M1MATHS Home Explanations and practice for each highschool maths topic A free online textbook 
The full explanations in simple language make it suitable for independent study.
Help is offered (no cost) to schools thinking of using these materials. Click Home>Contact. 
Reviews This website is absolutely AMAZING and we use it regularly! Thank you for such a wonderful resource! Michelle Pacey, Middle School Math Facebook Group Thank you so much! So much effort but blessing so many especially me! The topics and levels are welllaid out, the font, size and spacing are readerfriendly. Love the interesting bits of background info that makes selflearning easy. Suitable for WA OLNA test revision, Primary Maths Extension (which I'll be using) and also good recap for Year 11/12 Essential/General Maths. I'd also be using the Maths Games! If you print/publish it into loose leaf folders, I'd buy it! For the love of Maths and learners, thank you! Anna Tan, Middle School Math Facebook Group 
Overview of M1Maths 
The M1Maths materials cover school maths from whole numbers to calculus. They should be useful for students from Year 5 or 6 to the end of high school. The core materials consist of about 130 Knowledge modules, each dealing with one mathematical topic and 4 Skills modules (all accessible through the Modules menu). There are also various other materials that could be useful for students and teachers (accessible through the Extras buttons). Knowledge Modules The Knowledge modules are divided into 7 strands (Number, Algebra, Measurement, Geometry, Statistics, Probability and Calculus) and 6 levels (Level 1 corresponding to maths from about Year 5 to Year 7 and Level 6 corresponding to about Years 11 to 12 for students who do calculus). The assignment of topics to levels won’t necessarily correspond exactly to any particular curriculum, but modules to cover all aspects of most curricula should be easy to find at about the expected level with a short search of the module list for the relevant strand. Each Knowledge module has 5 sections: Summary: This is a statement of the main ideas. It is suitable for reference or revision after the module has been studied. Learn: This section is a fuller explanation of the ideas along with practice exercises. The exercises could be used after classroom teaching or selfguided students may be able to use the explanations and exercises to learn independently. Solve: This section consists of a number of problems which require students to apply the knowledge gained from the module as well as to use some original thinking. Revise: This section consists of a number of Revision Sets, each with a few questions designed to maintain knowledge of that module after the work on it has been completed. There is at least one set for each module; the plan is to eventually have three or four sets for each. Cycling through the revision sets for the modules that have been covered so that each module is revisited every few weeks might be helpful. This could be a regular homework task. Answers: This section contains the answers to the questions in the Learn, Solve and Revise sections. Some modules also have a LeadIn which contains an activity to prepare for the learning. Learning by Thinking Modules These are alternative versions of some of the knowledge modules. They are distinguished by being green on the Modules menu rather than the usual straw colour and are labelled LbT. They develop the same knowledge, but do it by leading the student through a sequence of problems in which they should develop the required knowledge themselves rather than being given the procedures. The idea is that this will improve the student’s problemsolving skills, but, more importantly, it will ensure that the knowledge built forms a logical structure and avoids the common problem of students memorising procedures rather than understanding the ideas behind them. Memorised procedures are easily forgotten, whereas knowledge worked out logically is generally going to be reproduceable at any time later. Learning Approach taken in the Knowledge Strands The learning sequence in the strands varies from fairly conventional in the Number, Measurement, Geometry and Calculus strands to somewhat unconventional in the Algebra, Statistics and Probability strands. The deviation from convention is designed to ensure that the concepts build upon each other in ways that are always meaningful and applicable to life and to ensure that concepts make sense and, as far as possible, are obvious to the students in light of what they already know. Clicking on the strand names in the dropdown navigation menu will provide more information on the approach taken in each strand. Skills Modules The Skills modules cover Mental Arithmetic, Problem Solving, Investigating and Communication. Each has sections corresponding to the same levels as the knowledge modules. They contain explanations of the skills and how to acquire them, and sets of practice questions with answers. Use of the skills modules would allow students to pay explicit attention to developing these aspects of their mathematical prowess. Other Materials The Extras buttons lead to other materials which could be useful for students and teachers. Uses for the Modules The M1Maths modules could be used in a number of ways.

