M1 MATHS Explanations and practice for each topic from whole numbers to calculus. A free online textbook. To find a topic, use the menu below. Level 1 is about Years 57, Level 6 Years 1112. Or Ctrl+F to search. 
Main Menu 
Extras for Students Extras for Teachers 
Programs Tests Curriculum Correlation 

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 modules. 
N11  pdf docx  Whole numbers 

4 h  
N12  pdf docx  Fraction Meanings 

3 h  
N13  pdf docx  Fraction Conversions 

3 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  
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 
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 
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 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 
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  
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 
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 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 
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  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 
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 
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 
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 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 
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 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 
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 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 
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  Higherorders 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 One module covers all levels. Click on the required format. Word documents need to be downloaded and opened in Word to display properly. 
pdf docx 

Skills: Problem Solving One module covers all levels. Click on the required format. Word documents need to be downloaded and opened in Word to display properly. 
pdf docx 

Skills: Investigating One module covers all levels. Click on the required format. Word documents need to be downloaded and opened in Word to display properly. 
pdf docx 

Skills: Communicating One module covers all levels. Click on the required format. Word documents need to be downloaded and opened in Word to display properly. 
pdf docx 

Programs Each country in the world, and often each state, specifies a different maths curriculum for its students. However, up to Year 10 at least, these curricula all tend to contain basically the same maths topics, just arranged in a different sequence and maybe assigned to different year levels. So, for a school work program up to Year 10, it should be possible to assign the corresponding M1 Maths module to each topic in the curriculum and then to work through those modules accordingly. A possible program for the Australian Years 710 curriculum is given below under the Curriculumpaced link. Alternatively, if there is some freedom regarding the internal structure of the school program used, it should be possible to work progressively through Levels 1, 2, 3 . . . over the Years up to Year 10. The idea of calling them Levels 1 to 5 rather than 7 to 10 is that it is not necessary to lockstep the M1 Maths levels to the school year levels. Rather, it allows a program where students work through the levels at a pace which suits their background, ability, aspirations and dedication. Such a program would allow students to master concepts before moving on to other concepts which depend on them, a luxury often not afforded by lockstep programs. Clicking the Studentpaced link below will lead to a suggestion for this type of program. The Progress Tracker link below is a spreadsheet that could be used to record progress with such a studentpaced program. Click on the required format. Word documents and spreadsheets need to be downloaded and opened in Word or Excel to display properly. 
Curriculumpaced pdf docx Studentpaced pdf docx Progress Tracker xlsx 
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  
Skills  pdf docx 
Version C  Level 1  Level 2  Level 3  Level 4  Level 5 

Knowledge  pdf docx  
Skills  pdf docx 
Version D  Level 1  Level 2  Level 3  Level 4  Level 5 

Knowledge  pdf docx  
Skills  pdf docx 
Curriculum Correlation Being Australian, I have produced correlation tables showing which M1 Maths knowledge module corresponds to each of the syllabus elements 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. 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 pdf docx  Years 1112 Maths Methods pdf docx 
Queensland Syllabuses 

Years 1112 Essential Maths pdf docx  Years 1112 Maths Methods pdf docx 
Years 1112 General Maths pdf docx  Years 1112 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 

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 
Search... To search for a particular string, word or phrase on this web page, press Ctrl+F. For more detailed instructions, see below for the browser you are using. To find modules which mention 'equation', search for 'equation'. If you want also to find 'equate', 'equating' etc., search for 'equat'. 
Chrome  Press Ctrl+F (or click on the white upward arrow on an orange background on the far right of the address bar, then choose 'Find...') You will get a small dialogue box near the top right of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Up and Down arrows in the dialogue box to move to other occurrences. 
Safari  Press Ctrl+F You will get a small box with a magnifying glass near the top right of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Enter key to scroll through other occurrences. 
Firefox  Press Ctrl+F (or click on the three horizontal bars on the far right of the address bar, then choose 'Find in This Page...') You will get a small dialogue box near the bottom left of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Up and Down arrows in the dialogue box to move to other occurrences. 
Edge  Press Ctrl+F (or click on the three dots on the far right of the address bar, then choose 'Find on Page...') You will get a small dialogue box near the top left of the screen. Enter the word you wish to find. You will be taken to an occurrence of it on the page. Use the Left and Right arrows in the dialogue box to move to other occurrences. 
Other Browsers  Most other browsers work in very similar ways. It shouldn't be hard to find the search function. 
Astronomy Below are links to some astronomy resources developed while running an astronomy club at Canterbury College 
The Dark Side The club website with details of the program, activities etc. Space Facts PowerPoints on various aspects of astronomy used for instruction Tidbits Short interesting astronomical articles 
Background image: https://pixabay.com/illustrations/beachbackgroundseaocean3892386/ (cropped) (Creative Commons licence)