MATHEMATICS: SPECIALIST
RESOURCE LIST—WEB BASED RESOURCES
2011/19994[v2]
Mathematics Specialist; Resource list—web based resources
1
Copyright
© School Curriculum and Standards Authority, 2012
This document—apart from any third party copyright material contained in it—may be freely copied, or communicated on an intranet, for
non-commercial purposes by educational institutions, provided that it is not changed in any way and that the School Curriculum and
Standards Authority is acknowledged as the copyright owner.
Teachers in schools offering the Western Australian Certificate of Education (WACE) may change the document, provided that the
School Curriculum and Standards Authority’s moral rights are not infringed.
Copying or communication for any other purpose can be done only within the terms of the Copyright Act or by permission of the
Authority.
Copying or communication of any third party copyright material contained in this document can be done only within the terms of the
Copyright Act or by permission of the copyright owners.
Disclaimer
Any resources such as texts, websites and so on that may be referred to in this document are provided as examples of resources that
teachers can use to support their learning programs. Their inclusion does not imply that they are mandatory or that they are the only
resources relevant to the course.
2
Mathematics Specialist; Resource list—web based resources
MATHEMATICS: SPECIALIST
RESOURCE LIST—WEB BASED RESOURCES
The following links will direct you to websites outside the Authority’s site. The School Curriculum
and Standards Authority has no control over the content of materials accessible on the sites that
are cross-referenced. It is the responsibility of the user to make decisions about the relevance and
accuracy, currency and reliability of information found on these websites. Linking to these sites
should not be taken as endorsement of any kind. We cannot guarantee that the links will work all
of the time and we have no control over availability of the linked pages. It is your responsibility to
check that this information is accurate.
Mathematics: Specialist web-links
The resources listed on the next pages are linked to different units in the Mathematics: Specialist
course. The links were live when accessed in July 2012. The resources are classified as:
App
Dat
XL
ASt
ATe
Qu
Act
These are Java Applets with dynamic capabilities which could be used to
demonstrate mathematical relationships to a class or could be used by students.
The datasets, often in .txt (text), .dat (data) or .csv (comma separated variable
files) form have been chosen to suit the development or assessment of the
statistical relationships described in the Mathematics units.
Excel files that could be used by students or for demonstration.
These articles could be provided to students to stimulate interest in statistics or to
demonstrate questionable use of statistics. They are from the database provided
by the Mercury newspaper in Hobart, but the issues addressed are of national
relevance.
These articles are included as a resource for teachers. They report approaches
to statistics teaching, classroom use of data sets and historical background.
Questions are included that could be used for assessment or in teaching.
Activities: The links in this category describe classroom activities.
This document is two parts
Part 1: ................................................................................... Websites by Mathematical Content
Part 2: .............................................................................................................. Websites by units
Mathematics Specialist; Resource list—web based resources
3
Part 1: Websites by Mathematical Content
The descriptions in this section are in the following order:
 Website title
 Website URL
 Pathway or web navigation steps - this pathway will guide the reader to the particular page
of the website. The pathway looks like this (see below) and tells the reader where to find
the link to the next page or site.
 ► Continuity and limits ►An informal graphical view of continuity.