Contact 
M1Maths is produced, maintained and progressively improved by David Ilsley in Brisbane, Australia. Please feel free to make contact if you are a teacher thinking of trialling or using the materials in your school and would like some help. Support can be provided at no cost. Support will need to be mostly online, though it could include school visits for schools in Southeast Queensland. Also feel free to make contact if you have any questions, comments, feedback or suggestions. These will help to improve the site. Comments about things like incorrect answers, unclear language, poor explanations and even typos are very welcome, will be acted upon and will be acknowledged unless requested otherwise. The following have helped to improve the site: Rex Boggs, Dario Lucisano. 
Contact can be made using the boxes below. Your comment will not be visible to other users. Alternatively, you can send an email to d.ilsley@gmail.com. Or you can use a Microsoft Form. There is also a Facebook Group for people who are happy for their comments to be seen by others and to engage in discussions. This can be accessed via this link: M1Maths Facebook Group 
Brief Biography David Ilsley grew up and went to school in England. He studied Natural Science at Cambridge University, majoring in Geology and obtaining 1st Class Honours and a Masters Degree. He moved to Australia to pursue research work in Geology at the Australian National University in Canberra and then worked for mining companies for a few years. After marrying, he decided that the life of an exploration geologist (with many long periods away from home) wasn’t totally compatible with married life or bringing up children and enrolled in a Diploma of Education at the University of Queensland. After qualifying, he taught at a number of high schools in SE Queensland. This work was interspersed with periods as a regional mathematics adviser, a writer of Senior Mathematics materials for Open Learning, a curriculum developer for the 2002 Queensland P10 Maths Syllabus and a classroom coach training teachers in middle schools in the Bronx, New York. David has published articles in professional journals and presented at conferences and was vice president of the Queensland Association of Mathematics Teachers and editor of their journal Teaching Mathematics from 1998 to 2000. The M1Maths materials were developed progressively over much of this teaching career and were initially published on the Internet in 2019. Now retired and just doing occasional relief teaching, he works on further development of the materials along with pursuing his interests in travel, astronomy and gardening his hectare of land in Logan City. 
Usage Rights 
Except where otherwise stated, the M1Maths website (m1maths.com) is copyrighted under Creative Commons Attribution 4.0 License CC BYNC 4.0. This allows the materials to be printed, copied, adapted and stored locally. It also allows them to be republished for noncommercial purposes as long as clear attribution is made to M1Maths (m1maths.com). Please contact David Ilsley on d.ilsley@gmail.com with inquiries re any other uses. Some of the resources on this site are based on material the author produced for classroom use while working for the Queensland Department of Education. Queensland Department of Education material is used under the Creative Commons Attribution 4.0 Licence CC BY 4.0. Also, some of the resources are based on material the author produced for classroom use while working for Canterbury College. These are used with permission. The clip art is from Art Explosion 300 000 by Nova Development, purchased by the author. 
Reviews 
The following are some comments people have made about M1 Maths, mainly on Facebook groups. They are included here with permission. Further comments, complimentary or critical, are always welcome. (See the 'Contact' section above.) This website is absolutely AMAZING and we use it regularly! Thank you for such a wonderful resource! Michelle Pacey, Middle School Math Facebook Group Thank you so much! So much effort but blessing so many especially me! The topics and levels are welllaid out, the font, size and spacing are readerfriendly. Love the interesting bits of background info that makes selflearning easy. Suitable for WA OLNA test revision, Primary Maths Extension (which I'll be using) and also good recap for Year 11/12 Essential/General Maths. I'd also be using the Maths Games! If you print/publish it into loose leaf folders, I'd buy it! For the love of Maths and learners, thank you! Anna Tan, Middle School Math Facebook Group These are so very well done David! This will save me so much time going ahead with online teaching, especially since I've always wanted to trial flipped classroom learning. Piyumi Fernando, QLD Teachers Facebook Group I recommend to all of you!!! Please go there, you will just love mathematics. BroCharleskwaku Odoom De Optimistic, Math and Beyond Facebook Group Thank you, David! This is such an amazing living legacy project and you are so generous to share it. It will be a huge help to us. Alexandra Edgar, QLD Teachers Facebook Group Thanks for sharing! I've just started my Maths teaching career so this really helps. Yvette Millan, Mathematics Teachers of NSW Facebook Group This is so incredibly generous of you. Having taught for 30+ years myself I know the work that would have gone into this. There's a special place in Heaven for you. Jenny Cawood, Australian Secondary Mathematics Teachers 712 Facebook Group This is amazing, David! I’m definitely using them and will let you know how I go. Thank you! Neelam Naidu, Queensland Senior Mathematics Teachers Facebook Group Thank you for sharing this TERRIFIC resource David Ilsley. We need more veteran teachers like yourself who are willing to help the next generation. May you be richly blessed for all your hard work. Thanks again mate. Nile Sheep, Australian Secondary Mathematics Teachers 712 Facebook Group I love the Settler/Zoomer resources. Callum Day, Australian Secondary Mathematics Teachers 712 Facebook Group I’ve used the lessons on modelling and they were fantastic. Soph Em, Queensland Senior Mathematics Teachers Facebook Group I would like to thank you very much for creating this website. It is such a great website. It is user friendly and has resources to both help in extending the high achievers and reinforcing concepts for the slow learners. Thank you so much for putting in so much effort to provide us teachers with such great resources. Indra Kumar, Email communication 
MODULES M1Maths 
Number Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 1 is Years 57, Level 6 Years 1112. The Number strand is treated in a fairly conventional way. The emphasis is on students developing number sense and a range of methods and short cuts for computation. Visual conception of fractions is promoted before symbolic manipulation. The visual approach is more amenable to students developing their own methods and short cuts and, once concepts have been gained, they are less likely to be forgotten. 
N1: Number  Level 1 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 1 modules. 
N11  pdf docx  Whole numbers 
 4 h  
N12  pdf docx  Fraction Meanings 
 3 h  
N13  pdf docx  Fraction Conversions 
 3 h  N12 
N13  pdf docx  Fraction Conversions  Alternative 'Learn' Section: Learning by Thinking  4 h  N12 
N14  pdf docx  Negatives 
 1 h  
N15  pdf docx  Calculators 
 1 h  N13 N14 
N16  pdf docx  Powers 
 2 h  N11 N15 
N17  pdf docx  Order of Operations 
 3 h  
N18  pdf docx  Common Fraction Operations 1 
 2 h  N13 
N19  pdf docx  Decimal Operations 1 
 3 h  N13 
N110  pdf docx  Rounding and Approximation 
 3 h  N15 N19 
N2: Number  Level 2 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
N21  pdf docx  Number Sets 
 2 h  
N22  pdf docx  Fractions of Numbers 
 2 h  
N23  pdf docx  Rates 

