MATHEMATICS
COMBINED RESOURCE LISTS
2012/22067
Mathematics: Combined resource lists
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 School
Curriculum and Standards 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.
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Mathematics: Combined resource lists
MATHEMATICS
COMBINED RESOURCE LISTS
The following links will direct you to websites outside the School Curriculum and Standards
Authority site. The 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.
This list of resources was prepared using the advice provided by the Course Advisory Committee.
This list is prepared in the following parts:
PART 1: .................................................................... INTRODUCTION/SELECTION PROCESS
PART 2: ............................................................................................... PRINT RESOURCE LIST
PART 3: ....................................................WEB RESOURCE LIST FOR NUMBER & ALGEBRA
and SPACE & MEASURE
PART 4: ............................................................... RESOURCE LIST FOR CHANCE AND DATA
Mathematics: Combined resource lists
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PART 1: INTRODUCTION/SELECTION PROCESS
MATHEMATICS
RESOURCE LISTS—INTRODUCTION
Selection Guidelines
The selection of resources is the responsibility of each school and the following points need to be
considered at all times:
 The lists are recommendations only and are not exhaustive. Each school should decide on
specific titles for their students in consultation with their school community and sector
guidelines.
 Some courses have set texts. Check the current syllabus.
 The recommended resources are to be used to support teaching and learning only and not as
a substitute for the syllabus; the syllabus is what is used to develop examination questions and
all teaching should be directly linked to the syllabus.
 Any selection process requires the use of the current syllabus. Syllabus documents are
subject to changes. Users who down load and print copies of a syllabus are responsible for
checking for updates. Advice about any changes made is provided through the School
Curriculum and Standards Authority.
Types of resource lists
The following resource lists are provided for this course: Introduction which includes Guidelines,
Process, Professional Associations/Suppliers and Journals; Print materials; Websites and a
Combined Recourse List.
Selection Process
Step 1:
Read the current syllabus
Check the School Curriculum and Standards Authority website to see if you have the
current syllabus; check the e-Circular to see if any minor changes have been made.
Step 2:
Narrow the choice of resources to match the decisions made by your school.
Check the following:
 which stage/s does your school offer ? Stage p, 1, 2 and 3
 which units are part of this course, for example, PMAT 1A, 1B, 1C, 1D, 1E;
Stage 2A, 2B, 2C, 2D; 3A, 3B, 3C, and 3D?
 which units are being taught this semester/year?
 what is the focus of the units being taught?
This course has no specific contexts.
Step 3:
Some of these resources may be in your school. Check your library and the relevant
learning area library.
Step 4:
There are no set texts for this course.
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.
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Mathematics: Combined resource lists
Professional Associations
Mathematics Association of Western Australia
http://www.mawainc.org.au/
Australian Association of Mathematics Teachers
http://www.aamt.edu.au/
AAMT This national association provides information and links to each State Association.
Journals
The Australian Mathematics Teacher
http://www.aamt.edu.au/
Published by AAMT with a focus on teaching mathematics to 11 to 16 year olds.
Editor: Bruce White. Frequency: 4 issues p.a.
ISSN 0045-0685
Australian Senior Mathematics Journal
http://www.aamt.edu.au/
Published by AAMT with a focus on teaching mathematics to senior secondary and early tertiary
students.
Edited by Jill Brown and Gloria Stillman. Frequency: 2 issues p.a.
ISSN 0819-4564
Specialist Resource Suppliers
Most mathematics books and equipment can be bought from your regular school suppliers.
Mathematics: Combined resource lists
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PART 2: PRINT RESOURCE LIST
MATHEMATICS
RESOURCE LISTS – PRINT MATERIALS
Stage 1
THOMSON S, FORSTER I, Workable Maths for WA-WACE 1BMAT
Melbourne, Nelson,185 pages
ISBN9780170136013
THOMSON S, FORSTER I, Workable Maths for WA-WACE 1CMAT
Melbourne, Nelson,201 pages
ISBN9780170136037
THOMSON S, FORSTER I, Workable Maths for WA-WACE 1DMAT
Melbourne, Nelson,202 pages
ISBN9780170184724
THOMSON S, FORSTER I, Workable Maths for WA-WACE 1EMAT
Melbourne, Nelson,208 pages
ISBN9780170184755
SADLER, AJ (2008). Unit 2A Mathematics
Perth: Sadler Family Trust, 216 pages
ISBN 09957762984
Stage 2
THOMSON S, FORSTER I, Workable Maths for WA-WACE 2AMAT,
Melbourne, Nelson, 193 pages
ISBN97801701360006
SADLER, AJ (2008). Unit 2B Mathematics
Perth: Sadler Family Trust, 200 pages
ISBN 0957762992
THOMSON S, FORSTER I, Workable Maths for WA-WACE 2BMAT,
Melbourne, Nelson, 194 pages
ISBN9780170136020
SADLER, AJ (2008). Unit 2C Mathematics
Perth: Sadler Family Trust, 212 pages
ISBN 9780980493306
SADLER, AJ (2008). Unit 2D Mathematics
Perth: Sadler Family Trust, 175 pages
ISBN 9780980493313
LEE, O.T. (2011). Mathematics 2CD - Revision Series.
