MATHEMATICS
RESOURCE LIST—WEB BASED RESOURCES
This package contains references to selected websites which
support the content areas of Mathematics for Number & algebra
and Space & measurement.
2011/21620
Mathematics: Resource list—web based resources
1
Copyright
© School Curriculum and Standards Authority, 2012
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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: Resource list—web based resources
MATHEMATICS FOR NUMBER & ALGEBRA AND
SPACE & MEASUREMENT
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.
The resources listed on the next pages are linked to different units in the Mathematics: Specialist
course. The links were live when accessed in August 2011. 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.
Mathematics: Resource list—web based resources
3
Part 1: Websites by Mathematical Content: Number and Algebra
The following links will take the reader to the front end of a given website. For example
http://www.calculusapplets.com/
It is policy that School Curriculum and Standards Authority does not provide ‘deep links’ due to
copyright issues. There is however a pathway included which will guide the reader to the particular
page of the website. The pathway looks like this 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.
Patterns
University of Surrey
http://www.mcs.surrey.ac.uk/
Suitable for 1EMAT §1.3.1
Examines applications of Fibonacci sequence in nature
►Search ►R Knott ►The Fibonacci Numbers and Golden Section in Nature – 1
Algebra balance scales – negatives
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
This version includes negative numbers and negative coefficients on x
Suitable for 2AMAT §1.3.5, 2BMAT §1.3.1, 1.3.2 (linear equations)
►Algebra 9-12►Algebra Balance Scales - Negatives
Scale and ratio
Balanced Assessment
http://balancedassessment.concord.org
Our library of assessment tasks ►The task is titled, ‘Ostrich and Seahorse’
A short task suitable for Stage 1 units
This could be used in conjunction with 1CMAT §2.1.4 and 2.1.5
Linear inequalities
The baby name wizard
http://www.babynamewizard.com/
The Baby Name Wizard is a fascinating website that graphically displays the number of babies with
different names over the years
You can easily track the popularity of different names. Suitable for 1CMAT §3.6.1
►Graph a name
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Mathematics: Resource list—web based resources
Compound interest simulator
Illuminations
http://illuminations.nctm.org
Consider investments over a period of time, based on the possibility of regular repayments Can be
done in conjunction with Finance in 2CMAT §1.4.1
►Activities ►Search ►Compound Interest Simulator
Functions
Hippocampus
http://www.hippocampus.org
Definition and vertical line test (2CMAT §1.2.6)
►Calculus and Advanced Maths ►Calculus AB ►Scroll to ►Vertical line test
Function Notation
http://www.hippocampus.org/
Also suitable for (2CMAT §1.2.6, 3AMAT §1.2.6)
►Calculus and Advanced Maths ►Calculus AB ►Function Notation
Domain and Range
Hippocampus
http://www.hippocampus.org/
suitable for (3AMAT §1.2.3)
►Calculus ►Calculus AB1 ►Domain and Range
Piecewise functions
Hippocampus
http://www.hippocampus.org/
Piece-wise functions suitable for 3BMAS §5.5.
Concord Consortium
http://seeingmath.concord.org/
This website allows the user to graph piecewise linear functions.
►Resources ►Seeing Math Interactives ►Piecewise Linear Grapher
Exponentials and logarithms
Analyzemaths
http://www.analyzemath.com/
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
►Math and Precalculus ►Graphs of Functions, Equations and Algebra ► Exponential Functions
or Find Exponential Function Given its Graph
Mathematics: Resource list—web based resources
5
Logarithmic functions
Analyzemaths
http://www.analyzemath.com/
This site is suitable for introducing logarithmic functions and some of the properties associated with
this function. Can be used for 3AMAS §3.5
Analyzemaths
http://www.analyzemath.com/
This site can be used to examine the relationship between logarithmic and exponential functions.
Suitable for 3AMAS §3.3
►Math and Precalculus ►Graphs of Functions, Equations and Algebra ►Logarithmic Functions
Tower of Hanoi
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
Forming a rule to solve the Tower of Hanoi
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
Could be used for 3AMAS §3.2 (Establish and use properties of exponential functions), or
3AMAT §1.2.1(Solve simple power equations)
►Virtual library ►Algebra 9-12 ►Scroll down to ►Tower of Hanoi
Solving equations
Shodor
http://www.shodor.org/
A classic Connect Four game.