4 h  
N24  pdf docx  Ratios 
 2 h  N23 
N25  pdf docx  Decimal Operations 2 
 3 h  N22 
N26  pdf docx  Negative Operations 
 3 h  
N27  pdf docx  Common Fraction Operations 2 
 3 h 
N3: Number  Level 3 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 3 modules. 
N31  pdf docx  Scientific Notation 
 2 h  
N32  pdf docx  Simple Interest 
 3 h  
N32  pdf docx  Simple Interest  Alternative 'Learn' Section: Learning by Thinking  5 h  
N33  pdf docx  Proportion 
 2 h 
N4: Number  Level 4 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 4 modules. 
N41  pdf docx  Compound Interest 
 3 h  
N41  pdf docx  Compound Interest  Alternative 'Learn' Section: Learning by Thinking  4 h 
N5: Number  Level 5 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 5 modules. 
N51  pdf docx  Simplifying Surds 
 2 h  A52 
N6: Number  Level 6 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 6 modules. 
N61  pdf docx  Complex Numbers 
 9 h  
N62  pdf docx  Vectors 
 10 h  
N63  pdf docx  Matrices 
 5 h 
Algebra Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 1 is Years 57, Level 6 Years 1112. The learning sequence for Algebra is somewhat unconventional. Algebra is treated as the study and use of relations, a relation being information which allows us to find the value of one quantity if we know the value of another quantity. As such, all new knowledge is presented as a technique for solving reallife problems: nothing is introduced as an abstract idea or as something that will be needed later. This avoids the common lament of 'When are we ever going to use this?' By the time a student reaches the end of Level 4 or 5, s/he will know evrything a student taught traditionally will know, but the knowledge will seem more coherent, meaningful and useful. 
A1: Algebra  Level 1 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 1 modules. 
A11  pdf docx  Relations 1 
 3 h  
A12  pdf docx  Relations 2 
 3 h  A11 
A13  pdf docx  Patterns 
 3 h  A12 
A14  pdf docx  Discrete vs Continuous Relations 
 2 h  A13 
A15  pdf docx  Substitution 
 3 h  A14 
A16  pdf docx  Equations 
 7 h  A15 
A2: Algebra  Level 2 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
A21  pdf docx  Writing Equations 
 3 h  
A22  pdf docx  Collecting Terms 
 2 h  A21 
A23  pdf docx  Expanding 
 3 h  A22 
A3: Algebra  Level 3 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 3 modules. 
A31  pdf docx  Undoing the Unknown 
 3 h  
A32  pdf docx  Choosing the Unknown 
 2 h  A31 
A33  pdf docx  Squares and Fractions 
 4 h  A32 
A34  pdf docx  Rearranging Formulae 
 2 h  A33 
A35  pdf docx  Solving by Graphing 
 2 h  
A36  pdf docx  Domain and Range 
 2 h  
A37  pdf docx  Functions 
 3 h  A36 
A38  pdf docx  Linear Functions 
 5 h  A37 M33 
A39  pdf docx  Reciprocal Functions< 
 2 h  A38 
A310  pdf docx  Index Laws 15 
 4 h  
A310  pdf docx  Index Laws 15  Alternative 'Learn' Section: Learning by Thinking  5 h 
A4: Algebra  Level 4 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 4 modules. 
A41  pdf docx  Factorising 
 5 h  
A42  pdf docx  Quadratic Functions 
 6 h  A41 
A43  pdf docx  Simultaneous Equations  Linear 
 6 h  
A44  pdf docx  Inequalities 
 1 h  
A45  pdf docx  Algebraic Fractions 
 3 h  A41 
A46  pdf docx  Algebraic Proofs 
 2 h 
A5: Algebra  Level 5 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 5 modules. 
A51  pdf docx  Polynomial Functions 
 3 h  < 
A52  pdf docx  Index Laws 610 
 3 h  
A52  pdf docx  Index Laws 610  Alternative 'Learn' Section: Learning by Thinking  4 h  
A53  pdf docx  Power Functions 
 2 h  A52 
A54  pdf docx  Exponential Functions and Logs 
 5 h  A52 
A55  pdf docx  Simultaneous Equations  General 
 6 h  A53 A54 
A56  pdf docx  Finding Formulae for Functions 
 3 h  A55 
A57  pdf docx  Model Functions 
 3 h  A56 
A58  pdf docx  Calculator Equation Solving 
 1 h  A51 
A59  pdf docx  Algebraic Transformations 
 4 h  
A510  pdf docx  Further Relations 
 5 h  A51 
A511  pdf docx  Trigonometric Functions 
 5 h  M51 
A512  pdf docx  Trigonometric Equations 
 5 h  A511 M51 
A513  pdf docx  Logs 
 7 h  A54 
A6: Algebra  Level 6 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 6 modules. 
A61  pdf docx  Combinations and the Binomial Expansion 
 6 h  
A62  pdf docx  Arithmetic Sequences 
 4 h  
A63  pdf docx  Geometric Sequences 
 3 h  A62 
A64  pdf docx  Linear Programming 
 3 h  
A65  pdf docx  Further Methods of Proof 
 3 h  
A66  pdf docx  Loci and Conic Sections 
 4 h 
Measurement Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 1 is Years 57, Level 6 Years 1112. The Measurement strand is treated fairly conventionally except that students are encouraged to be able to find perimeters, areas, volumes etc. through common sense methods before being introduced to the formulae. This hopefully will avoid the tendency of students to rely on memorising formulae rather than understanding the mathematical concepts. 
M1: Measurement  Level 1 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 1 modules. 
M11  pdf docx  Dimensions, Size and Mass 
 5 h  
M12  pdf docx  Time 1 
 2 h  
M13  pdf docx  Unit Conversion 
 2 h  M11 M12 
M14  pdf docx  Length, Area and Volume 1 
 2 h  M11 M13 
M14  pdf docx  Length, Area and Volume 1  Alternative 'Learn' Section: Learning by Thinking  3 h  M11 M13 
M2: Measurement  Level 2 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
M21  pdf docx  Graduated Scales 
 2 h  
M22  pdf docx  Time 2 
 5 h  
M23  pdf docx  Length, Area and Volume 2 
 6 h  N22 G24 
M23  pdf docx  Length, Area and Volume 2  Alternative 'Learn' Section: Learning by Thinking  8 h  N22 G24 
M3: Measurement  Level 3 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 3 modules. 
M31  pdf docx  Pythagoras 
 3 h  
M32  pdf docx  Trigonometry 
 6 h  M31 
M33  pdf docx  Slope 
 2 h  M32 
M34  pdf docx  Length, Area and Volume 3 
 8 h  M31 
M34  pdf docx  Length, Area and Volume 3  Alternative 'Learn' Section: Learning by Thinking  8 h  M31 
M4: Measurement  Level 4 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 4 modules. 
M41  pdf docx  Length, Area and Volume 4 
 4 h  
M41  pdf docx  Length, Area and Volume 4  Alternative 'Learn' Section: Learning by Thinking  5 h 
M5: Measurement  Level 5 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 5 modules. 
M51  pdf docx  Unit Circle and Trig Identities 
 4 h  
M52  pdf docx  Solving Triangles 
 5 h  M51 
M6: Measurement  Level 6 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 6 modules. 
M61  pdf docx  Radians 
 5 h  
M62  pdf docx  Exact Trig Values 
 3 h  M61 
Geometry Level 1 Level 2 Level 3 Level 4 . . . . . . . . . . Level 1 is Years 57, Level 6 Years 1112. The Geometry strand is treated fairly conventionally, though experiences are designed to encourage the development of knowledge of theorems etc. through discovery rather than rote learning. 
G1: Geometry  Level 1 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 1 modules. 
G11  pdf docx  Drawings 
 3 h  M11 
G12  pdf docx  Angles 
 2 h  
G13  pdf docx  Position 
 3 h  G12 