Applecross, WA: Academic Task Force, 255 pages
ISBN 978-0-9807249-6-7
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Mathematics: Combined resource lists
Stage 3
SADLER, AJ (2008). Unit 3A Mathematics
Perth: Sadler Family Trust, 234 pages
ISBN 978098049332 0
SADLER, AJ (2008). Unit 3B Mathematics
Perth: Sadler Family Trust, 192 pages
ISBN 9780980493375
LEE, O.T. (2009). Mathematics 3AB - Revision Series.
Applecross, WA: Academic Task Force, 381 pages
ISBN 978-0-9751270-9-4
WILLIAMS, G & K (2012). Creelman Exam Questions – Mathematics 3AB
Applecross, WA: Academic Task Force, 221 pages,
ISBN 978-1-74098-092-0
WILLIAMS, G & K (2013). Creelman WACE Exam Questions - Mathematics 3AB.
Applecross, WA: Academic Task Force
ISBN 978-1-74098-141-5
SADLER, AJ (2008). Unit 3C Mathematics
Perth: Sadler Family Trust, 216 pages
ISBN 9780980493344
SADLER, AJ (2008). Unit 3D Mathematics
Perth: Sadler Family Trust, 179 pages
ISBN 9780980493351
LEE, O.T. (2010). Mathematics 3CD - Revision Series.
Applecross, WA: Academic Task Force, 342 pages
ISBN 978-0-9807249-1-2
WILLIAMS, G & K (2012). Creelman Exam Questions - Mathematics 3CD.
Applecross, WA: Academic Task Force, 215 pages
ISBN 978-1-74098-093-7
WILLIAMS, G & K (2013). Creelman WACE Exam Questions - Mathematics 3CD.
Applecross, WA: Academic Task Force
ISBN 978-1-74098-142
Mathematics: Combined resource lists
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PART 3: WEB RESOURCE LIST
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.
This document lists the Websites by units
The following links will take the reader to the front end of a given website. For example
Name of Website
URL eg: http://nlvm.usu.edu/
It is policy that the 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 (see below) tells the reader where to find the link to the next page or site.
►Select ►Data Analysis 9-12 ►Spinners
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Mathematics: Combined resource lists
Websites by Mathematical Content
Number and Algebra
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
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
Mathematics: Combined resource lists
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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
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
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Mathematics: Combined resource lists
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)
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
Mathematics: Combined resource lists
11
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
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
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Mathematics: Combined resource lists
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’
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
Mathematics: Combined resource lists
13
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
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
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Mathematics: Combined resource lists
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
Mathematics: Combined resource lists
15
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
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Mathematics: Combined resource lists
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’
Mathematics: Combined resource lists
17
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
Examines applications of Fibonacci sequence in nature
http://www.mcs.surrey.ac.uk/
►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
18
Mathematics: Combined resource lists
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
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
Mathematics: Combined resource lists
19
1.3.2 App
Solving simple linear inequalities
Waldomaths
http://www.waldomaths.com/
►Search ►Line ►Page 2 ►Straight line inequalities and inequations
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
20
Mathematics: Combined resource lists
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)
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’
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
Mathematics: Combined resource lists
21
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
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
22
Mathematics: Combined resource lists
1.2.2 App
Transformations using Quadratic Transformer
Seeing maths
http://seeingmath.concord.org/
►Free Secondary Maths Interactives ►Scroll to ►Quadratic Transformer
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
Mathematics: Combined resource lists
23
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
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
24
Mathematics: Combined resource lists
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
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
Mathematics: Combined resource lists
25
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
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
26
Mathematics: Combined resource lists
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
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
Mathematics: Combined resource lists
27
PART 4: PRINT RESOURCE LIST
MATHEMATICS: CHANCE AND DATA
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 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.
