M1MATHS Home   Explanations and practice for each high-school 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 well-laid out, the font, size and spacing are reader-friendly. Love the interesting bits of background info that makes self-learning 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 self-guided 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 Lead-In 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 problem-solving 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 drop-down 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.
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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 P-10 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 BY-NC 4.0. This allows the materials to be printed, copied, adapted and stored locally. It also allows them to be re-published for non-commercial 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 well-laid out, the font, size and spacing are reader-friendly. Love the interesting bits of background info that makes self-learning 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 7-12 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 7-12 Facebook Group I love the Settler/Zoomer resources. Callum Day, Australian Secondary Mathematics Teachers 7-12 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 5-7, Level 6 Years 11-12. 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 pre-requisite Level 1 modules. |
N1-1 | pdf     docx | Whole numbers |
4 h
|
| N1-2
| pdf     docx
| Fraction Meanings 3 h
|
| N1-3
| pdf     docx
| Fraction Conversions 3 h
| N1-2
| N1-3
| pdf     docx
| Fraction Conversions Alternative 'Learn' Section: Learning by Thinking 4 h
| N1-2
| N1-4
| pdf     docx
| Negatives 1 h
|
| N1-5
| pdf     docx
| Calculators 1 h
| N1-3 N1-4
| N1-6
| pdf     docx
| Powers 2 h
| N1-1 N1-5
| N1-7
| pdf     docx
| Order of Operations |
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 pre-requisite Level 2 modules. |
N2-1 | pdf     docx | Number Sets |
2 h
|
| N2-2
| pdf     docx
| Fractions of Numbers 2 h
|
| N2-3
| pdf     docx
| Rates 4 h |
N2-4
| pdf     docx
| Ratios 2 h
| N2-3
| N2-5
| pdf     docx
| Decimal Operations 2 |
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 pre-requisite Level 3 modules. |
N3-1 | pdf     docx | Scientific Notation |
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 pre-requisite Level 4 modules. |
N4-1 | pdf     docx | Compound Interest |
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 pre-requisite Level 5 modules. |
N5-1 | pdf     docx | Simplifying Surds |
2 h
| A5-2
| |
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 pre-requisite Level 6 modules. |
N6-1 | pdf     docx | Complex Numbers |
9 h
|
| N6-2
| pdf     docx
| Vectors |
Algebra Level 1       Level 2       Level 3       Level 4       Level 5       Level 6 Level 1 is Years 5-7, Level 6 Years 11-12. 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 real-life 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 pre-requisite Level 1 modules. |
A1-1 | pdf     docx | Relations 1 |
3 h
|
| A1-2
| pdf     docx
| Relations 2 3 h
| A1-1
| A1-3
| pdf     docx
| Patterns 3 h
| A1-2
| A1-4
| pdf     docx
| Discrete vs Continuous Relations 2 h
| A1-3
| A1-5
| pdf     docx
| Substitution 3 h
| A1-4
| A1-6
| pdf     docx
| Equations 7 h
| A1-5
| |
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 pre-requisite Level 2 modules. |
A2-1 | pdf     docx | Writing Equations |
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 pre-requisite Level 3 modules. |
A3-1 | pdf     docx | Undoing the Unknown |
3 h
|
| A3-2
| pdf     docx
| Choosing the Unknown 2 h
| A3-1
| A3-3
| pdf     docx
| Squares and Fractions 4 h
| A3-2
| A3-4
| pdf     docx
| Rearranging Formulae 2 h
| A3-3
| A3-5
| pdf     docx
| Solving by Graphing 2 h
|
| A3-6
| pdf     docx
| Domain and Range
| 2 h
|
| A3-7
| pdf     docx
| Functions 3 h
| A3-6
| A3-8
| pdf     docx
| Linear Functions 5 h
| A3-7 M3-3
| A3-9
| pdf     docx
| Reciprocal Functions< |
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 pre-requisite Level 4 modules. |
A4-1 | pdf     docx | Factorising |
5 h
|
| A4-2
| pdf     docx
| Quadratic Functions 6 h
| A4-1
| A4-3
| pdf     docx
| Simultaneous Equations - Linear |
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 pre-requisite Level 5 modules. |
A5-1 | pdf     docx | Polynomial Functions |
3 h
| <
| A5-2
| pdf     docx
| Index Laws 6-10 3 h
|
| A5-2
| pdf     docx
| Index Laws 6-10 Alternative 'Learn' Section: Learning by Thinking 4 h
|
| A5-3
| pdf     docx
| Power Functions 2 h
| A5-2
| A5-4
| pdf     docx
| Exponential Functions and Logs 5 h
| A5-2
| A5-5
| pdf     docx
| Simultaneous Equations - General 6 h
| A5-3 A5-4
| A5-6
| pdf     docx
| Finding Formulae for Functions 3 h
| A5-5
| A5-7
| pdf     docx
| Model Functions 3 h
| A5-6
| A5-8
| pdf     docx
| Calculator Equation Solving 1 h
| A5-1
| A5-9
| pdf     docx
| Algebraic Transformations 4 h
|
| A5-10
| pdf     docx
| Further Relations 5 h
| A5-1
| A5-11
| pdf     docx
| Trigonometric Functions |
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 pre-requisite Level 6 modules. |
A6-1 | pdf     docx | Combinations and the Binomial Expansion |