Introduction to calculus
Calculus Applets
http://www.calculusapplets.com/
This is a series of interactive activities exploring the calculus topics listed below. It allows the user
to explore the behaviour of functions and their graphs through dynamic java applets. These are
useful to both student for study and the teacher for demonstrating concepts.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
►Using the Graphing Tools
►Continuity and Limits
►Introduction to the Derivative
►Differentiation Short Cuts
►Applications of Differentiation
►Introduction to the Definite Integral
►Constructing Anti-derivatives
►Integration Techniques
►Applications of Integration
►Differential Equations
►Sequences and Series
Equation Plotter
http://mathplotter.lawrenceville.org/
This is a series of interactive activities exploring the calculus topics listed below. It allows the user
to explore the behaviour of functions and their graphs through dynamic java applets. These are
useful to both student for study and the teacher for demonstrating concepts. 3CMAS 2.4
►Graph (Functions)
►Draw (Geometric objects)
►Plot (Data and Statistics)
►Rotate (Surfaces and solids}
Equation Plotter
http://mathplotter.lawrenceville.org/
This is a series of interactive activities exploring the calculus topics listed below. It allows the user
to explore the behaviour of functions and their graphs through dynamic java applets. These are
useful to both student for study and the teacher for demonstrating concepts. 3CMAS 2.4
►Graph (Functions)
►Draw (Geometric objects)
►Plot (Data and Statistics)
►Rotate (Surfaces and solids}
4
Mathematics Specialist; Resource list—web based resources
PUMAS
http://pumas.jpl.nasa.gov/
Area
This task could be used as an activity for 3AMAS. It is not directly related to the course, but
explores areas of different shapes, the isoperimetric theorem and relates to algebraic formulae.
► Examples ► Examples by title ► Isoperimetric Geometry
Balanced Assessment
http://balancedassessment.concord.org
Circle properties
A short task for 3AMAS which requires students to use properties of circles to establish information
about circles. It is titled, “Oops! Glass Top”. Could be tied in with 3AMAS 2.2
► Our library of assessment tasks ► Oops! Glass Top
Enrich
http://nrich.maths.org/public/
Circles
In ‘Proof with circles’ you are given a circle of radius 1 unit and two circles of radius a and b which
touch each other and also touch the unit circle. Prove that you can always draw a 'flower' with six
petals with the unit circle in the middle, and six circles around it having radii
a, b, b/a, 1/a, 1/b and a/b such that each outer circle touches the unit circle and the two circles on
either side of it. A possible investigation for 3AMAS 2.7 or 3DMAT 2.3.3
►Search Enrich for Flower
►Flower (Stage 5)
Calculus Applets
http://www.calculusapplets.com/
Continuity
This site explores when a function is continuous or discontinuous.
Suitable for 3BMAS §5.1(Functions)
► Continuity and limits ►An informal graphical view of continuity
Waldomaths
http://www.waldomaths.com/Cubic1NL.jsp
Cubic polynomials
Examine the graphs of cubic polynomials of the form y  ax3  bx 2  cx  d .
Suitable for 2DMAT 1.2.6
►Search Waldomaths for Polynomials ► Polynomials (cubic quadratic, and linear,) graphs
Mathematics Specialist; Resource list—web based resources
5
Calculus Applets
http://www.calculusapplets.com/
Differentiation
A series of applets exploring differentiation including introductory activities. Suitable for 3BMAS 4
and 5, 3CMAS 5 and 6, 3BMAT 1.3
►Introduction to the derivative
Analyzemath
http://www.analyzemath.com/logfunction/
Logarithms
This site is suitable for introducing logarithmic functions and some of the properties associated with
this function. This can also be used to examine the relationship between logarithmic and
exponential functions. Suitable for 3AMAS 3.3 and 3AMAS 3.5.
►Index for Logarithms
Analyzemath
http://www.analyzemath.com/expfunction/
Exponentials
The following sites are suitable for 3CMAT 1.2.4, when introducing e and for 3BMAS 4.3, 4.4 when
introducing e and investigating growth and decay.
►Index for exponentials
Analyzemath
http://www.analyzemath.com/Graphing.html
Graphs of functions
Revision of graphing the equations of absolute values, cubic, linear, polar, quadratics, and
reciprocal, square root and trigonometric functions. Suitable for 3AMAS
►Left hand column ► Graphing
Calculus Applets
http://www.analyzemath.com
Integrals
A series of applets exploring Integration – suitable for 3CMAS 5.2, 5.4, 6.3
http://www.calculusapplets.com/
►6. Introduction to the definite integral
►7. Constructing anti-derivatives
►8. Integration techniques
6
Mathematics Specialist; Resource list—web based resources
Analyzemath
http://www.analyzemath.com
Inverse functions
Examples and ideas are very good for examples of Inverse Functions and is suitable for 3AMAS
4.4.