Part 4 lists the Websites by units only
The following links will take the reader to the front end of a given website. For example
http://nlvm.usu.edu/
It is policy that the 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 (see below) tells the reader where to find the link to the next page or site.
►Select ►Data Analysis 9-12 ►Spinners
28
Mathematics: Combined resource lists
PAMAT/PBMAT
PA 3.1.1; PB 3.5.1; PB 3.5.2
Dat
US Pharmacopeial
http://www.usp.org/audiences/consumers/
Free download of pictograms after free registration
►Select ►Downloading the USP Pictogram Library
PA/PB 3.1
ATe
Teaching Statistics
http://www.rsscse.org.uk/ts/
This is an International journal for teachers. It caters for teachers of pupils up to 19 years
An article on collecting, recording and grouping categorical data
Content could be adapted to suit Year 11-12 interests
►Scroll down to Select ►Getting the best from teaching statistics ►Primary School focus
►Graphing in the Primary school
PA/PB 3.1
Dat #(2)
WA Australian Bureau of Meteorology
http://www.bom.gov.au/wa
Weather and climate data from WA Australian Bureau of Meteorology —
►Climate Information
1AMAT
3.1.1 App
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
This is a library of Data analysis and Probability simulation software such as; Spinners or Coin
tossing
►Select ►Data Analysis 9-12 ►Spinners
3.3.2 Dat
ASt
Government of Western Australia Database
http://wa.gov.au/
Summarises road fatalities by region
►Select ►Community safety ►Fatal crash statistics
3.4.7 Dat #(2)
Australian Bureau of Meteorology
http://www.bom.gov.au/climate/how/
►Select ►How to get climate data
Mathematics: Combined resource lists
29
3.5.6 Qu
Kida Maths Games
http://www.netrover.com/~kingskid/Math/math.htm
This worksheet generator will make hundreds of different worksheets. It does not use stored
sheets. Great for primary graphing
►Select ►Make graph worksheets
1BMAT
3.2.1 ATe
Teaching Statistics
http://www.teachingstatistics.co.uk/?page_id=357#one
is an International journal for teachers which caters for teachers of pupils up to 19 years.
Article on the use of data cards in the journal Teaching Statistics—cards could be adapted to suit
Year 11 interests
►Select ►Getting the best of teaching statistics ►Students’ Understanding ►Data handling ►An
introduction to higher order processes
3.3.5 Dat
ASt
Government of Western Australia Database
http://wa.gov.au/governmentservices/communitysafety/roadsafetyawareness/
(Road fatalities by region) Learner drivers material that includes information on road fatality causes
►Select ►Fatal crash statistics
3.2.6 ATe
Journal of Statistics Education
http://www.amstat.org/publications/
The Early History of Average Values and Implications for Education by Arthur Bakker
►Search this site ►Arthur Bakker ►The Early History of Average Values and Implications for
Education
3.2.6 Qu
Coventry University Mathematics Support Centre
http://www.coventry.ac.uk/ec/maths_centre/statistics_ws.html
Worksheets and diagnostic tests on average
►Select ►Averages
3.2.6 ; 3.2.7 ; 3.2.8 ; 3.3.7
App
WISWEB- Freudenthal Institute
http://www.fi.uu.nl/wisweb/en/
Generates horizontal bar graph for your own or provided data
Vertical value bar can be dragged. Suit graphical introduction to ‘average’ as a representative
value, mean as a balance point, median as middle value, and spread
►Select ►applets (in text) ►Statistics and Probability ►Minitool 1
30
Mathematics: Combined resource lists
3.3.3 Dat #2)
Australian Bureau of Meteorology
http://www.bom.gov.au/climate/data/
Weather data
►Climate Information
3.3.7 App #(5)
WISWEB
Generates Dot-plots for student’s own or provided data
Suit establishing mean, median and mode as typical or representative values
http://www.fi.uu.nl/wisweb/en/
►Select: applets (in text) ►Statistics and Probability ►Minitool 2
1CMAT
3.1.1 Dat #(2)
Australian Bureau of Meteorology—Weather data
http://www.bom.gov.au/climate/data/
►Climate Information
3.1.1 Act
Australian Bureau of Meteorology
http://www.bom.gov.au/lam/Students_Teachers/learnact.htm#ma