Before playing a chip, your group first has to solve an equation. The teacher can set the time limit
and the level of difficulty of the equation before the game starts. Includes linear equations with one
step, or two steps and variables on both sides of the equation; also has quadratic equations.
Suitable for 2AMAT §1.3.5, 2BMAT §1.3.1, §1.3.2 (linear equations)
and 2CMAT §1.3.2 (quadratic equations)
►Educators ►Interactive ►Learners Activities ►Arithmetic Four
Functions
Graphing lines and simple transformations
Balanced Assessment
http://balancedassessment.concord.org
Suitable for 2AMAT §1.2.4, §1.2.5 are used in the short calculator investigation, ‘Twinkle, Twinkle’
►Our library of assessment tasks ►‘Twinkle Twinkle’
Balance method for solving equations
Maths is fun
http://www.mathsisfun.com/
A program that graphically demonstrates the balance method for solving equations. Suitable for
2AMAT §1.3.5, 2BMAT §1.3.1, §1.3.2 (linear equations).
►Algebra ►Balance when Adding and Subtracting (animation)
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Mathematics: Resource list—web based resources
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
This virtual manipulative allows you to solve simple linear equations through the use of a balance
beam. Suitable for 2AMAT §1.3.5, 2BMAT §1.3.1, §1.3.2 (linear equations).
►Algebra Grades 9-12►Algebra Balance Scales
Features of graphs
Analyzemaths
http://www.analyzemath.com/
This site can be used when commencing work on graphs and the features of the graphs. For
example, intercepts for a parabola. Suitable for 2CMAT §1.2.4 Not all of the functions displayed
could be examined overall in 3AMAT §1.2.4
►Math and Precalculus ►Graphs of Functions, Equations and Algebra ►Scroll down to
appropriate function
Linear graphs – suitable for 2AMAT 1.2.4, 2CMAT §1.2.1
Absolute value – suitable for 3BMAS §5.5
Quadratic – suitable for 2CMAT §1.2.2, §1.2.3, §1.2.4, §1.2.5
Foss Mountain Design.
http://www.home.earthlink.net:80/~fossmountdesign/Algebra.html
For quadratic equations – use the quadratic or vertex form.
Linear Transformer and Function Analyser
Seeing Maths
http://seeingmath.concord.org/
Also with lines – a great site to investigate transformations. Suitable for 2AMAT §1.2.4 and §1.2.5
►Try Free Secondary Math Interactives ►Scroll to ►Linear Transformer or Function Analyser
Inverse functions
Analyze maths
http://www.analyzemath.com/
Examples and ideas are very good for examples of Inverse Functions. Some notational errors.
Suitable for 3AMAS §4.4
►Math and Precalculus ►Graphs of Functions, Equations and Algebra ►Scroll down to
appropriate function (After rational functions)
Graphs of functions
Analyze maths
http://www.analyzemath.com/Graph1/GraphFunctionsTutorials.html
Identifying Graphs to match equations – quadratics, cubics, absolute values, square root and
reciprocal
Can be used when working with transformations in 3AMAS, 4.7
Investigating various transformations on graphs, suitable for 3AMAS §4.7
http://www.analyzemath.com/Graph1/Graph1.html
Mathematics: Resource list—web based resources
7
Domain and range
Analyze maths
http://www.analyzemath.com/
Finding the domain and range for various functions. Suitable for 3AMAT §1.2.3
(Note – not all the functions displayed will be known to students working on 3AMAT)
►Math and Precalculus ►Graphs of Functions, Equations and Algebra ►Scroll down to ►Graph,
Domain and Range of Common Functions
Quadratic functions
Analyze maths
This site can be used to examine quadratic graphs and some of their features. Would only be
suitable for more able students doing 2CMAT §1.2.4 and §1.2.5
http://www.analyzemath.com/
►Math and Precalculus ►Analytic tutorials ►Scroll down to ►Quadratic functions ►Problem (1)
Quadratic functions and use of formulae
Balanced Assessment
http://balancedassessment.concord.org
A short task suitable for Stage 2 (2CMAT)
The task is titled, ‘Para-Ball-A’. Suitable for 2CMAT §1.2.5
►Our library of assessment tasks ►Para-Ball-A
Quadratic transformer
Seeing Maths
http://seeingmath.concord.org
A great site to view the graphs for quadratic equations and transformations that occur. See
Quadratic Transformer (Graphs 2CMAT §1.2.2, §1.2.3,
Transformations 3AMAT §1.2.2)
►Try Free Secondary Math Interactives ► Scroll to ► Quadratic Transformer
Proofs—quadratic formula
NRICH
http://nrich.maths.org/
Given the steps in the proof of the quadratic equation, students need to place these steps in the
correct order
Suitable for 3AMAT §1.3.1 for extension
►Search ►Proof sorter Quadratic equation ►Scroll to ‘Proof sorter Quadratic equation’
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Mathematics: Resource list—web based resources
Calculus
Distance-time Graphs
NRICH
http://nrich.maths.org/
Introduction to questioning in Calculus
This is a series of interactive pages on distance-time graphs
Take your dog for a walk
NRICH
http://nrich.maths.org/
A clever interactive introduction to rate via distance-time graphs. The full-screen version would be
useful if this is done as a whole class activity.