►Search this site for ► Applications and use of inverse functions
Calculus Applets
http://www.calculusapplets.com/
Limits
These sites assist in to development of the concept of limits.
Suitable for 3BMAS 4.1, 4.2, 4.3 and 5, (Limits)
► Continuity and Limits ► An Informal, Graphical View of Continuity
► Intermediate Value Theorem
► Informal View of Limits
► One- and Two-Sided Limits and When Limits Fail to Exist
► Limits at Infinity
►Table View of Limits
► Formal Definition of Limits
► Definition of Continuity Using Limits
Hippocampus
http://www.hippocampus.org/
Piecewise functions
This website allows the user to graph piecewise linear functions.
Suitable for 3BMAS §5.5.
►Calculus ►Calculus AB1 for AP ► Browse Topics Alphabetical ► Piecewise
Equation plotter
http://mathplotter.lawrenceville.org/
Polar graphs
This website shows different polar graphs – suitable for 3CMAS §2.4
► Graph (Functions) ► Polar equations
Absorb
http://www.absorblearning.com/
Solving trigonometric equations
A highly effective interactive animation illustrating the sine and cosine graphs formed by rotating a
point around the unit circle. Suitable as an introduction to 3BMAS §2.2
►Absorb Mathematics
►Free Resources
►Sine and cosine graphs
Mathematics Specialist; Resource list—web based resources
7
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
Towers of Hanoi
Forming a rule to solve the Tower of Hanoi
The Towers of Hanoi puzzle is an engaging and challenging problem for middle school students
and an application of exponential functions. It also is the setting for a proof by mathematical
induction that the minimum number of moves M to move n disks from one disk to another is given
by M = 2^n - 1.
Could be used for 3AMAS 3.2 (Establish and use properties of exponential functions), or 3AMAT
1.2.1(Solve simple power equations).
►Algebra 9-12
►Scroll down to Towers of Hanoi
PUMAS
http://pumas.jpl.nasa.gov/Trigonometry
A short task based on how far a person can see to the horizon suitable for 3AMAS 2.7
►Search for How far can you see
► How far can you see
Geoscience Australia
http://www.ga.gov.au OR http://www.ga.gov.au/geodesy/astro/index.jsp
Transformations of trigonometric functions
This site includes data suitable to fit a Sine curve to the minutes of daylight and day of the year.
Suitable for 3BMAS 2.2.
►Earth and monitoring
►Geodesy &GPS
►Astronomical information
> Geodesy & GPS > Astronomical Information
Absorb
http://www.absorblearning.com/
Transformations of trigonometric graphs
All 3 websites below are suitable for 3BMAS 2.2 showing the effect of varying the value of the
three parameters in y = asin(bx)+c
►Resources
►Search for ‘Interactive animation’
►Key words ‘Trigonometric functions’
►Scroll down to
►Shifting the graph of the sine function
►Vertically stretching the graph of the sine function
►Horizontally stretching the graph of the sine function
8
Mathematics Specialist; Resource list—web based resources
Illuminations
http://illuminations.nctm.org/
Vectors
Simple uses of vectors to introduce magnitude and direction, suitable for 3AMAS 1.2
Change the magnitude and direction of a vector to try to hit the stationary island.
The previous activity was just a warm-up for this activity, where you try to hit the moving school of
fish.
►Activities
►Search 9-12
►Scroll down to ‘Vector investigation: Boat to the island’
Equation Plotter
http://mathplotter.lawrenceville.org/
Vector addition
A Geogebra applet to interactively illustrate vector addition. From The Lawrenceville School Math
Department Website. Suitable for 3AMAS 1.7 and 1.8
►Draw geometric objects
►Vector addition
Equation Plotter
http://mathplotter.lawrenceville.org
Investigating slope of a curve at a point. Suitable for 3BMAT 1.3.1
►Graph ►The Secant line
Equation Plotter
http://mathplotter.lawrenceville.org/
Examining the unit circle, when solving trigonometric equations, Suitable for 3BMAS 2.5
►Draw ►Unit circle
Equation Plotter
http://mathplotter.lawrenceville.org/
Basics of trigonometric graphs, y = sin x and y = cos x, a background for 3BMAS 2.2 –
►Graph ►Sine and Cosine graphs
Equation Plotter
http://mathplotter.lawrenceville.org/
Investigating transformations of trigonometric functions.