Teaching notes and student worksheet on El Niño climate conditions
►Select ►What’s the chance of rain ►Teachers’ lesson plan 3
3.2.1 ATe
The Centre for Innovation in Mathematics Teaching (CIMT)
http://www.cimt.plymouth.ac.uk/default.htm
Probability misconceptions
►Select ►CIMT Search (right hand column) ►Search Page ►Misconceptions 10B
3.1.1 App
National library of virtual manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
Set up a spinner then operate the spinner and the results are recorded on column graph
►Select ►Data Analysis 9-12 ►Spinners
Interactivate
http://www.shodor.org/interactivate/
Set up a spinner then operate the spinner and the results are recorded in a table
►Select ►Learners Tools ►Probability ►Adjustable Spinner
Mathematics: Combined resource lists
31
3.2.1 ; 3.2.2 Qu
Diagnostic tests and worksheets on probability
http://www.coventry.ac.uk/ec/maths_centre/statistics_ws.html
►Select ►Probability 1
3.2.3 Dat #(1)
Australian Transport Safety
http://www.atsb.gov.au/
Database on aviation, marine, rail and road safety figures including fatalities by state, year, gender
etc
►Select ►Road Safety (left panel) ►Fatal Road Crash Database (right panel) ►Accept the
conditions
3.2.3 Dat ASt
Government of Western Australia
Database (Road fatalities by region)
Learner drivers material that includes information road fatality causes
http://wa.gov.au//
►Select ►Community Safety ►Road safety and awareness ►Fatal crash statistics
3.4.1 ; 3.5.1 ; 3.6.1 ; Dat
Ate
Bike race info
http://www.bikeraceinfo.com
ASt
Time series data on the Tour de France giving the year of race, age of winner, no trend average
speed data 1903-2007
BBC Sport
http://news.bbc.co.uk/sport1/hi/other_sports/cycling/2064819.stm
Year of race, average speed of winner, linear trend
Suggested task: Students ask questions about the data, predict the answers, and graph the data to
answer the questions Information and stories about the race
►Select ►Tour De France (left)
3.6.1 App
Baby name wizard
http://www.babynamewizard.com/namevoyager
Interpret frequency graphs. Type in a name or first letter(s) of a name
Select: boys, girls or both
►Select ►Launch Name Voyager
32
Mathematics: Combined resource lists
1DMAT
3.2.5 Ate
ASt
Encyclopaedia Titanica
http://www.encyclopedia-titanica.org/
Information on the Titanic
3.2.2 Dat
ASt
Government of Western Australia Database
http://wa.gov.au//
(Road fatalities by region) Learner driver’s material that includes information road fatality causes
►Select ►Community Safety ►Road safety and awareness ►Fatal crash statistics
3.2.4 ATe
Journal of Statistics Education
http://www.amstat.org/publications/
The Early History of Average Values and Implications for Education by Arthur Bakker
►Search this site ►Arthur Bakker ►The Early History of Average Values and Implications for
Education
3.3.1 ASt
The MacTutor History of Mathematics archive
http://www-history.mcs.st-and.ac.uk/
Polar Area Diagram
►Select ►Biographies index ►Search ►Nightingale
3.1.5 ; 3.2
Dat #(2)
Climate Data Online- Australian Bureau of Meteorology
http://www.bom.gov.au/climate/data/
Climate Data Online provides access to a range of statistics, historical weather observations,
climatology maps, and other Australian climate data
►Climate Information
1EMAT
3.1.1 App
Interactivate
http://www.shodor.org/interactivate/
Set up a spinner then operate the spinner and the results are recorded in a table
►Select ►Learners Tools ►Probability ►Adjustable Spinner
Mathematics: Combined resource lists
33
3.1.1 ; 3.3.2 Qu
Probabilistic learning activities network
Choose the spinner that could have generated given results http://www.planetqhe.com/
►Select ►Experimental versus theoretical ►Spinner ►Activity Button
3.2.2 & 3.2.3 Qu
Coventry University Mathematics Support Centre
http://www.coventry.ac.uk/ec/maths_centre/statistics_ws.html
Diagnostic tests and worksheets on probability
►Select ►Probability 1
2.1.2 ; 3.2.3 Qu
Balanced Assessment
http://balancedassessment.concord.org/
Probability and reverse area calculations