G2: Geometry  Level 2 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
G21  pdf docx  Maps and Scales 
 2 h  
G22  pdf docx  Geometric Figures 
 5 h  
G23  pdf docx  Properties of Polygons 
 5 h  
G24  pdf docx  Geometric Vocabulary 
 2 h  
G25  pdf docx  Transformations and Symmetry 
 3 h  G22 
G26  pdf docx  Congruence 
 3 h  G22 
G3: Geometry  Level 3 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 3 modules. 
G31  pdf docx  Similarity 
 3 h 
G4: Geometry  Level 4 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 4 modules. 
G41  pdf docx  Geometric Proofs 
 4 h  
G42  pdf docx  Networks 
 3 h 
Statistics Level 1 Level 2 Level 3 Level 4 Level 5 . . . . . Level 1 is Years 57, Level 6 Years 1112. The main use students will have in later life for the statistics they learn is in interpreting data presentations and critically assessing data presentations that make a point. These are thus the primary thrusts of the strand, though other skills like presenting data (especially with technology), calculating statistical measures etc. are covered. Most data presentations in the media are not one of the 'standard' types normally learnt at school. Thus, time is devoted to learning to understand, interpret and read unfamiliar data presentations. With this skill, reading the 'standard' types comes fairly naturally. 
S1: Statistics  Level 1 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 1 modules 
S11  pdf docx  Data Displays 1 
 6 h  
S12  pdf docx  Data Summary 
 2 h 
S2: Statistics  Level 2 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
S21  pdf docx  Data Collection 
 2 h 
S3: Statistics  Level 3 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 3 modules. 
S31  pdf docx xlsx  Spreadsheets 
 4 h  
S32  pdf docx  Data Displays 2 
 5 h  
S33  pdf docx  Critiquing 
 3 h  S32 
S34  pdf docx  Data Types 
 1 h  
S35  pdf docx  Data Distributions 
 2 h  S32 
S4: Statistics  Level 4 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 4 modules. 
S41  pdf docx  Quantiles and Spread 
 5 h  
S42  pdf docx  Linear Regression 
 3 h 
S5: Statistics  Level 5 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 5 modules. 
S51  pdf docx  Grouped Data 
 3 h 
Probability Level 1 Level 2 Level 3 Level 4 . . . . . Level 6 Level 1 is Years 57, Level 6 Years 1112. Many textbooks treat probability very poorly. One common error is to define probability as the number of outcomes in the event divided by the number of outcomes in the sample space. This depends on the probability of all outcomes in the sample space being equal, something often not mentioned. The definition is also circular in that the definition of probability depends on the idea that the probabilities of the outcomes are equal and thus on knowing what probability means. A more appropriate definition of probability is the fraction of times that something will happen in the long run and this is the way it is introduced here. Probabilities can be determined using data, symmetry or guesswork, guesswork being required for untestable and unrepeatable events like finding there is an afterlife if you die. By the end of the course, student will be able to do all the usual calculations, but will have a more solidly grounded concept of what it is all about. 
P1: Probability  Level 1 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 1 modules. 
P11  pdf docx  Probability 
 8 h  N13 
P2: Probability  Level 2 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
P21  pdf docx  Compound Events 
 5 h  
P22  pdf docx  Twoway Tables 
 1 h  P21 
P23  pdf docx  Venn Diagrams 
 3 h 
P3: Probability  Level 3 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 3 modules. 
P31  pdf docx  Tree Diagrams 
 3 h 
P4: Probability  Level 4 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 4 modules. 
P41  pdf docx  Complex Probabilities 
 4 h 
P6: Probability  Level 6 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 6 modules. 
P61  pdf docx  Sets 
 2 h  
P62  pdf docx  Conditional Probability 
 3 h  
P63  pdf docx  Discrete Random Variables 
 5 h  
P64  pdf docx  Binomial Distributions 
 5 h  P63 A61 
P65  pdf docx  Continuous Random Variables 
 5 h  P63 C610 
P66  pdf docx  Normal Distributions 
 5 h  P65 
P67  pdf docx  Confidence Intervals for Proportions 
 4 h  P64 
P68  pdf docx  Confidence Intervals for Means 
 3 h  P67 
Calculus . . . . . . . . . . . . . . . . . . . . . . . . . Level 6 Level 1 is Years 57, Level 6 Years 1112. Calculus is treated fairly conventionally, though time is spent developing some of the basic concepts like how rates of change appear on graphs in practical situations. Also, differentials are given individual meaning, rather than just their ratio. This makes things like the chain rule easier to understand. 
C6: Calculus  Level 6 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 6 modules. 
C61  pdf docx  Velocity Graphically 
 4 h  
C62  pdf docx  Velocity Algebraically 
 6 h  C61 
C63  pdf docx  Velocity by Rule 
 6 h  C62 
C64  pdf docx  Other Relations 
 4 h  C63 
C65  pdf docx  Applications of Derivatives 
 8 h  C64 
C66  pdf docx  Chain, Product and Quotient Rules 
 7 h  C65 
C67  pdf docx  Other Derivatives 
 5 h  C66 
C68  pdf docx  Mastering Differentiation 
 12 h  C67 
C69  pdf docx  Differential Equations 
 10 h  C68 
C610  pdf docx  Integration 
 14 h  C69 
C611  pdf docx  Pert 
 4 h  C610 
C612  pdf docx  Higherorder Derivatives 
 3 h  C610 
C613  pdf docx  Graph Sketching 
 4 h  C68 
C614  pdf docx  Optimisation 
 6 h  C68 
C615  pdf docx  Simpson's Rule 
 2 h  C610 
Skills Mental Arithmetic Problem Solving Investigating Communicating It might be argued that, for many students, skills like mental arithmetic and problem solving will be more important to them in life than being able to do things like solve quadratic equations, use trigonometry and find the midpoint of a line segment. Thus it is hoped that significant time will be devoted to skills development. Often, curricula and programs are so tightly packed with content knowledge that the teaching of skills tends to be squeezed out. However, in the longer run, having the skills can allow students to develop the content knowledge more quickly. Not only this, the learning will be more soundly based and thus better retained. This idea is elaborated here. Devoting a quarter to a third of learning time to the skills is probably appropriate. To this end, a lot of material is provided in the modules on Mental Arithmetic, Problem Solving, Investigating and Communicating. Investigating is a skill ignored in many programs, but it can be helpful in convincing students that mathematics is something that they can develop themselves in response to a need rather than something handed down from on high in immutable and unquestionable form and without which no progress can be made. Unlike with the knowledge modules, each skill is presented as a single module divided into sections for the different levels. 
Skills: Mental Arithmetic Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
pdf docx 

