Aussie Educator

Mathematics

mathematics [plural n., usually treated as singular]

the branch of science concerned with number, quantity, and space, either as abstract ideas [pure mathematics] or as applied to physics, engineering, and other subjects [applied mathematics].
- ORIGIN from Greek mathema ‘science’, from manthanein ‘learn’
.
Oxford Dictionaries

Mathematics is one of the core learning areas, with language, in all schools. While it can be studied as an individual subject, it is also found in most others through the use of its numbering and measurement systems. It is especially important in Science subjects.

This page looks at core areas of Mathematics - Algebra, Calculus, Fractions, Geometry, Problem Solving, Real Life Mathematics and other special areas.

Another page linked to this area is the Mathematics Teaching Resources page.

Core Areas

Algebra

  • Animated Mathematics
    ‘This website shall explain mathematical concepts visually when possible, have clear examples that shows all the algebraic steps, and practice questions and complete solutions’.
  • Basic Rules of Algebra
    The first of a number of sections looking at different aspects of Algebra.
  • Basic Word Problems
    Algebra.Help. Overview and use of examples.
  • Free Algebra Tutorials
    ‘If you have problems solving equations, simplifying expressions, working with fractions, radicals, polynomials, you have come to the right place ! We have lots of tutorials on all aspects of basic algebra - just click on the topic to display the tutorial. Free’.
  • Introduction to Algebra
    A basic introduction covering areas from Variables to sequences. 11 sections in all.

Polynomials

A Mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Videos

Calculus

Textbooks

  • Calculus
    Online text by Gilbert Strang. MIT Open Courseware. Has both an Instructor’s manual and a student Study Guide.
  • Visit the Textbooks page for a listing of this and other area’s textbooks available for free, online or in downloadable format.
  • The Calculus Page
    Annotated links for students and instructors. Tutorials, problems, examination samples, animations, tools & software, history, more.
  • Tutorials for the Calculus Phobe
    ‘The tutorials explain calculus audio-visually, and are the equivalent of a personal tutoring session. More than just boring lectures, the topics come alive with Flash animation. To view a lesson, simply click on its name’.

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Decimals

Plus related fractions.

  • Decimal Numbers
    From “What a Decimal Is” to practice in converting them to fraction or percentages.
  • Decimals and Percent
    Khan Academy. ‘Understanding decimals conceptually, using operations with decimals, rounding and estimating with decimals, and converting decimals’.
  • Decimals, Whole Numbers, Exponents
    Similar to the other sites but considerably more detail. From Decimal numbers to square roots.
  • Kids Online Resources
    Annotated links. Fractions, decimals, percentages. Several of the sites are listed here. Part of a larger Mathematics resource site.

Fractions

  • Fractions
    Khan Academy. ‘Understanding fractions conceptually, using operations with fractions, and converting fractions’.
  • Fractions [2]
    Information, primarily in text format. Quality information. 24 sections.
  • Fractions [3]
    Visual. What is … , practice, equivalent fractions, reducing, improper and mixed numbers, multiply, divide, add, subtract.
  • Fresh Baked Fractions
    Uses a game. multiple levels. Choose the “Odd Man Out”.
  • Visual Fractions
    Identify, rename, compare, add, subtract, multiply, divide. Worksheets, Fraction Maker.

Geometry

  • Circumference and Area of Circles
    Free lessons, with additional lessons able to be purchased. Maths Goodies.
  • Curriki Geometry
    ‘Curriki Geometry is designed with flexibility in mind. You can customise Curriki Geometry in a manner that works best for you’. Uses Project Based Learning.
  • Geometry
    Simple home page leads to directories including Basic Terms, Space Figures, Basic Solids. Angles, figures, polygons, area, perimeter, coordinates, basic solids. Presentation is plain but clear.
  • Geometry [Khan Academy]
    ‘This is a first year, high-school level course on Geometry [which is based on Euclid’s elements]. It revisits many of the basic geometrical concepts studied in earlier courses’.
  • Geometry [LearningMath]
    ‘Geometry introduces geometric reasoning as a method for problem solving. Throughout the first nine sessions, you will explore the properties of geometric figures and begin to explore the basis of formal mathematical proofs and solid geometry’. Includes videos.
  • Geometry [MathsisFun]
    ‘The idea behind the site is to offer mathematics as well as some fun bits and to combine the two wherever possible’. Covers all areas of Geometry.
  • Geometry Calculators
    Access Plane Geometry and Solid Geometry Calculators. Select “Geometry”, either of the two options, then specific calculators.
  • Geometry Calculators and Solvers
    ‘Easy to use online geometry calculators and solvers for topics in geometry such as calculate area, volume, distance, points of intersection’. Links to tutorials, help in geometry and other areas of mathematics.
  • Geometry Centre
    ‘Patterns, Shapes, Symmetry ! You will find these themes everywhere in the Geometry Centre. Browse through an exhibit, or jump right in and start experimenting !’ Interactive material.
  • Geometric Solids and Their Properties
    Online, activity based lessons. Multiple filters. National Council of Teachers of Mathematics, USA.
  • K-12 Internet Geometry Resources
    Directories of annotated links. Classroom materials, software, internet projects, interactive resources, discussion forums, more.
  • Perimeter
    ‘Activities and lesson plans for measuring perimeter. Interactive exercises, quizzes, games, worksheets. eThemes resources on area of polygons and circumference’.
  • Perimeter & Area of Polygons
    Free lessons, with additional lessons able to be purchased from Maths Goodies.
  • Teacher Features
    Select “Maths”, then “Measurement and Geometry”, then individual topics. ‘Our resources are aligned with the Australian National Curriculum’.