Investigating Transformations i.e. y = a sin (b(x – c)) + d. Suitable for 3BMAS 2.2
►Graph ► Transformations of functions
Mathematics Specialist; Resource list—web based resources
9
Part 2: Websites by units
The descriptions in this section are in the following order:
 Website title
 Website URL
 Syllabus dot point
web classification
Topic description
 Description of web content.
 Web navigation steps e.g. ► Graphs ►Vectors
3AMAS Mathematics: Specialist
Interactive Maths
http://www.intmath.com/
1.1
Qu
Vectors
This website defines vectors. It then gives examples and definitions relating to operations and rules
which apply to vectors.
► Graphs ►Vectors
Illuminations
http://illuminations.nctm.org/
1.2
App Vectors
Includes simple uses of vectors to introduce magnitude and direction.
Change the magnitude and direction of a vector to try to hit the stationary island.
The previous activity was just a warm-up for this activity, where you try to hit the moving school of
fish.
►Activities ► Search 9-12 ►Scroll down to ‘Vector investigation: Boat to the island’
Balanced Assessment
http://balancedassessment.concord.org
1.2
ASt
Angles
A short challenge, for students to give a logical argument to contradict a geometric situation. The
task is titled, “Detective Stories”.
► Our library of assessment tasks ► Detective Stories
Equation Plotter
http://mathplotter.lawrenceville.org/
1.7, 1.8
App Vector addition
Vector multiplication by a scalar.
A GeoGebra applet to interactively illustrate vector addition. From The Lawrenceville School Math
Department Website.
► Draw► Vector addition
10
Mathematics Specialist; Resource list—web based resources
Interactive Maths
http://www.intmath.com/
2.1
Qu
Radian measure
The website below defines radian measure and summarises the conversions between radians and
degrees.
http://www.intmath.com/
This website includes some applications using radian measure.
► Trigonometry ► Trigonometric functions ► Applications of radian measure
Balanced Assessment
http://balancedassessment.concord.org
2.2
ASt
Circle properties
This is a short task which requires students to use properties of circles to establish information
about a table. It is titled, “Oops! Glass Top”. This could serve as an introduction for this topic.
► Our library of assessment tasks ► Oops! Glass Top
Waldomaths
http://www.waldomaths.com/
2.5
App The sine and cosine rules
Investigate the use of the sine and cosine rules in triangles. Also includes calculations for the area
of a triangle.
► Search ► Cosine rule ► The cosine rule (Law of cosines)…
Enrich
http://nrich.maths.org/
2.7
App Proof with circles
You are given a circle of radius 1 unit and two circles of radius a and b which touch each other and
also touch the unit circle. Prove that you can always draw a 'flower' with six petals with the unit
circle in the middle, and six circles around it having radii
a, b, b/a, 1/a, 1/b and a/b such that each outer circle touches the unit circle and the two circles on
either side of it. A possible investigation.
►Search Enrich for Flower ►Flower (Stage 5)
PUMAS
http://pumas.jpl.nasa.gov/
2.7
ASt
Trigonometry – Applications
A short task based on how far a person can see to the horizon.
► Examples ► How far can you see
Mathematics Specialist; Resource list—web based resources
11
National Library of Virtual Manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
3.2
App Forming a rule
The Tower of Hanoi puzzle is an engaging and challenging problem for middle school students and
an application of exponential functions. It also is the setting for a proof by mathematical induction
that the minimum number of moves M to move n disks from one disk to another is given by M =
2^n - 1.