Skills: Problem Solving Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
pdf docx 

Skills: Investigating Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
pdf docx 

Skills: Communicating Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the prerequisite Level 2 modules. 
pdf docx 

FOR STUDENTS M1Maths 
Free Maths Websites This is a list of good free websites for students of secondary maths under the six categories below. Websites designed more for teachers are listed in the Extras for Teachers section. 
Explanations 

Site  Content  Comments 

Video lessons on most secondary maths topics  Just search for the topic. Generally, many options available.  
Systemmatic lessons on maths topics from Year 1 to University  A vast site. Lessons are spoken and simultaneously handwritten/drawn.  
Facts and explanations covering Years 710 maths  A good reference where one can easily look up mathematical facts. Well organised.  
Written and video explanations of maths ideas, Years 710  American site. No practice.  
Explanations and examples covering secondary maths  Comprehensive coverage of secondary maths in the UK.  
Video Maths lessons for middle school to college maths in the US 
 
Video lessons for Years 5 to 10 and higherlevel algebra.  American site connected to MATHhelp  
Video'd lessons on secondary maths  Eddie Woo is a teacher in Sydney. This is his Youtube channel.  
Text explanations and some examples and exercises covering the Australian curriculum to Year 10 and Maths Methods  Organised as modules.  
All seconday maths  Includes 1500 video lessons.  
Equivalent Fractions  An entertaining animated story about natural numbers, rational numbers and equivalent fractions.  
About 1000 videos covering secondary maths and some tertiary maths  Good explanations of how to do things, though not always why the methods work or applications of the methods. 
Practice and Problems 
Site  Content  Comments 