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Mathematics Help

  • Australian Curriculum Lessons
    Check Mathematics lessons for specific year levels and topics, e.g. ‘Identifying 3D Shapes Lesson Plan for Years 3/4’.
  • Eric Weisstein’s World of Mathematics
    Encyclopaedia of terms, derivations, equations.
  • Free Mathematics How-to Library
    Provided for 12 areas of Mathematics from Algebra to Trigonometry. Each has specific topics which are covered, e.g. Algebra → Evaluating Expressions.
  • Great Maths Websites to Explore
    Australian collection. Links are well annotated. Many sites use an interactive process.
  • Math.com
    Help site. Formulae are explained, even an indicator on resources [US based].
  • Mathematical Animations
    144 files covering a wide range of mathematical activities and areas. ‘ ’. Wikimedia Commons.
  • Mathematics Dictionary and Glossary for Students
    ‘With over 2 000 terms defined, this dictionary is ideal for supporting students who are studying mathematics or related subjects. The definitions of terms and concepts included within our dictionary include the majority of words that students will come across when studying mathematics at secondary school’.
  • Mathematics Internet Library
    Part of the Student Internet Library. Links for mathematical assistance.
  • Maths Links and Online Tools
    University of Vienna. ‘Selected links which are relevant for learning and teaching of mathematics’. Emphasis on tertiary level. Grouped under Tools, Links [by topic], Collections.
  • Number for Primary
    Centre of Learning Innovation, NSW. Links to resources and assistance with Online Tools, Early Stage 1, Stage 1, Stage 2 and 3, teachers, parents.
  • Online Math Help & Learning Resources
    ‘Materials for teaching and learning online. Find interesting and fun stuff to help your kids, students and children to enjoy, appreciate and learn numbers, counting, arithmetic, fractions, computation, geometry, statistics, set theory, trigonometry and even algebra and matrices !’
  • Skillswise - Numbers
    BBC. ‘English and Maths for adults’. Major topics with multiple sub-topics. Videos, games, more.
  • Visual Math Learning
    ‘Free educational site featuring an interactive on-line tutorial for teaching elementary mathematics and basic arithmetic for grades K-12 at the pre-algebra level’.

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Numerals & Numbers

Number systems - how they looked, when they were used, how they changed, more.

Other Information

Other Specific Mathematical Areas

Probability

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Problem Solving

Real Life Mathematics

  • Introducing MegaMaths
    Real-life mathematics using fun activities based on everyday things. Alternate site.
  • Maths in Daily Life
    Practical usage of maths for skills and understanding as you ‘look at the language of numbers through common situations, such as playing games or cooking’.
  • Moneystuff
    Designed to help young people learn how to develop independent living skills and handle personal finances.
  • PUMAS - Practical Uses of Math and Science
    ‘A collection of brief examples showing how maths and science topics taught in K-12 classes can be used in interesting settings, including everyday life’. More than 80 examples.
  • Real Life Maths
    ‘Uses images to highlight mathematical concepts found in life, in the environment, and everyday experiences’. USA.
  • Real World Investigations : Level 6
    DET, Victoria. ‘Using relevant and/or interesting situations is a key to helping students see the usefulness of maths and focus on the processes needed to solve problems’.
  • Real World Problems - Uses of Maths
    ‘Explore some real-world problems being solved by mathematicians. These problems are designed to be accessible to students in Grades 9-10 and later. Solutions are provided’. Canada.
  • TED-Ed Mathematics
    ‘Build a lesson around any TED-Ed Original, TED Talk or YouTube video’. Select from the numerous Maths in Real Life options available, e.g. Music and Maths : The genius of Beethoven.

Trigonometry

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