6 h
|
| A6-2
| pdf     docx
| Arithmetic Sequences 4 h
|
| A6-3
| pdf     docx
| Geometric Sequences |
Measurement Level 1       Level 2       Level 3       Level 4       Level 5       Level 6 Level 1 is Years 5-7, Level 6 Years 11-12. 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 pre-requisite Level 1 modules. |
M1-1 | pdf     docx | Dimensions, Size and Mass |
5 h
|
| M1-2
| pdf     docx
| Time 1 2 h
|
| M1-3
| pdf     docx
| Unit Conversion |
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 pre-requisite Level 2 modules. |
M2-1 | pdf     docx | Graduated Scales |
2 h
|
| M2-2
| pdf     docx
| Time 2 5 h
|
| M2-3
| pdf     docx
| Length, Area and Volume 2 6 h
| N2-2 G2-4
| M2-3
| pdf     docx
| Length, Area and Volume 2 Alternative 'Learn' Section: Learning by Thinking 8 h
| N2-2 G2-4
| |
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 pre-requisite Level 3 modules. |
M3-1 | pdf     docx | Pythagoras |
3 h
|
| M3-2
| pdf     docx
| Trigonometry 6 h
| M3-1
| M3-3
| pdf     docx
| Slope 2 h
| M3-2
| M3-4
| pdf     docx
| Length, Area and Volume 3 8 h
| M3-1
| M3-4
| pdf     docx
| Length, Area and Volume 3 Alternative 'Learn' Section: Learning by Thinking 8 h
| M3-1
| |
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 pre-requisite Level 4 modules. |
M4-1 | pdf     docx | Length, Area and Volume 4 |
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 pre-requisite Level 5 modules. |
M5-1 | pdf     docx | Unit Circle and Trig Identities |
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 pre-requisite Level 6 modules. |
M6-1 | pdf     docx | Radians |
Geometry Level 1       Level 2       Level 3       Level 4       . . . . .       . . . . . Level 1 is Years 5-7, Level 6 Years 11-12. 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 pre-requisite Level 1 modules. |
G1-1 | pdf     docx | Drawings |
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 pre-requisite Level 2 modules. |
G2-1 | pdf     docx | Maps and Scales |
2 h
|
| G2-2
| pdf     docx
| Geometric Figures 5 h
|
| G2-3
| pdf     docx
| Properties of Polygons |
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 pre-requisite Level 3 modules. |
G3-1 | 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 pre-requisite Level 4 modules. |
G4-1 | pdf     docx | Geometric Proofs |
Statistics Level 1       Level 2       Level 3       Level 4       Level 5       . . . . . Level 1 is Years 5-7, Level 6 Years 11-12. 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 pre-requisite Level 1 modules |
S1-1 | pdf     docx | Data Displays 1 |
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 pre-requisite Level 2 modules. |
S2-1 | 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 pre-requisite Level 3 modules. |
S3-1 | pdf     docx xlsx | Spreadsheets |
4 h
|
| S3-2
| pdf     docx
| Data Displays 2 |
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 pre-requisite Level 4 modules. |
S4-1 | pdf     docx | Quantiles and Spread |
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 pre-requisite Level 5 modules. |
S5-1 | pdf     docx | Grouped Data |
3 h
|
| |
Probability Level 1       Level 2       Level 3       Level 4       . . . . .       Level 6 Level 1 is Years 5-7, Level 6 Years 11-12. 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 pre-requisite Level 1 modules. |
P1-1 | pdf     docx | Probability |
8 h
| N1-3
| |
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 pre-requisite Level 2 modules. |
P2-1 | pdf     docx | Compound Events |
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 pre-requisite Level 3 modules. |
P3-1 | 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 pre-requisite Level 4 modules. |
P4-1 | 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 pre-requisite Level 6 modules. |
P6-1 | pdf     docx | Sets |
2 h
|
| P6-2
| pdf     docx
| Conditional Probability 3 h
|
| P6-3
| pdf     docx
| Discrete Random Variables 5 h
|
| P6-4
| pdf     docx
| Binomial Distributions |
Calculus . . . . .       . . . . .       . . . . .       . . . . .       . . . . .       Level 6 Level 1 is Years 5-7, Level 6 Years 11-12. 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 pre-requisite Level 6 modules. |
C6-1 | pdf     docx | Velocity Graphically |
4 h
|
| C6-2
| pdf     docx
| Velocity Algebraically 6 h
| C6-1
| C6-3
| pdf     docx
| Velocity by Rule 6 h
| C6-2
| C6-4
| pdf     docx
| Other Relations 4 h
| C6-3
| C6-5
| pdf     docx
| Applications of Derivatives 8 h
| C6-4
| C6-6
| pdf     docx
| Chain, Product and Quotient Rules 7 h
| C6-5
| C6-7
| pdf     docx
| Other Derivatives 5 h
| C6-6
| C6-8
| pdf     docx
| Mastering Differentiation 12 h
| C6-7
| C6-9
| pdf     docx
| Differential Equations 10 h
| C6-8
| C6-10
| pdf     docx
| Integration 14 h
| C6-9
| C6-11
| pdf     docx
| Pert 4 h
| C6-10
| C6-12
| pdf     docx
| Higher-order Derivatives 3 h
| C6-10
| C6-13
| pdf     docx
| Graph Sketching |
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 mid-point 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 pre-requisite 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 pre-requisite 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 pre-requisite 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 pre-requisite 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     Practice & Problems     Games     Tools     Interest     Other |