►Select ►Our library of assessment tasks ►Dart boards
3.3.4 App
Gizmos- Online Learning
http://www.explorelearning.com
Probability of landing in a defined area on a dart board. Simulates firing darts at a board
Conduct multiple trials, record results. Are the results what you would expect by chance
►Select ►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Probability ►Geometric Probability Activity A or B
3.5.1 Dat
ASt
Government of Western Australia Database
http://wa.gov.au/
(Road fatalities by region) Learner driver’s material that includes information road fatality causes
►Select ►Community safety ►Road safety and awareness ►Fatal crash statistics
2AMAT
3.1.1 ATe
Teaching Statistics
http://www.rsscse-edu.org.uk/tsj/?page_id=72
Is an International journal for teachers which caters for teachers of pupils up to 19 years
This article on sampling bias
►Search ►RW Madsen: Making students aware of bias
34
Mathematics: Combined resource lists
3.1.1 App
Maths Stuff
http://www.subtangent.com/
Suitable for probability investigation – similar to Pascal’s Triangle
A wonderful interactive version of this classical device
►Select ►Go to Investigations ►Go to Galton's Quincunx
3.2.5 ATe
Journal of Statistics Education
http://www.amstat.org/publications/jse/v11n1/bakker.html
The History of Average values and its implications for Education
►Search ►Archive (1993-2011) ►2003 (v11) ►Volume 11, Number 2 (July 2003) ►Arthur
Bakker ►The History of Average values and its implications for Education
3.2.7 Dat
Journal of Statistics Education
http://www.amstat.org/publications/jse/
Rowing team data: identify the data and explain the outlier
►Data archive ►Scroll down ►Rowing.dat
3.2.4 ; 3.3.3 ; 3.3.4 Dat #(3)
Climate Data Online- Australian Bureau of Meteorology
http://www.bom.gov.au/climate/data
Access to a range of weather data from a wide range of locations
►Select ►Climate Information
3.3.1 ; Dat
ASt
Government of Western Australia Database
http://wa.gov.au/
(Road fatalities by region) Learner drivers material that includes information on road fatality causes
►government services ►community safety ►road safety awareness ►Select ►Fatal crash
statistics
2BMAT
3.2.1 Dat #(3)
Australian Bureau of Meteorology - Weather data
http://www.bom.gov.au/climate/data/
Access to a range of weather data from a wide range of locations
►Climate Information
Mathematics: Combined resource lists
35
3.2.2 ; 3.2.3 Quid
Coventry University Mathematics Support Centre
http://www.coventry.ac.uk/ec/maths_centre/statistics_ws.html
Diagnostic tests and worksheets and on probability
►Select ►Probability 1
3.2.4 Dat
Government of Western Australia Database
http://wa.gov.au/
(Road fatalities by region) Learner driver’s material that includes information on road fatality
causes
►government services ►community safety ►road safety awareness ►Fatal crash statistics
3.4.1 Dat
The World Clock website
http://www.peterrussell.com/Odds/WorldClock.php
Various data sources
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)
3.4.2 Dat
Athletix
http://www.athletix.org/
Athletics records over the 20th century till now
►Select ►Statistics ►Scroll to ►World Records Progression
3.4.2 ; 3.5.1 Dat #(1)
Government of Western Australia Database
http://wa.gov.au/
(Road fatalities by region) Learner driver’s material that includes information on road fatality
causes
►government services ►community safety ►road safety awareness ►Fatal crash statistics
3.4.2
Dat ; Ate ; ASt
Bike race info
http://www.bikeraceinfo.com
Time series data on Tour de France giving the year of race, age of winner, no trend average speed
data 1903-2007 Suggested tasks: Students ask questions about the data, predict the answers,
and graph the data to answer the questions e.g. Compare the average speed of winner over the
years. Is there a linear trend?
►Tour de France
36
Mathematics: Combined resource lists
3.5.3 Dat #(5)
Australian Bureau of Statistics
http://www.abs.gov.au
Data Collection and Sampling: Shock Population Figures
Fertility rates by age group given as babies per thousand women.