Suitable for 3AMAT §2.1 Rate
►Search ►Take your dog for a walk ►Scroll to ‘Take your dog for a walk’
Steady free fall
NRICH
http://nrich.maths.org/public/viewer.php?obj_id=4851&part=
In this activity, you drop a ball onto a ramp of your own design and see the graph of vertical
distance versus time. This task also includes some challenges for students. Suitable for
3AMAT §2.1 Rate
► Search► Steady free fall ►Scroll to ‘Steady free fall’
Average velocity
Virtual Institute of Applied Science
http://www.vias.org/
Distance, time and velocity are an ideal means to understand the concept of derivatives. By
reducing the time interval until it becomes zero, the average velocity approaches the instantaneous
velocity, which is equal to the first derivative of the distance (with respect to time). This is available
as a zip file that can be downloaded. Suitable for 3BMAT §1.3.1
►Mathematics ►Scroll on left to ►Learning by simulation ►Mathematics ►Scroll to ‘Tangent and
first derivative’
Area under curve
Virtual Institute of Applied Science
http://www.vias.org/
Choose a function and see the effect on the Riemann sum when you change the slice width. The
file itself can be downloaded and installed on your computer or network. Suitable for 3CMAT §1.4.9
►Mathematics ►Scroll on left to ►Learning by simulation ►Mathematics ►Scroll to ‘Riemann
Sum’
Lou Talman
http://clem.mscd.edu/~talmanl/HTML/FTOC.html
This animation from Lou Talman is a dynamic representation of the area function we introduce in
the standard proof of the Fundamental Theorem of Calculus. Suitable for 3CMAT §1.4.12
Mathematics: Resource list—web based resources
9
Average velocity and displacement
University of Oregon Physics Department
http://jersey.uoregon.edu//
Drop the ball in a vacuum under the influence of gravity. Set the green line to start the timer and
the red line to stop the timer. From the time taken, estimate the average velocity over this time
interval. Suitable for 3BMAT §1.3.1
►Mechanics ►1D Motion ►Free Fall
Limits and Continuity
Calculus Applets
http://www.calculusapplets.com/
These sites explore when a function is continuous or discontinuous and help to develop the idea of
limits. Suitable for 3BMAT §1.3
►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
Differentiation
Calculus Applets
http://www.calculusapplets.com/
A series of applets exploring differentiation and which includes introductory activities. Suitable for
3BMAT§1.3, 3CMAT§1.4 and 3DMAT§1.2
►Introduction to the Derivative
►Average Velocity and Speed
►Instantaneous Velocity
►Derivative at a Point
►Derivative Function
►A Tabular View of the Derivative
►Second Derivative
►A Tabular View of the Second Derivative
►Twice Differentiable
Integrals
Calculus Applets
http://www.calculusapplets.com/
A series of applets exploring Integration – suitable for 3CMAT §1.4.9 to §1.4.15, 3DMAT §1.2
►Introduction to the Definite Integral
►Approximating Distance Travelled With a Table
►Approximating Distance Travelled With a Graph
►Riemann Sums and The Definite Integral
►Fundamental Theorem of Calculus
►Average Value
►Properties of Definite Integrals
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Mathematics: Resource list—web based resources
Space and measurement
Transformations
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
With this virtual manipulative you can create objects with pattern block pieces and explore
transformations of the plane
Suitable for 2AMAT §2.2.1
►Geometry 9-12
►Transformations translations
►Transformations rotations
►Transformations reflection
►Transformations dilation
►Transformations compositions
Platonic solids
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
This virtual manipulative allows you to display, rotate, and resize Platonic solids. It also allows you
to select vertices, edges, and faces, and observe that the number of vertices minus the number of