  Explanations |
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  Site |   Content |   Comments |
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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 hand-written/drawn. | |
Facts and explanations covering Years 7-10 maths | A good reference where one can easily look up mathematical facts. Well organised. | |
Written and video explanations of maths ideas, Years 7-10 | 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 higher-level 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 7-10 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 on-line quizzes on any topic. Multiple-choice questions are projected on a screen and students answer on an Internet-capable 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 1-8 Maths | Students have to solve maths problems to make progress. | |
Arithmetic, Years 3-11 | Site includes a small collection of maths games. | |
Arithmetic, Years 2-8 | A game that practises arithmetic. | |
Arithmetic, Years 2-8 | 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 K-8 | Games, books and videos involving maths | |
Amusing song about calculus | Clever take-off 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 f-word, 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 state-specified 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 |
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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 curriculum-paced 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 higher-level maths in senior. |
Year 7: Level 1 M1-1..4 A1-1..3 N1-1..5 G1-1..3 S1-1..2 N1-6..10 A1-4..6 P1-1 |
Year 8: Level 2 M2-1..3 N2-1..4 G2-1..6 A2-1..3 P2-1..3 S2-1..2     |
Year 9: Level 3 N3-1..3 A3-1..5 G3-1 P3-1 S3-1..3 M3-1..4 A3-6..10   |
Year 10: Level 4 N4-1 A4-1..3 M4-1 P4-1 A4-4..6 G4-1     |
Year 10: Level 5 A5-1..8 N5-1 M5-1..2 A5-9..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 - Student-Paced Program |
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In a student-paced 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 lock-step progression through the material which might suit average to slightly above-average students, but which restricts the more able and enthusiastic students and leaves those students who have not yet mastered the pre-requisite 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 student-paced program. This is why the material is divided into Levels 1 to 6 rather than year-levels 7 to 12. The student-paced 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. Student-paced 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 pre-requisite 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 year-to year (or shorter-term 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 11-12 Mathematical Methods syllabus. Being a Queenslander, I have done the same for the Queensland Years 11-12 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 |
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Years 7-10 Maths v8.4   (Implementation up to 2023)       pdf       docx Years 7-10 Maths v9.0   (Implementation 2024)       pdf       docx A summary of the essential points of the Australian Years 7-10 Maths Curriculum is provided here. The full Australian curriculum can be viewed at v9.australiancurriculum.edu.au. |
Queensland Syllabuses |
Years 11-12 Essential Maths  pdf       docx Years 11-12 Maths Methods   pdf       docx Years 11-12 General Maths   pdf       docx Years 11-12 Specialist Maths   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 | |
4-Corner 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 face-to-face 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 not-too-serious 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 higher-order 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 | Little-known 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 non-standard 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 1-10 | Challenging problems that teachers and top-gun students might enjoy | |
Serious Problems 1-10 - Solutions | Worked solutions to serious problems | |
Serious Problems 11-20 | Challenging problems that teachers and top-gun students might enjoy | |
Serious Problems 11-20 - Solutions | Worked solutions to serious problems | |
Serious Problems 21-30 | Challenging problems that teachers and top-gun students might enjoy | |
Serious Problems 21-30 - Solutions | Worked solutions to serious problems | |
Serious Problems 31-34 | Challenging problems that teachers and top-gun students might enjoy | |
Serious Problems 31-34 - 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 |
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  Site |   Content |   Comments |
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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 P-10. | 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. UK-based. |
Background image: https://pixabay.com/illustrations/beach-background-sea-ocean-3892386/ (cropped) (Creative Commons licence) |