Average number of babies born in per woman in her life time = total fertility rate
►Search on Cat. no. 3301.0 Select ► TABLE 1 BIRTHS ►Summary ►States and territories
►1996–2006
3.5.5 App
Interactivate
http://www.shodor.org/interactivate/
Fit trend lines by eye (practice for students—marginal value unless they analyse where they go
wrong)
►Select ►Learners Tools ►Statistics ►Regression ►Practice in fitting lines by eye ►Add points
to graph by clicking ►Select ►Fit Own Line ► Move Fit Line ► Click and drag green points
►When satisfied Select ►Display line of best fit
3.6.1 Gra
ATe
Australian Bureau of Meteorology
http://www.bom.gov.au/
Graph of wheat yields by State 1975-1990
Shows how good Western Australian yields counterbalance poor Eastern States yields
The graph could be used for class discussion or assessment
►Climate ►Search ►Western Australia to the rescue ►Australian climate extremes
3.6.2 App
Gizmos- Online Learning
http://www.explorelearning.com/
Predict from trend lines
Useful for demonstrating that trend lines are made of points (a property that many students do not
understand) and that prediction is from points on the trend line and not individual data points
(because individual data may suffer measurement error and random variation)
►Select ►Browse Gizmos ►Grades 9-12 ►Data analysis and probability ►Analysing and
displaying data ►Solving using trend lines
3.5 ; 3.6
Dat
Statsci.org
http://www.statsci.org/data/first.html A portal for statistical science and the discipline of statistics
Deaths in custody: proportion and trend
Suggested task: What questions could be answered with this data? Analyse the data numerically
and graphically in order to answer the questions. What social issues do the data raise?
►Select ►Resources ►OzDASL ►First Course in Statistics ►Comparison of proportions
►Aboriginal Deaths in Custody
Mathematics: Combined resource lists
37
2CMAT
3.1.1 ; 3.1.5 App
Waldomaths
http://www.waldomaths.com/
Guess and check the meaning of set notation
►Select ►ages16-19 ►Scroll down to Probability and Statistics►Venn Diagrams 1
3.3.1 ; 3.4.4 App ASt
Yellowstane National Park
http://www.yellowstone.net/
Data from Yellowstone geyser Ask students to describe the data with different class intervals
►Geysers ►Old faithful
3.4.4 ; 3.5.2 App
WISWEB- Freudenthal Institute
http://www.fi.uu.nl/wisweb/
Dot-plots for own or provided data, up to two sets
Divide scale into equal intervals and superimpose histogram, then hide data. Suit linking mean,
median and mode to central tendency, and establishing mean and median as viable for comparing
data sets
►Select ►applets (in text) ►Drop down box ►Statistics and Probability ►All age groups (Drop
down box) ►Minitool 2
3.4.7 ; 3.5.6 Dat
Journal of Statistics Education
Hat size, circumference--linear trend, interpret the gradient
http://www.amstat.org/publications/jse/
►Data archive ►Scroll down to ►hats.dat and hats.txt
3.4.7 ; 3.5.5 ; 3.5.6 Ate
Dat
Teaching Statistics
http://www.rsscse-edu.org.uk/tsj/
Is an International journal for teachers which caters for teachers of pupils up to 19 years
Article on investigating the dimensions of eggs
►Getting the best from teaching statistics ► Scroll down to section 9 ►The Golden Egg
Royal Alberta Museum
http://www.royalalbertamuseum.ca/
Egg data Select: World Species
►Collections & Research ►Life sciences ►Ornithology ►(Scroll down to) ►Eggs A virtual
exhibition
38
Mathematics: Combined resource lists
3.4.7 ; 3.5.6 Dat
Journal of Statistics Education
http://www.amstat.org/publications/jse/
Life span of the fruit fly against number of companions--linear trend
►Data archive ►Scroll down to ►fruitfly.dat and fruitfly.txt
3.4.7 ; 3.5.6 Da
ATe
NCTM resources
http://illuminations.nctm.org/LessonsList.aspx?grade=4&standard=all
Generate own data, Bungee-jumping Barbie—linear relationship, variation between samples
Suggested use: groups generate data, fit a trend line, obtain the equation, compare with other
groups and explain why their trend lines differ
(Variation between samples due to measurement error and hidden variables such as different
elasticity of the rubber bands) Plug-in required
►Lessons ►Check box 9-12 ►Check box Data analysis & Probability ►Barbie Bungee
3.5.5 & 3.5.6 App
Gizmos-Online Learning
http://www.explorelearning.com/
Predict from trend lines. Contextualised data
