## 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.

- About Polynomials

‘Introduces polynomial functions, shows you how to draw graphs of polynomials, as well as find zeros and turning points’. - Polynomial

Forms, functions & equations, elementary properties, advanced examples, history, solving, polynomials & calculus, abstract algebra, classifications, extensions of the concept, links including to calculators for this area. Wikipedia. - Polynomial Expressions, Equations, and Functions

‘Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions’. Khan Academy. - Polynomials [Maths is Fun]

First of a series of pages with explanations and examples. Student questions to test understanding. - Polynomials : Definitions/Evaluation

Text and formulae presentation. - Polynomial [Wolfram Mathworld]

Information, examples, links to further information. Senior Secondary, Tertiary. - Polynomial Worksheets

Collection covering polynomials and polynomial functions.

#### Videos

- Factor Polynomials Using the GCF

Video on the topic. Khan Academy. Links to related videos on the right. - Polynomials

Multiple videos covering aspects of this topic.

#### Calculus

- Calculus and Analysis

Wolfram MathWorld. 28 sections, each containing multiple sub-sections. - Differential Calculus

Khan Academy. ‘Differential calculus deals with the study of the rates at which quantities change. It is one of the two principle areas of calculus’. Another site is Integral Calculus. - Mathematics Online Tutorials

Tutorials for Pre-Calculus, Single Variable Calculus, Multi-Variable 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’.

#### 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’.

#### 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’.

#### Numerals & Numbers

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

- Arabic
- Babylonian
- Egyptian
- Greek
- Indian
- Math & Numbers in Early History
- Roman
- Roman Numerals, History and Use

#### Other Information

- Number and Place Value Resources

Scootle. 180+ classroom and teacher resources. - Real Numbers

Scootle. 50+ classroom and teacher resources.

#### Other Specific Mathematical Areas

- Metric Measurement Links

Pinterest, 128 Pins. Covers Mathematics and Science. - Using Units of Measurement

Scootle. 10+ classroom and teacher resources. - What’s Special About This Number ?

Find distinctive facts about numbers from 1 to 9 999. Links to information about the specific fact and include examples of how to discover the information as well as what it is.

#### Probability

- Maths is Fun - Probability

Brief text presentation. Multiple short videos on specific aspects. Links to related information. - Powerhouse Museum : Gambling

‘Learn about mathematics and probability, as applied to lotto, instant scratchies, roulette, poker machines’. Teacher section. Australian. - Probability

The first of 10 lessons plus exercises on the area of Probability. - Statistics and Probability

Scootle. 30+ classroom and teacher resources.

#### Problem Solving

- House of Math Word Problems for Children

‘To help elementary school [Grade 1st through 6th] children boost their math problem solving and critical-thinking skills’. Fee-based. - Interactive Maths - Word Problems

Choose from the multiple options available. - Maths : Solving Problems : Word and Real Life
Problems

Choose from an extensive list with problem options in multiple presentation formats - PDF, Word, PowerPoint. UK. - Problem Solving Teaching Ideas

Collection presented for multiple age levels. UK. - Maths Word Problems

‘Learn how to solve math word problems with Thinking Blocks, videos, and interactive practice’. USA.

#### 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

- SOS Mathematics - Trigonometry

Tutorials covering aspects of trigonometry. - Trigonometry

Learn about trigonometry. - Trigonometry [Khan Academy]

Sections cover ‘Basic Trigonometry; Unit Circle Definitions of Trig Functions; Graphs of Trig Functions; Trig identities and examples’. - Trigonometry [Math Warehouse]

‘Theorems, formula, rules and Worksheets’. - Trigonometry [Wolfram MathWorld]

‘Angles, Directed Angles, General Trigonometry, Spherical Trigonometry, Surveying, Trigonometric Functions@Trigonometric Identities, Trigonometric Inequalities’. - Trigonometry Tutorials & Problems

‘Free tutorials and problems on solving trigonometric equations, trigonometric identities and formulas can also be found’.