-Y8 Integers: Adding and Subtracting -Worksheet (MathsTeachersOnly.com) -Whole number addition and subtraction (~11 minute video) by Darren Smyth (https://maffsguru.com)
Multiplication and Division of Integers	Whole number multiplication and division (17 minute video) by Darren Smyth (https://maffsguru.com)
Order of Operations
Substituting Integers

4. Fractions and Percentages

FRACTIONS AND PERCENTAGES

Representing and comparing quantities (original resource unavailable) -activities designed to develop students' understanding of fractions, decimals, percentages and standard form. Teacher resources for these activities are also included. (NRICH Maths).
Fractions, decimals and percentages- a playlist of 9 short videos on how to to compare fractions and compare decimals, and to convert between fractions, decimals and percentages by Rex Boggs.
A free online interactive percentage game that involves planning a park with a range of different features such as grass, water, woodland, flowers and playgrounds. Students read what percentage of the park each feature should cover and try to make it happen. Then they are asked to achieve the same goal using decimals.
Y8 Fractions, Decimals and Percentages -13 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

Skills	Description (Reference)
Fractions	What are fractions?(17 minute video) by Darren Smyth (https://maffsguru.com)
Equivalent fractions	Equivalent and simplified fractions(13 minute video) by Darren Smyth (https://maffsguru.com)
Mixed Numbers	Mixed numbers (16 minute video) by Darren Smyth (https://maffsguru.com)
Fraction Walls	Fraction Wall manipulative by Jonathan Hall (https://mathsbot.com)
Ordering fractions
Operations with fractions
-Adding	Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here. Free worksheet “Fraction-Addition and Subtraction” -adding subtracting fractions found at Mathster.com. More free worksheets on many other topics can also be found here.
-Subtracting	Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here.
-Multiplying	Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here.
-Dividing	Division of fractions lesson ( https://www.mathsisfun.com/) Free worksheet “Fraction-Four Rules” -adding subtracting, multiplying and dividing fractions found at Mathster.com. More free worksheets on many other topics can also be found here.
Percentages	Which coupon should I use? Dan Meyer’s Three-Act Maths task
Percentages and unitary methods
Percentage of a number
Decreasing and Increasing by a percentage
Calculating percentage change

5. Decimals

DECIMALS

SKILLS	DESCRIPTION (REFERENCE)
Operations with decimals	Adding and subtracting decimals (~10 minute video) by Darren Smyth (https://maffsguru.com)
Terminating and recurring decimals
Rounding decimals
Significant figures
Scientific notation
Scientific notation using significant figures
Converting fractions, decimals percentages

6. RATIOS AND RATES

RATIOS AND RATES

SKILLS	DESCRIPTION (REFERENCE)
Introducing ratios
Simplifying ratios
Dividing quantities in given ratios
Scale drawings
Introducing rates
Ratios and rates and the unitary method
Speed

7. FINANCIAL MATHS

FINANCIAL MATHS

Recursion and Financial Maths Review for VCE Further Maths (40 min video)-An overview of the key skills required for Recurrence & Financial Modelling, covering some examples from past VCAA papers.

Recursion and Financial Modelling Summary (pdf) for VCE Further Maths from the Maths dept of St Leonard's College.

SKILLS	DESCRIPTION (REFERENCE)
Profits and discounts
Shares and Dividends
Income taxation
Number patterns
The Fibonacci sequence
Arithmetic sequences
Using a recurrence relation to generate an arithmetic sequence and its graph
Using a recurrence relation to model linear growth: simple interest
Using a recurrence relation to model linear decay: flat-rate depreciation
Using a rule to determining the nth term for linear growth or decay
Geometric sequences
Using a recurrence relation to generate a geometric sequence and its graph
Using a recurrence relation to model geometric growth: compund interest investment
Using a recurrence relation to model geometric decay: reducing balance depreciation
Using a rule to determining the nth term for geometric growth or decay
Effective annual interest rate

8. Indices

INDICES

Skills	DESCRIPTION (Reference)
Index notation
Index laws
Negative indices
Scientific notation	What is standard form? by Pythagoras and That (UK site)
Fractional indices

9. SURDS

SURDS

SKILLS	DESCRIPTION (REFERENCE)
Irrational numbers and surds
Simplifying surds
Adding and subtracting surds
Multiplying and dividing surds
Binomial products
Rationalising the denominator

10. Sequences and Series

SEQUENCES AND SERIES

-A great activity for teaching arithmetic sequences- "Expressing Number Patterns" by Bob Lochel found at Desmos.com

-Sequences and Series - A pdf guide for teachers: Principal author: Peter Brown (http://amsi.org.au/ESA_ Senior_Years/seniors_years. html)

11. Counting methods

COUNTING METHODS

Skills	DESCRIPTION (Reference)
Permutations
Permutations with restrictions
Permutations with like objects
Combinations
Combinations with restrictions
Pacal's triangle
The pigeon-hole principle
The inclusion-exclusion principle