edges plus the number of faces is always equal to 2 (Euler's formula). Suitable for 1CMAT §2.3.2,
§2.3.3, §2.3.4
►Geometry 9-12
►Platonic solids
►Platonic solids duals
►Platonic solids slicing
Proof with circles
NRICH
http://nrich.maths.org/
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 ►Flower (Stage 5)
Gradient at a point
Mathplotter
http://mathplotter.lawrenceville.org/
Investigating slope of a curve at a point. This applet shows the tangent line at any point on a curve
and the matching derivative graph. Suitable for 3BMAT §1.3.1 and 3DMAT§1.2.1
►Graphs (Functions) ►Derivatives
Mathematics: Resource list—web based resources
11
Part 2: Websites by units
1BMAT
3.3.5 App
Mean and median
National Council of Teachers of Mathematics
http://standards.nctm.org/
This website looks at the effect on mean and median when changing a single score
►Examples ►Scroll to ►6.6 Comparing Properties of the Mean and the Median through the use
of Technology
1CMAT
2.1.4 ASt
Ratios
Balanced Assessment
http://balancedassessment.concord.org
The task is titled, ‘Ostrich and Seahorse’. This could be used as an introduction to this topic.
►Our library of assessment tasks ►‘Ostrich and Seahorse’
2.3.2 ; 2.3.3 ; 2.3.4 App
Platonic solids
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
This virtual manipulative allows you to display, rotate, and resize Platonic solids. It also allows you
to select vertices, edges, and faces, and observe that the number of vertices minus the number of
edges plus the number of faces is always equal to 2 (Euler's formula).
►Geometry 9-12
►Platonic solids
►Platonic solids duals
►Platonic solids slicing
1EMAT
1.1.2 ASt
Rounding and accuracy
PUMAS
http://pumas.jpl.nasa.gov/
This task based on the theme, ‘Think Locally, Act Globally’. It explores the idea impact on the
environment one individual may make and then extends this idea, using estimation, to the impact
on the Earth. This task could be modified for use in other stages.
►Examples ►Examples by title ►Scroll to ‘Learn to think Locally, globally’
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Mathematics: Resource list—web based resources
1.2.1 App
Locating and plotting points
WISC-Online
http://www.wisc-online.com
►Learning objects ►ABB/ELL ►Math ►Scroll to ►Plotting Points on a Coordinate System
1.3.1 ASt
One and two-step Rules
University of Surrey
http://www.mcs.surrey.ac.uk/
Examines applications of Fibonacci sequence in nature
►Search ►R. Knott ►Fibonacci numbers and the Golden Section ►fibnat.html
2AMAT
1.2.4 ASt
Linear graphs and simple transformations are used in the short calculator investigation,
‘Twinkle, Twinkle’
Balanced Assessment
http://balancedassessment.concord.org
►Our library of assessment tasks ►‘Twinkle, Twinkle’.
1.2.4 ; 1.2.5 App
The Linear Transformer and Function Analyser can be used to investigate linear graphs
Seeing Maths
http://seeingmath.concord.org/
►Free Secondary Maths interactives ►Transformation of Linear functions ►Function analyser
1.3.5 App
Solving equations
Shodor
http://www.shodor.org/
A classic Connect Four game
Before playing a chip, your group first has to solve an equation. The teacher can set the time limit
and the level of difficulty of the equation before the game starts. Includes linear equations with one
step, or two steps and variables on both sides of the equation; also has quadratic equations
►Activities and lessons ►Interactivate ►Activities ►Algebra ►Algebra Four
1.3.5 App
A program that graphically demonstrates the balance method for solving equations
Maths is fun
http://www.mathsisfun.com/
►Algebra ►the basics ►Balance when Adding and Subtracting
Mathematics: Resource list—web based resources
13
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
Another virtual manipulative allows you to solve simple linear equations through the use of a
balance beam.