Includes modules on all Australian Curriculum topics up to Year 10 and Maths Methods  Text explanations and some examples and exercises.  
Practice at interpreting and reading graphs  Various graphs from the New York Times containing real data.  
Arithmetic and algebra worksheets  Generated printable worksheets in arithmetica and basic algebra. Questions can be randomised so they are different each time.  
Worksheets for many Years 710 topics  Printable worksheets. Answers available. A pay site, but with a bit of free material avaliable.  
A collection of questions, problems, puzzles, activities, instructional videos etc.  An extensive site produced by one person in the UK.  
Several hundred mathematical problems suitable for solution by writing computer programs.  You can register your solutions. Each problem has been solved by hundreds to hundreds of thousands of users. 
Games 
Site  Content  Comments 

A site where one can make up online quizzes on any topic. Multiplechoice questions are projected on a screen and students answer on an Internetcapable device and compete to get the top score.  Widely used in schools. Students enjoy it.  
Problem solving  Large collection of games, though many aren't terribly mathematical.  
Game based on Years 18 Maths  Students have to solve maths problems to make progress.  
Arithmetic, Years 311  Site includes a small collection of maths games.  
Arithmetic, Years 28  A game that practises arithmetic.  
Arithmetic, Years 28  An NCTM site containing maths games and challenges. Designed to encourage families to do maths together. 
Tools 
Site  Content  Comments 

A graphing package for functions and geometry with various tools and other teaching/learning resources.  A site widely used in schools.  
Many facilities, including graphing functions, plotting data, evaluating equations, exploring transformations.  A site widely used in schools.  
A calculator which will do symbolic manipulations like solving equations, finding indefinite integrals etc. 
 
Online coding in Logo  Site that allows coding in Logo and turtle graphics 
Interest 
Site  Content  Comments 

Interactive Mathematics Miscellany and Puzzles.  Good for generating interest and spurring investigations.  
Various, Years K8  Games, books and videos involving maths  
Amusing song about calculus  Clever takeoff of 'I Will Survive'. Worth showing to calculus students.  
10^275 times zoom into the Mandelbrot Set  Trippy patterns of artistic merit as well as mathematical interest.  
Video and song  A fairly shallow zoom into the Mandelbrot Set, but with a catchy song about the fractal. The song contains the fword, though it's not very obvious.  
Zoom into various fractals  Artistic merit as well as mathematical interest.  
Video of a set of swinging balls  A set of balls with slightly differing frequencies produce various patterns.  
Thousands of mathematical quotations 
 
Collection of fractal art images  Artistic application of maths. Have to log in to Pinterest to see all images.  
A large collection of mathematical tricks as well as other materials  Part of www.pedagonet.com 
Other Sites 
Site  Content  Comments 

All secondary maths with an emphasis on worked examples  A site which would complement M1Maths. It covers fairly much the same topics but with more worked examples. 
Astronomy 
The link below is to the website of an astronomy club. The site contains astronomy information, particularly under the buttons: 'Space Facts', 'Tidbits', 'Glossary' and 'Internet Resources'. 
FOR TEACHERS M1Maths 
Learning and Assessment Programs Many different maths curricula are specified around the world and many different school programs are written in accordance with these. However, up to about Year 10, these curricula and programs all tend to contain basically the same maths topics, just arranged in a different sequence and maybe assigned to different year levels. Furthermore, school programs up to Year 10 are in most cases not required to match the statespecified timings exactly, as long as students have covered the required material by the end of the period concerned. For schools wishing to use the M1Maths materials as their primary student text, a number of options for learning and assessment programs are described below, but hybrids of these and completely different approaches are of course possible. 
Option 1  Fitting the M1Maths Modules to the Existing Program 

For a school program up to Year 10, it should be possible to assign the corresponding M1Maths module(s) to each topic in the program and then to work through those modules accordingly. This is basically the same as using a commercial textbook with the school program. 
Option 2  Using the M1Maths Levels as the School Program 
This is a suggestion for a curriculumpaced school program based on M1 Maths. A schedule of modules could be decided upon, assigning the Level 1 modules to Year 7, the Level 2 modules to Year 8 and so on. The following is one possible sequence. Note that Level 5 is for students aspiring to the higherlevel maths in senior. 
Year 7: Level 1 M11..4 A11..3 N11..5 G11..3 S11..2 N16..10 A14..6 P11 
Year 8: Level 2 M21..3 N21..4 G21..6 A21..3 P21..3 S21..2

Year 9: Level 3 N31..3 A31..5 G31 P31 S31..3 M31..4 A36..10

Year 10: Level 4 N41 A41..3 M41 P41 A44..6 G41

Year 10: Level 5 A51..8 N51 M51..2 A59..13

The skills would need to be developed in parallel with the knowledge. Knowledge and skills might be assessed once a term or at other intervals. The level tests below are one way to do this. Students could sit say the Level 2 test at the end of each term in Year 8 and see their progress as the year goes on and they learn more. Any students who work ahead of the class would be suitably rewarded. 
Option 3  StudentPaced Program 