►Algebra 9-12 ►Scroll down to Towers of Hanoi
Analyzemath
http://www.analyzemath.com/expfunction
3.3
Qu
Exponentials and logarithms
The following sites are suitable for 3CMAT §1.2.4, when introducing e and for 3BMAS §3.3, §3.4
when introducing e and investigating growth and decay.
►Maths and Pre-calculus ► graphing ► Graphs of Exponential Functions ► exponential
functions
Interactive Maths
http://www.intmath.com/
3.3
Qu
Exponentials and logarithms
These sites can be used to examine the relationship between logarithmic and exponential
functions as well as their graphs.
►Maths and Pre-calculus ► Exponential and logarithms ► 1. Definitions ►2. Graphs …
Analyzemath
http://www.analyzemath.com/
3.5 & 3.6
Logarithms
This site is suitable for introducing logarithmic functions and some of the properties associated with
this function. This can also be used to examine the relationship between logarithmic and
exponential functions.
►Maths and Pre-calculus► graphing ► Graphs of Logarithmic Functions ► logarithmic functions
Analyzemath
http://www.analyzemath.com/Graphing.html
4.6
Qu
Graphs of functions
Tutorials on quadratic, cubic, absolute value, square root and reciprocal.
►Maths and Pre-calculus► graphing ► Graphs of Logarithmic Functions ► logarithmic functions
12
Mathematics Specialist; Resource list—web based resources
Analyzemath
http://www.analyzemath.com/
4.6
App Revision of graphing
The equations of absolute values, cubic, linear, polar, quadratics, and reciprocal, square root and
trigonometric functions. Investigating various transformations on graphs Suitable for 3AMAS
► Math and Pre-calculus ►graphing
3BMAS Mathematics: Specialist
Equation Plotter
http://mathplotter.lawrenceville.org/
2.2
App Transformations of sine, cosine and tangent functions
Basics of trigonometric graphs, y = sin x and y = cos x – Investigating transformations of
trigonometric functions
► Graphs ► Sine and cosine graphs
Equation Plotter
http://mathplotter.lawrenceville.org/mathplotter/mathPage/transformations.htm
2.2
App
Investigating transformations i.e. y = a sin (b(x – c)) + d
► Graphs ► Transformations of functions
Absorb Learning
http://www.absorblearning.com/
2.2
App Investigating transformations
A highly effective interactive animation illustrating the sine and cosine graphs formed by rotating a
point around the unit circle.
►Resources ►Search for ‘Interactive animation’ ►Key words ‘Trigonometric functions’
►Scroll down to ►Shifting the graph of the sine function ►Vertically stretching the graph of the
sine function ►Horizontally stretching the graph of the sine function
Geoscience Australia
http://www.ga.gov.au
2.2
Data Investigating transformations
This site includes data suitable to fit a sine curve to the minutes of daylight and day of the year.
►Earth and monitoring ►Geodesy &GPS ►Astronomical information
OR http://www.ga.gov.au/geodesy/astro/index.jsp
►Earth Monitoring ► Geodesy & GPS ► Astronomical Information
Mathematics Specialist; Resource list—web based resources
13
Waldomaths
http://www.waldomaths.com
2.3
App Trigonometric graphs
This site could be used as a lead in to 3BMAS §2.3
And shows the basic form of trigonometric graphs. i.e. y = sin x, cos x and tan x.
► Search Waldomaths ► Graphs of trigonometric functions
Equation Plotter
http://mathplotter.lawrenceville.org/
2.5
App The Unit circle
Suitable for examining the unit circle, when solving trigonometric equations.
► Draw geometric objects ► Unit circle
Calculus applets
http://www.calculusapplets.com/
3.4
App
Growth and decay
The following site is suitable for introducing Growth and decay.
► Differential equations ►Growth and decay
Alalyzemath
http://www.analyzemath.com/
3.4
Qu
Growth and decay
Pre-calculus Tutorials ► Scroll to ► Exponential and Logarithmic Functions and Equations ►
Tutorials on Exponential functions 2
Calculus applets
http://www.calculusapplets.com/
4.1
App Continuity
These sites explore when a function is continuous or discontinuous.