►Algebra ►6-8 ►Algebra Balance Scales
2.2.1 App
Transformations
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
With these Virtual Manipulatives you can create objects with pattern block pieces and explore
transformations of the plane
►Geometry ►9 – 12 ►Transformations of Reflection or Rotation or Translation
2BMAT
1.3.1; 1.3.2 App
Solving Equations
Shodor
http://www.shodor.org/
A classic Connect Four game. Before playing a chip, your group first has to solve an equation. The
teacher can set the time limit and the level of difficulty of the equation before the game starts.
Includes linear equations with one step, or two steps and variables on both sides of the equation;
also has quadratic equations.
►Activities and lessons ►Interactivate ►Activities ►Algebra ►Algebra Four
1.3.1; 1.3.2 App
A program that graphically demonstrates the balance method for solving equations
Maths is fun
http://www.mathsisfun.com/
►Algebra ►the basics ►Balance when Adding and Subtracting
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
Another virtual manipulative allows you to solve simple linear equations through the use of a
balance beam.
►Algebra ►6-8 ►Algebra Balance Scales
1.3.2 App
Solving simple linear inequalities
Waldomaths
http://www.waldomaths.com/
►Search ►Line ►Page 2 ►Straight line inequalities and inequations
14
Mathematics: Resource list—web based resources
3.4.1 Dat
Time series data
Peter Russell
http://www.peterrussell.com/
The World Clock website has continuously updated information about the world such as the world
population, number of births, number of deaths, number of cars and the number of barrels of oil
produced. It is a wonderful discussion starter for a number of maths topics including time series
data and rates of change (gradient)
►More ►World Clock
2CMAT
1.1.4 ASt
Calculation errors
Pumas
http://pumas.jpl.nasa.gov/
This task could be used as an activity when examining estimation and calculation. It explores the
calendar and the calculation and errors that have occurred to approximate the length of the Earth
year.
►Examples ►Examples by title ►How many days are in the year?
1.2.2 App
Features of quadratic graphs
Seeing Maths
http://seeingmath.concord.org
►Seeing Maths Secondary ►Interactive software and related activities ►Quadratic Transformer
Interactive Maths
http://www.intmath.com/
►Algebra ►Quadratic Equations ►Scroll to ‘What is in this Chapter?’►Equations in Quadratic
form
1.2.3 ; 1.2.4 App
Features of quadratic graphs
Seeing Maths
http://seeingmath.concord.org/
►Seeing Maths Secondary ►Interactive software and related activities ►Quadratic Transformer
1.2.4 Qu
Features of graphs
AnalyzeMaths
http://www.analyzemath.com
This site can be used when commencing work on graphs and the features of the graphs. For
example, intercepts for a parabola. Suitable for 2CMAT §1.2.4. Not all of the functions on this site
will be known to students at this level
►Math and Precalculus ►Graphs of functions equations and algebra ►Quadratic Functions
(Standard or general form)
Mathematics: Resource list—web based resources
15
1.2.4 ; 1.2.5 Qu
Quadratic functions
AnanyzeMaths
http://www.analyzemath.com/quadraticg/
This site can be used to examine quadratic graphs and some of their features. Would be suitable
for more able students
►Index ►Tutorials
1.2.5 ATe
Quadratic functions and use of formulae –The task is titled, ‘Para-Ball-A’
Balanced assessment
http://balancedassessment.concord.org
►Our library of assessment tasks ►‘Para-Ball-A’
1.2.6 ASt
Use Function notation
Hippocampus
http://www.hippocampus.org/?
This site also examines the definition of a function.