12. Number and proof

NUMBER AND PROOF

Introduction to two-column algebra and geometry proofs free downloads (Introducing Two-Column Geometry Proofs: A Different Approach -post by mathgiraffe.com)

Skills	DESCRIPTION (Reference)
Direct proof	Two pages of notes including examples and exercises contributed to the Mathcentre Community Project by Katy Dobson, University of Leeds (http://www.mathcentre.ac.uk/students/topics/proofs/direct/)
Proof by induction	Two pages of notes including examples and exercises contributed to the Mathcentre Community Project by Katy Dobson, University of Leeds (http://www.mathcentre.ac.uk/students/topics/proofs/proof-by-induction/) Two pages of further examples contributed to the Mathcentre Community Project by Katy Dobson, University of Leeds (http://www.mathcentre.ac.uk/students/topics/proofs/proof-by-induction/)
Proof by contrapositive
Proof by contradiction
Equivalent statements
Disproving statements

13. Algebraic expressions

ALGEBRAIC EXPRESSIONS

-Y9 Algebra 24- pages of fill-in class notes with handwritten solutions (MathsTeachersOnly.com)

-Y10 Quadratic Equations -15 pages of fill-in class notes with handwritten solutions (MathsTeachersOnly.com)

-Y10_10A Quadratics: One-page summary for factorising quadratic expressions and solving quadratic equations (MathsTeachersOnly.com)

-A hands-on activity on how to teach collecting like terms using reversible (white/red) unit squares and strips-Ppt (13 slides)

-Quadratic Factorisation and Expansion worksheet -18 practice questions (MathsTeachersOnly.com)

SKILLS	DESCRIPTION (REFERENCE)
The language of algebra	-Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Substituting and evaluating	-Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Equivalent expressions	-Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Like terms	-Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Adding and subtracting terms	-Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Multiplying and dividing terms	-Y7 Algebra-6 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Expanding expressions	-Binomial expansions A worksheet of 12 practice questions on binomial expansions including answers (MathsTeachersOnly.com) -Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Year 9 Algebra: Harder Expansions - 3-page fill-in worksheet with harder expansion problems involving binomial and trinomial factors. Solutions included
Expanding binomial products	-Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Expanding perfect squares	-Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Factorising expressions by taking out common factors	-Y8 Algebra-14 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Factorising using the difference of perfect squares	-Factorising using DOPS- see the first 3:48 mins of the 8:19 min Vimeo video “Factorising quadratics” by Bryn Humberstone -Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Factorising by grouping	-Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Factorising quadratic trinomials of the form x²+bx+c	-Factorising using the cross-method- see “Factorising quadratics” by Bryn Humberstone (after 3:49 min) (Vimeo video 8:19 mins) -Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Factorising quadratic trinomials of the form ax²+bx+c	-see “Factorising quadratics” by Bryn Humberstone (after 3:49 min mark) (Vimeo video 8:19 mins) -Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Factorising quadratic trinomials by completing the square	-Completing the Square-Geometrically- a 4-page worksheet with handwritten solutions providing a geometrical explanation of 'completing the square' (MathsTeachersOnly.com) -Factorising quadratics by completing the square -video (9:46min) by Bryn Humberstone -Factorising by Completing the Square (~19 minute video) by Darren Smyth (https://maffsguru.com)
Simplifying algebraic fractions	-Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com) -Refer to Dan Meyer's blog for a way to introduce simplifying algebraic fractions. -Y10_10A Algebraic Fractions Worksheet- A one-page worksheet of 6 practice questions, including answers, involving adding, subtracting, multiplying and dividing algebraic fractions.(MathsTeachersOnly.com)
Multiplying and dividing algebraic fractions	-Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Adding and subtracting algebraic fractions	-Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)
Solving equations with algebraic fractions	-Y9 Algebra-24 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

14. Polynomials

POLYNOMIALS

SKILLS	DESCRIPTION (REFERENCE)
Adding, subtracting and multiplying polynomials
Division of polynomials
The remainder theorem
The factor theorem
The rational-root theorem
Solving cubic polynomial equations
Solving cubic polynomial equations and inequalities

15. Solving linear equations and inequations

SOLVING LINEAR EQUATIONS AND INEQUATIONS

Linear equations resources which include problems, games and articles found at NRICH.