Useful for demonstrating that trend lines are made of points (a property that many students do not
understand) and that prediction is from points on the trend line and not individual data points
(because individual data may suffer measurement error and random variation). Plug-in required
►Select ►Browse Gizmos ►Grades 9-12 ►Data analysis and probability ►Analysing and
displaying data ►Solving using trend lines
3.3.1 ; 3.4.1 ; 3.5.1 Dat
Infoplease
http://www.infoplease.com/ipa/A0004372.html
Infant mortality and life expectancy for selected countries
Suggested tasks: Ask students to pose questions about the data, represent the data in order to
answer their questions, comment on any unusual or notable things about the data, and explain
their results in terms of their knowledge about the countries
A fuller investigation of this data and related datasets is suggested for 3AMAT
►Select ►Health and Social Statistics ►Infant mortality and life expectancy for selected countries
3.6.3 Dat #(3)
Australian Bureau of Meteorology http://www.bom.gov.au/climate/how/
Weather data
►Climate Information
Mathematics: Combined resource lists
39
2DMAT
3.1.1 ; 3.2.2 Act
Maths 300
http://www.curriculum.edu.au/maths300/
Crazy animals--sample space, probability and simulation
Suggested activity: Students
 Draw animals/alien on card (at home) using the template (web link--Draw your own animal
book), and cut the template in three
 Create animals in groups of 3 or 4 and draw a tree diagram that shows the sample space
 Calculate probabilities
 Use the random number generator on their calculators to determine animals/aliens
 Check experimental results against theoretical probabilities and discuss
►Select ►Free sample tour ►Crazy animals
3.2.2 ; 3.2.3 ; 3.3.1 ; 3.3.2
Interactivate
http://interactivemaths.net
App
Probability, events with multiple stages
Use sliders to choose how many layers of pegs and the probability of going left. Click on ‘Release
repeatedly to release the balls’. Reset to start again
Suggested tasks:
 Ask students to derive the probability for each container with 2 layers and different p (left)
probabilities and test with the applet
 Consider what would be an appropriate number of trials
 Check experimental results against theoretical probabilities and explain differences
 Consider 3, 4, layers and generalise probabilities
►Select ►Statistics ►Go to page 2 ►Galton’s Quincunx
3.3.2 App
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
Based on a game show Stick or switch
This probability game is an electronic version of the game based on the idea of sticking to a
strategy
►Data analysis and probability ►9-12 ►Stick or Switch
3.3.3 App #(5)
Gizmos- Online Learning
http://www.explorelearning.com
Capture/Recapture
Choose number tagged, number recaptured
Displays number and % that are tagged among those recaptured
Dynamic display of fish and actual total
Are the results what you would expect by chance?
Free use for 5 minutes
To save time, print screen dump to explain setup to students
►Select ►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Inferences and predictions ►Estimating population size
40
Mathematics: Combined resource lists
3.2.4 ATe #(5)
Teaching Statistics
http://www.rsscse.org.uk/ts/gtb/contents.html
Contains articles on capture/recapture. A practical study of the capture/recapture method of
estimating population size
►Getting the best from teaching statistics ►Scroll down to section 4 ►How many fish are in the
pond?
3.4.1 Dat #(3)
ATe
Australian Bureau of Meteorology - Weather data
http://www.bom.gov.au/climate/how/
►Climate Information
3.4.4 ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/
History of Sampling
►Publications ►Scroll down to Dissertations ►Scroll down to 2004 Arthur Bakker ►Full version
►p. 61
3.5 ; 3.6
ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/
Article on teaching spread/variability
►Publications ►Select: SERJ ►Current issue and Archives ►Volume 4, Number 1 ►Joan
Garfield and Dani Ben-Zvi
3.5.2 Ate App
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/
Ideas for teaching and testing standard deviation
►Publications ►Select ►SERJ ►Current issue and Archives ►Select ►Volume 4, Number
1►Contents ►Bob Delmas and Yan Liu ►pp. 60-63
Rice Virtual Lab in Statistics
http://onlinestatbook.com/stat_sim/
Applet that relates to the above.