►An informal graphical view of continuity
App Calculus applets
http://www.calculusapplets.com/
4.1 and 4.2
Limits:
These sites assist to develop the idea of limits with a formal approach.
► Continuity and Limits ► An Informal, Graphical View of Continuity
► Intermediate Value Theorem ► Informal View of Limits ► One- and Two-Sided Limits and
When Limits Fail to Exist ► Limits at Infinity ►Table View of Limits ► Formal Definition of Limits
14
Mathematics Specialist; Resource list—web based resources
Foss Mountain Design
http://www.home.earthlink.net:80/~fossmountdesign/Algebra.html
4.5
App Piecewise functions
The website below is suitable for examining features of the graphs of Absolute Value Function
Seeing Math Concord Consortium
http://seeingmath.concord.org/sms_interactives.html
4.5
App
Piecewise functions
►Seeing secondary Maths ► Resources ► Seeing Maths Inter-actives ► Piecewise linear
grapher
Hippocampus
http://www.hippocampus.org/?
4.5
Qu
Piecewise functions
►Introductory Calculus ► Functions and graphs ►Piecewise defined functions
Interactive Math
http://www.intmath.com/
6.1
Qu
Complex numbers
This site introduces the concept of complex numbers and then proceeds through some simple
operations with complex numbers.
► Complex numbers ► Basic definitions ►
Waldomaths
http://www.waldomaths.com/
Complex numbers
6.3
App
This site applies the basic operations to complex numbers, representing the original numbers and
the result as points in the complex plane.
► Search Waldomaths ► Complex numbers
Mathematics Specialist; Resource list—web based resources
15
3CMAS Mathematics: Specialist
Waldomaths
http://www.waldomaths.com/Diff1N.jsp
2.4
App
Differentiating Trigonometric Functions
► Ages 16-19 ►Core Mathematics ►Differentiating sine and cosine
Waldomaths
http://www.waldomaths.com/Diff1N.jsp
4.3
App Differentiating Trigonometric Functions
Calculus applets
http://www.calculusapplets.com/
4.3
App Area under and between curves
This website can examine the area under the curve of any given function
► 3 Basic anti-derivatives
Interactive Math
http://www.intmath.com/
4.3
Qu
Area between curves
► Applications-integration ► 3 Area-between 2 curves
Equation Plotter
http://mathplotter.lawrenceville.org/
7.2
App Polar Graphs
This website shows different polar graphs.
► Graphs ► Polar equations
16
Mathematics Specialist; Resource list—web based resources
3DMAS Mathematics: Specialist
Interactive Math
http://www.intmath.com/
1.1 to 1.5
Qu
Matrices and linear equations
This website introduces matrices and uses simple operations, such as addition, subtraction and
scalar multiplication, between matrices.
► Algebra ► Matrices and determinants ► Choose the Topic from the index on left
►Determinants and Large determinants ►Matrices ►Multiplication of matrices ►Finding the
inverse
Interactive Math
http://www.intmath.com/
1.1
Qu
Matrix operations
This website introduces matrices and uses simple operations, such as addition, subtraction and
scalar multiplication, between matrices.
► Matrices and determinants ►3_Matrices
Interactive Math
http://www.intmath.com/
1.2
Qu
Matrix multiplication
This website examines the process of matrix multiplication and some of the related properties.
► Matrices and determinants/ ► 4_Multiplication of-matrices
Interactive Math
http://www.intmath.com
1.4
Qu
Inverse Matrix
This website defines the inverse matrix and determinant
► Matrices and determinants ► 5 Finding the Inverse of a matrix.
Interactive Math
http://www.intmath.com
1.5
Qu
Inverse Matrix operations
This website develops the use of the inverse matrix to solve a system of linear equations.
► Matrices and determinants ► 6_Matrices and linear-equations
Mathematics Specialist; Resource list—web based resources
17