M1Maths

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.

• They could be used as an online textbook. The site contains everything that a textbook contains as well as quite a few things that textbooks don’t. The explanations are fuller than those given in most textbooks. The aim of this is to allow students to learn independently if they wish or need to. Using M1Maths in place of a commercial textbook could save a lot of money which could then be spent on other resources and experiences.
• As with all textbooks, M1Maths won’t follow the school program exactly. M1Maths modules can be assigned to each work unit in the school program.
• Alternatively, M1Maths could be used as the work program. Students would work through each level in turn. The sequence of modules within a level would need to be decided, but some model sequences are offered in the Programs section under Extras for Teachers. Programs could be curriculum-paced or student-paced as explained in the Programs section
• Students could use the practice exercises, problems and revision sets as an alternative to some or all of the exercises in a commercial textbook. This could act as a trial for schools thinking of replacing their commercial textbook with the M1Maths materials.
• The explanations could be used when teachers introduce and explain new concepts. Teachers could refer to or work through the explanations with the class. Those students who are up to it might learn to work through the explanations by themselves and thus increase their independence in learning.
• Students who can use the explanations independently could go through them at home prior to teacher explanation of the concepts in a ‘Flipped Classroom’ approach.
• Students who can and wish to could also use the explanations and exercises to go ahead of what their class is doing or to familiarise themselves with a topic before learning it formally.
• Students could use the explanation after the topic has been taught to revise or to remind themselves of things they have forgotten. This could be particularly valuable for students who have forgotten ideas from earlier years which may not be in the current textbook.
• Students who did not fully grasp concepts when taught could use the explanations at their own pace to get a different perspective of a concept, which might possibly make the penny drop.
• The materials could be useful for students who miss lessons.
• The explanations, practice questions and problems provide an excellent source of material for maths tutors (or parents) working with students from about Year 5 to Year 12.

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