►Algebra 1B ►Select-browse-topics-alphabetical ►‘Function Notation’
App 1.3.1
Factorising quadratic equations of the form ax2 + bx + c
Waldomaths
http://www.waldomaths.com/
►Search ►Quadratic functions ►Quadratic and Cubic transformations
1.3.2 App
Solving equations
Shodor
http://www.shodor.org/
A classic Connect Four game
Before earning a red or black counter your group first has to solve an equation. The teacher can
set the time limit and the level of difficulty of the equation befor e the game starts. Includes linear
equations with one step, or two steps and variables on both sides of the equation; also has
quadratic equations.
►Activities and lessons ►Interactivate ►Activities ►Algebra Four ►Algebra Four
App 1.3.2
Solving quadratic equations graphically
Waldomaths
http://www.waldomaths.com/
In this Java aplet the student is able to manipulate the parameters a, b and c in the general form of
the quadratic function: y=ax2+bx+c and see how the graph of the parabola is transformed
►Search ►Quadratic functions ►Graphs of Linear, Quadratic and Cubic Polynomial
16
Mathematics: Resource list—web based resources
App 1.4.1
Calculate compound interest recursively with technology
Illuminations
http://illuminations.nctm.org/
This website considers investments over a period of time, based on the possibility of regular
repayments
►Activities ►9-12 ►Scroll to ‘Compound interest simulator’
2DMAT
1.2.4 App
The website below examines reciprocal functions
Waldomaths
http://www.waldomaths.com/
This helps to assist students to distinguish between the different types of graphs and equations in §1.2.4
►Search ►Reciprocal ►Transformation of reciprocal functions
App 1.2.6
Graphs of cubic polynomials of the form y = ax3 + bx2 + cx + d
Waldomaths
http://www.waldomaths.com/Cubic1NL.jsp
►Search ►Cubic functions ►Linear, Quadratic and Cubic Polynomial Graphs - Waldomaths
3AMAT
1.2.1 App
Forming a rule to solve the Towers of Hanoi
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
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
►Algebra ►9 -12 ►Scroll to Towers of Hanoi
1.2.2 App
Transformations using Quadratic Transformer
Seeing maths
http://seeingmath.concord.org/
►Free Secondary Maths Interactives ►Scroll to ►Quadratic Transformer
Mathematics: Resource list—web based resources
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1.2.3 Qu
Domain and range
Analyzemaths
http://www.analyzemath.com/
Finding the domain and range for various functions
Select Domain and Range
(Note – not all the functions displayed will be known to students working on 3AMAT)
►Analytical tutorials ►Domain and Range of basic functions.html
Hippocampus
http://www.hippocampus.org/
►Algebra 1B ►Select-browse-topics-alphabetical ►‘Domain and Range’
1.2.6 Qu
Use function notation
http://www.hippocampus.org/
This site also examines the definition of a function
►Algebra 1B ►Select-browse-topics-alphabetical ►‘Function Notation’
1.3.1 App
Proofs – quadratic formula
NRICH
http://nrich.maths.org/
Given the steps in the proof of the quadratic equation, students need to place these steps in the
correct order
►Stage 4 & 5 ►Search ►Proof sorter – Quadratic Equation
1.3.3 App
Solving simultaneous quadratic equations
Waldomaths
http://www.waldomaths.com/
►Search ►Equations solved graphically ►Equations solved graphically - Waldomaths
2.1 App
Rate
NRICH
http://nrich.maths.org/
Walking the Dog - An interactive introduction to rate via distance-time graphs
The full-screen version would be useful if this is done as a whole class activity
►Stage 2►Search ►Take your dog for a walk
2.1 App
Steady Free Fall
NRICH
http://nrich.maths.org/
In this activity, you drop a ball onto a ramp of your own design and see the graph of vertical
distance versus time. This task also includes some challenges for students.
►Stage 4 & 5 ►Search ►Steady Free fall
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Mathematics: Resource list—web based resources
3BMAT
1.3.1 ASt
Historical introduction to Calculus
Interactive maths
http://www.intmath.com/
►Differentiation ►Introduction to calculus
1.3.1 App
Average velocity
Virtual Institute of Applied Science
http://www.vias.org/
Distance, time and velocity are an ideal means to understand the concept of derivatives. By
reducing the time interval until it becomes zero, the average velocity approaches the instantaneous
velocity, which is equal to the first derivative of the distance (with respect to time). This is available
as a zip file that can be downloaded.