In a studentpaced program, students work through the learning at a speed that suits their individual background, ability, aspirations and dedication, mastering more basic concepts before being expected to use them to develop more advanced concepts. This type of program is conducive to the develoment of a growth mindset in the students. Many education authorities, though, specify what should be taught in each year level to all students regardless of their present state of knowledge. This can produce a lockstep progression through the material which might suit average to slightly aboveaverage students, but which restricts the more able and enthusiastic students and leaves those students who have not yet mastered the prerequisite knowledge to get lost, to get disillusioned and to get further and further behind. In many cases, however, this requirement is not externally monitored and thus it is possible to use a program which allows all students to progress at their own pace and thus as far as suits their particular circumstances. M1Maths is particularly suited to such a studentpaced program. This is why the material is divided into Levels 1 to 6 rather than yearlevels 7 to 12. The studentpaced program links below are to a document which discusses the rationale for such an approach and gives a detailed account of such a program of learning and assessment. The Progress Tracker link is to a spreadsheet that can be used to record the students' progress within this program. Studentpaced program: pdf docx Progress Tracker: xlsx Click on the required format. Word documents and spreadsheets need to be downloaded and opened in Word or Excel to display properly. 
Level Tests The links below are to Knowledge tests and Skills test for each level from Level 1 to Level 5. The tests were produced by writing a question or two from each of the modules at that level, plus a scattering of questions from earlier levels. There will eventually be four versions of each test. However, not all have been written to date. These tests could be used as school tests. A version should be picked at random and minor changes made (e.g. changing some of the numbers, maybe changing the problems and the investigation). Students can then still use the versions below for test preparation / practice without invalidating the tests. The tests won't be high stakes after all. Alternatively, schools might decide to write their own tests from scratch. In that case, the tests below could be used as models. Click on the required format. Word documents need to be downloaded and opened in Word to display properly. 
Version A  Level 1  Level 2  Level 3  Level 4  Level 5 

Knowledge  pdf docx  pdf docx  pdf docx  pdf docx  pdf docx 
Skills  pdf docx  pdf docx  pdf docx  pdf docx  pdf docx 
Version B  Level 1  Level 2  Level 3  Level 4  Level 5 
Knowledge  pdf docx  pdf docx  pdf docx  
Skills  pdf docx  pdf docx  pdf docx  
Version C  Level 1  Level 2  Level 3  Level 4  Level 5 
Knowledge  pdf docx  pdf docx  
Skills  pdf docx  pdf docx  pdf docx  
Version D  Level 1  Level 2  Level 3  Level 4  Level 5 
Knowledge  pdf docx  pdf docx  
Skills  pdf docx  pdf docx  pdf docx 
Curriculum Correlation M1Maths covers the maths generally taught in secondary school (or middle and high school) up to and including calculus. The learning sequence broadly matches that used in most curricula, the ideas being assigned to levels in a way that makes for a logical progression which matches typical mathematical development and in which all prerequisite ideas have been met when they are needed. If the sequence in M1Maths is used, students should develop the appropriate and required learnings by the critical stages in their education and thus, learning should meet the requirements of authority curricula. Suggested detailed module sequences are available under Learning and Assessment Programs. However, because curricula vary in detail between authorities, the M1Maths sequence may not match any authority curriculum or school program exactly. If it is necessary to match learning to an authority curriculum on a yearto year (or shorterterm basis), using M1Maths as a regular text for learning will require the modules to be matched to the elements of the curriculum or program in use. Being Australian, I have done this for the Australian Years 7 to 10 syllabus and the Australian Years 1112 Mathematical Methods syllabus. Being a Queenslander, I have done the same for the Queensland Years 1112 syllabuses. The links below will take you to the various tables. These tables can also be used as templates for correlation with other curricula. I'm afraid I haven't done the same for other places. But, if anyone would like to produce them for their country or state, I would gladly include them here. Word documents need to be downloaded and opened in Word to display properly. 
Australian Curriculum 

Years 710 Maths v8.4 (Implementation up to 2023) pdf docx Years 710 Maths v9.0 (Implementation 2024) pdf docx A summary of the essential points of the Australian Years 710 Maths Curriculum is provided here. The full Australian curriculum can be viewed at v9.australiancurriculum.edu.au. 
Queensland Syllabuses 
Years 1112 Essential Maths pdf docx Years 1112 Maths Methods pdf docx 
Fun and Games These are fun activities and games which can be played as a class or by small groups. They help develop or reinforce the concepts addressed in the learning modules. Click the preferred format in the first column to download instructions and materials for that activity. Word documents need to be downloaded and opened in Word to display properly. The instructions are designed primarily for teachers to allow them to conduct the activity with a class. 
Activity  Format  Relevance  Description 

Bingo  Mental arithmetic (all levels)  A game of bingo where students have to perform simple mental computations to work out the numbers called  
Goodies and Baddies  General  A quiz game between one half of the class and the other. The questions can be made up to suit the needs of the class  
Group Problem Solving  Problem solving – persistence and cooperation  A competition in which students work in groups to try to solve more problems correctly than the other groups  
12 Question Challenge  Problem solving – persistence and cooperation  A competition in which students work in groups to try to solve more problems correctly than the other groups  
2 by 5 Challenge  Problem solving – persistence and cooperation  A competition in which students work in groups to try to solve more problems correctly than the other groups  
Relay  Problem solving – persistence and cooperation  A competition in which students work in groups to try to solve a series of problems more quickly than the other groups  
Number Facts Race  Number Facts Fluency  A race between groups in which students have to recall and state number facts  
Mind Reading  Problem solving  A simple magic trick for students to work out  
Twenty  Problem solving  A strategy game for students to work out so they can succeed in the challenge of beating the teacher  
Last One Standing  General  A quick class game that rehearses recollection of facts and mental arithmetic skills. Can be used as a break and leg stretch  
4Corner Quiz  General  This is a fun quiz involving movement that can be used to revise and reinforce any topic  
Target  Number sense, mental arithmetic,estimation, order of operations  A card game in which students use numbers to make an expression as close in value as possible to a given target number  
Back to Back  Geometry, Communication  An activity where students have to give clear and precise mathematical instructions  
Protractor Golf  Estimating and measuring angles and distances  A game for two in which students aim for holes on a paper golf course by estimating then measuring direction and distance  
Walk the Plank  Adding and subtracting positive and negative numbers  A simulation of walking the plank using addition and subtraction of positive and negative numbers to decide which direction and how far to go  
Fraction Line  Fraction meanings and fractions of numbers  A game where one half of the class competes against the other half to best estimate given fractions of the way along a line  
Fraction Dominoes  Fraction conversion  A game of dominoes to develop fluency with recognising different expressions of the same fraction and with fraction conversion  
Millionaire  Fractions of numbers  A board game that rehearses fractions among other things  
Stomp  Number facts and mental arithmetic  A board game for two  
Greedy Pig  Probability  A game mostly for fun, but which helps develop intuitive ideas of probability. It can be used with all levels 
Professional Development Articles Professional Development might be a bit of a grandiose title for this section, which consists of a bunch of random articles written over the years by David Ilsley. The articles bear some relation to mathematics education, though not all are terribly serious. Some of the articles have been published in association journals; some have been used in facetoface professional development; and some have just been written for lack of anything better to do. Word and Excel documents need to be downloaded and opened in Word or Excel to display properly. 
Title  Format  Summary 