An article on the method of determining the coefficients for complex equations of chemical reactions found at NRICH

Skills	Reference
Introduction to equations
Solving linear equations by inspection
Equivalent equations
Solving linear equations algebraically
Equations with algebraic fractions
Equations with pronumerals on both sides of an equation
Equations with brackets
Formulas and relationships	Formulas module by AMSI. A list of formulae are also listed at the end of this TIMES module.
Solving inequations
Solving simultaneous equations algebraically using substitution
Solving simultaneous equations algebraically using elimination

16. Solving quadratic equations and inequations

SOLVING QUADRATIC EQUATIONS

-101 uses of a quadratic equation: Part 1 and Part II by Plus Magazine (plus.maths.org)

Skills	Description (Reference)
Solving quadratic equations by factorising	-Year 10 Quadratic Equations - 15-pages fill-in class including hand-written solutions. (MathsTeachersOnly.com)
Solving quadratic equations by completing the square	Year 10 Quadratic Equations - 15-pages fill-in class including hand-written solutions. (MathsTeachersOnly.com) -Solving quadratics by completing the square ~12 min video by Darren Smyth -Completing the Square-Geometrically- a 4-page worksheet with handwritten solutions providing a geometrical explanation of 'completing the square'.(MathsTeachersOnly.com)
Solving quadratic equations by applying the quadratic formula.	-Year 10 Quadratic Equations - 15-pages fill-in class including hand-written solutions.
Solving quadratic inequations	-Year 10 Quadratic Equations - 15-pages fill-in class including hand-written solutions. (MathsTeachersOnly.com) - Solving Quadratic Inequations-video(2:36) by Freda Armstrong from Maths Turning Point

See also ALGEBRAIC EXPRESSIONS tab for expanding and factorising quadratics

17. Exponentials and logarithms

EXPONENTIALS AND LOGARITHMS

SKILLS	REFERENCE
Exponential growth and decay
Solving simple exponential equations
Logarithms and order of magnitude
Logarithmic scales
Logarithm laws	-A summary of Log laws and traps to avoid can be downloaded from Maths Turning Point.
Solving exponential equations using logarithms
Exponentials and Logarithms	Exponential and logarithms (original resource unavailable) -sample class notes and exercises by David Treeby (https://www.t2maths.com.au) Exponential and logarithms (original resource unavailable) -solutions to sample class notes and exercises by David Treeby (https://www.t2maths.com.au)

18. MATRICES

MATRICES

Summary Notes on Matrices pdf- A three-page summary covering all the concepts covered in the VCE Further Mathematics Matrices module (MathsTeachersOnly.com)

Matrices -20 pages of fill-in class notes and handwritten solutions (MathsTeachersOnly.com)

How to solve matrix equations using on a TI nspire CX CAS calculator (1:10 min video) produced by Carmen Popescu-Rose director and co-author of LegaC.

How to do matrix operations using a TI-nspire CX CAS calculator (3:56 min video) produced by Carmen Popescu-Rose director and co-author of LegaC resources

19. Complex numbers

COMPLEX NUMBERS

Complex numbers and quadratic equations: Chapter 5 notes and exercises (NCERT-National Council of Educational Research and Training)

Complex numbers and quadratic equations: Chapter 5 solutions (NCERT-National Council of Educational Research and Training)

A Visual, Intuitive Guide to Imaginary Numbers: Post by by Kalid Azad

Intuitive Arithmetic With Complex Numbers: Post by by Kalid Azad

Understanding Why Complex Multiplication Works: Post by by Kalid Azad

Skills	Description (Reference)
Equality and operations on complex numbers	Complex Numbers: One-page summary (Maths Vic Notes) Arithmetic of Complex Numbers: Two-page summary (Maths Vic Notes)
The modulus, conjugate and division of a complex number	Complex Numbers: One-page summary (Maths Vic Notes) Arithmetic of Complex Numbers: Two-page summary (Maths Vic Notes)
Argand diagrams and geometric representations of the basic operations on complex numbers
Geometric significance of multiplication by $i$
Polar form - the modulus–argument form of a complex number
Complex conjugate form to polar form
Basic operations on complex numbers in polar form
Solving quadratic equations over the complex numbers	Quadratics Funtions over C: One-page summary (Maths Vic Notes)
Solving polynomial equations over the complex numbers
Using De Moivre's theorem to solve equations
Sketching subsets of the complex plane

20. Graphs and Networks

GRAPHS AND NETWORKS

Undirected Networks summary -St Leonard's College

Networks and Decision Mathematics summary -Vic Maths Notes

Graphs and Networks Chapter by Pearson Global Schools

Skills	Description (Reference)
Graph theory basics	Graphs and Networks: two-page summary (Vic Maths Notes)
Isomorphic graphs
Connected graphs and bridges
Adjacency matrices	Matrix representation: one-page summary (Vic Maths Notes)
Planar graphs
Faces of a graph
Euler's formula	Euler's Formula for Planar Graphs: one-page summary (Vic Maths Notes)
Walks, trails and paths
Circuits and cycles
Traversable graphs	Traversable Graphs: one-page summary (Vic Maths Notes)
Eulerian trails and circuits
Hamilton paths and cycles
Weighted graphs and networks
The shortest path
Minimum spanning trees	The problem in Good Will Hunting (video ~4 mins) -A quick introduction to trees (Numberphile) Trees and spanning trees: one-page summary (Vic Maths Notes) Minimum Connector Problems: one-page summary (Vic Maths Notes)
Dijkstra's Algorithm for Shortest Path	Shortest Path Problems: one-page summary (Vic Maths Notes)