►Elementary calculus ►Learning by simulation ►Mathematics ► #1009 Tangent and First
Derivative
1.3.1 App
Average velocity and displacement
University of Oregon (Physics)
http://jersey.uoregon.edu/
Drop the ball in a vacuum under the influence of gravity
Set the green line to start the timer and the red line to stop the timer
From the time taken, estimate the average velocity over this time interval
►Select Mechanics ►1D Motion – Free Fall ►Choose this applet
1.3.1 App
Investigating slope of a curve at a point
Mathplotter
http://mathplotter.lawrenceville.org/
This website shows the tangent line at any point on a curve and the matching derivative graph
►Graph (Functions) ►The secant line
1.3.4 App
Examine tangents to the curve and their matching graphsWaldomaths
http://www.waldomaths.com/
►Search ►Gradient of tangents ►Tangents and Normals
1.3.5 App
Examine the derivative of functions and their matching graphsWaldomaths
http://www.waldomaths.com/
►Search ►Differentiating polynomials ►Calculus - Differentiating Polynomial Expressions
Mathematics: Resource list—web based resources
19
3CMAT
1.2.3 App
Examine exponential graphs and their matching derivative graphs
Waldomaths
http://www.waldomaths.com/
►Search ►Differentiating Exponentials 1 ►Differentiating Exponentials 1 - Waldo
1.2.3 App
Examine the graph of y = ex
Waldomaths
http://www.waldomaths.com/
►Search ►Exponential graphs and functions ►Exponential Graphs – Waldomaths
1.2.4 Qu
The following sites are suitable for examining e
Analyzemaths
http://www.analyzemath.com/
►Analytical Tutorials ►Scroll to ►Exponential and Logarithmic functions and equations
1.2.4 App
Examine exponential graphs and their matching derivative graphs
Waldomaths
http://www.waldomaths.com/
►Search ►Differentiating Exponentials 2 ►Differentiating Exponentials 2 - Waldo
1.4.2 Qu
This website summarises the product and quotient rule
Interactive maths
http://www.intmath.com/
►Differentiation ►Differentiation ►Differentiation of products and Quotients
1.4.5 App
Use a graph to examine the second derivative of a function
Waldomaths
http://www.waldomaths.com/
►Search ►Second derivative ►Second Derivatives, the gradient of the gradient - Waldomaths
1.4.6 Qu
Applications of differentiation
Interactive Maths
http://www.intmath.com/
The website below shows some applications of differentiation. This not directly related to the 1.4.6
(solving optimisation problems), but may be of interest to some students
►Differentiation ►Applications of Differentiation ►Introduction to Applications of Differentiation
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Mathematics: Resource list—web based resources
1.4.9 App
Area under curve
Virtual Institute of Applied Science
http://www.vias.org/
Choose a function and see the effect on the Riemann sum when you change the slice width. The
file itself can be downloaded and installed on your computer or network
►Mathematics ►Elementary calculus ►Learning by simulation ►Mathematics ►#1007 Riemann
Sum
1.4.9 App
Use the integral to establish the area under a curve
Waldomaths
http://www.waldomaths.com/
►Search ►Integrating polynomials ►Integrating Polynomials – Waldomaths
1.4.11 Qu
Indefinite integral
Interactive maths
http://www.intmath.com/
This website examines the antiderivative and the indefinite integral
►Integration ►Antiderivative and the indefinite integral ►Scroll to Antiderivative and the indefinite
integral
1.4.12 Qu
Area under a curve
Interactive maths
http://www.intmath.com/
This website leads to finding the area under a curve. It starts with finding the area of rectangles
under a curve
►Integration ►Area under the curve ►Scroll to Area under the curve
3DMAT
1.2.3 App
Fundamental Theorem of Calculus
Calculus Applets
http://www.calculusapplets.com/
This website can examine the area under the curve of any given function
►Scroll to ►6 Introduction to the definite integral ►First fundamental theorem
Mathematics: Resource list—web based resources
21
2.3.3 App
Proof with circles
NRICH
http://nrich.maths.org/
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
►Stage 4 & 5 ►Search ►Flower ►Flower Stage 5
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Mathematics: Resource list—web based resources