Polar Art  Some artistic polar function graphs  
A Mathematician's Glossary of Psychological Disorders  A bit of a joke  
Algebra as the Study of Relations  The philosophy behind the approach to algebra used in M1Maths.  
Bad Language in the Maths Classroom  A nottooserious article about the misuse of certain words in maths teaching  
Mathematical Quotes  Quotes about mathematics  some humorous, some more serious.  
Avoiding Confusion in Probability  Teaching programs and textbooks often cause students to develop misconceptions in elementary probability. This article suggests a way to avoid that. The article explains the philosophy behind the approach to probability used in M1Maths.  
A Single Area Formula for All 2D Shapes  A suggestion that students can learn the single area formula A = l x w x f for all 2D shapes  
Setting Up a School Orienteering Course  Some tips on setting up a course  
Is 9 a Random Number?  Some thoughts on what makes numbers random  
Numerical Solution of Differential Equations Using Spreadsheets  Using spreadsheets to solve differential equations numerically. The method is analogous to the numerical methods of finding definite integrals, but it can be applied to a much broader range of problems including those which lead to second and higherorder equations and those which lead to equations in several variables which have to be solved simultaneously. Download the spreadsheet in Excel so it renders properly.  
The Envelope Paradox  An interesting paradox  
The Envelope Paradox  Resolution  A resolution to the paradox above.  
The Unexpected Exam Paradox  An interesting paradox whose resolution is beyond me  
All Whole Numbers Can Be Expressed in Eleven Words or Less  Another paradox  
Fluid Resistance: Proportional to v or to v squared?  It can be either. An explanation of what determines which is the case in physical situations.  
Learning Mensuration Formulae  A suggetion for making mensuration formulae easier to remember and more difficult to confuse.  
Collective Nouns for Teachers  Littleknown collective nouns for groups of teachers  
Programming on the TI83 Calculator  Three sample programs to illustrate the programming potential of graphics calculators  
Bad Maths  Extending Pascal's Triangle to make Pascal's Hexagon.  
Finding Angles  Two methods for finding angles between intersectiong lines, one using geomety theorems, one using the idea of bearings  
Deviant Polynomials  A nonstandard general form for polynomials can be easier to get one's head around and can make curve sketching more intuitive.  
Entropy with Combinations  Using combinations to get a feel for entropy  
The Hairy Dog Theorem  My favourite mathematical theorem  
The Ham and Cheese Sandwich Theorem  An application of the concept of 'degrees of freedom'  
Round Things  An easy way to remember length, area and volume formulae for circles and spheres  
Piracy  A practical application of complex numbers  
Serious Problems 110  Challenging problems that teachers and topgun students might enjoy  
Serious Problems 110  Solutions  Worked solutions to serious problems  
Serious Problems 1120  Challenging problems that teachers and topgun students might enjoy  
Serious Problems 1120  Solutions  Worked solutions to serious problems  
Serious Problems 2130  Challenging problems that teachers and topgun students might enjoy  
Serious Problems 2130  Solutions  Worked solutions to serious problems  
Serious Problems 3134  Challenging problems that teachers and topgun students might enjoy  
Serious Problems 3134  Solutions  Worked solutions to serious problems  
Shifting the Emphasis from Memorising to Thinking  Queensland Association of Maths Teachers 
Free Maths Websites This is a list of good free websites for teachers of secondary maths. Sites designed more for students are included in the Extras for Students section. 
Resources for Teachers 

Site  Content  Comments 

Various resources for maths teachers.  The NCTM public site.  
Mathematics resources for children, parents and teachers  The Nrich Maths Project Cambridge, England. Designed to enrich learning.  
Lesson resources for many topics P10.  ACARA site.  
Online manipulatives, worksheets etc for primary and secondary maths  A lot of stuff to browse.  
Online manipulatives for many topics  Large collection. Requires Java. Can be a problem with some web browsers.  
Jo Boaler's Mindset approach to Maths Eduction  American site for teachers  
Database of resources for teachers including many for secondary maths  Searchable by subject and level. UKbased. 
Background image: https://pixabay.com/illustrations/beachbackgroundseaocean3892386/ (cropped) (Creative Commons licence) 