Change the values of the data set by "painting" the histogram with the mouse, clicking on
histogram
Statistics displayed at the side and on the graph
►Select ►Mean and median ►then click Begin (on left)
Mathematics: Combined resource lists
41
3.6.3 App
WISWEB- Freudenthal Institute
http://www.fi.uu.nl/wisweb/en/welcome.html
Dot-plots for own or provided data, up to two sets
Divide scale into equal intervals, superimpose histogram then hide data
Suit emphasising the benefit of using graphs as well as statistics to compare datasets
►Select ►applets (in text) ►Statistics and Probability ►Minitool 2
3.4
Dat
BBC
http://news.bbc.co.uk/sport
Olympic data for comparison: Results for heats and finals for Olympics
►Olympics
3.6.3 Dat
University of Queensland
http://www.maths.uq.edu.au/~mrb/java/CircleZap/
Generate data for comparison by clicking on red and green circles
To copy data into Excel, Highlight data, Right click and Select: Copy
►Paste into Excel ►Select: Data ►Text to Columns ►Delimited ►Next ►Space ►Finish
►Select ►Proceed
3AMAT
3.1.1 & 3.1.3 Qu
Coventry University Mathematics Support Centre
http://www.coventry.ac.uk/ec/maths_centre/statistics_ws.html
Diagnostic tests and worksheets and on probability
►Select ►Probability 2
3.2.4 App
Gizmos- Online Learning
http://www.explorelearning.com
Capture/Recapture
Choose number tagged, number recaptured
Displays number and % that are tagged among those recaptured
Dynamic display of fish and actual total
Are the results what you would expect by chance?
Free use for 5 minutes
To save time, print screen dump to explain setup to students
►Select ►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Inferences and predictions ►Estimating population size
42
Mathematics: Combined resource lists
3.2.4 ATe (5)
Teaching Statistics
http://www.rsscse.org.uk/ts/gtb/contents.html
This is an International journal for teachers which caters for teachers of pupils up to 19 years
Articles on capture/recapture
A practical study of the capture/recapture method of estimating population size
►Getting the best from teaching statistics ►Scroll down to section 4 ►How many fish are in the
pond?
3.3.1 ATe
Teaching Statistics
http://www.rsscse.org.uk/ts/gtb/
Is an International journal for teachers which caters for teachers of pupils up to 19 years
Article on sampling bias
►Getting the Best from Teaching Statisticst ►Scroll down to section 2 ►The BioSS Challenge –
A demonstration of sampling bias ►P Smart
3.3.1 ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/publications/dissertations/dissertations.php
History of Mathematics--sampling, median and quartiles
►Publications ►Scroll down to Dissertations ►Scroll down to 2004 Arthur Bakker ►Full version
►p. 61
3.4.2 ASt
York University
http://www.math.yorku.ca/SCS/Gallery/
Historical statistical graphs. Background when introducing boxplots
►Select ►The best statistical graphs ever drawn
3.4.2 ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/
Article on teaching boxplots
►Publications ►SERJ ►Current issue and Archives ►Scroll down ►Volume 5, Number 2
►Contents ►Maxine Pfannkuch
3.4.2 ; 3.5.1 ; 3.5.2 ; 3.5.3 ; 3.5.4
App
WISWEB- Freudenthal Institute
http://www.fi.uu.nl/wisweb/en/welcome.html
Dot-plots for own or provided data, up to two sets
Divide data into equal intervals and superimpose histogram
Divide data into four equal sized groups and superimpose boxplot
Suit introduction of boxplots, comparison of histograms and boxplots, effects of histogram intervals
and viability of IQR for comparison
►Select ►applets (in text) ►Statistics and Probability ►Minitool 2
Mathematics: Combined resource lists
43
3.4.2 ATe
Coventry University
http://www.mis.coventry.ac.uk/~nhunt/boxplot.htm
How to construct box plots in Excel
►Box plots in Excel by Neville Hunt
3.4.5 ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/publications.php?show=serj
Article on teaching spread/variability
►Publications ►SERJ ►Current issue and Archives ►Volume 4, Number 1 ►Joan Garfield and
Dani Ben-Zvi
3.4.5 Dat
Statsci.org - A portal for statistical science and the discipline of statistics
http://www.statsci.org/data/first.html
Skewed data
Kiama Blowhole eruptions
Time between Nerve Pulses
http://www.statsci.org/data/first.html
Australian Bureau of Statistics
http://www.abs.gov.au/websitedbs/cashome.nsf/Home/Home
The left hand and right hand response times are skewed
Explain why
►Select ►Visit the Teacher Area ►CensusAtSchool Data ►Information Tables ►Scroll down to
see ‘Table of left and right hand reaction times’
3.4.5 Dat
ATe
Gizmos- Online Learning
http://www.explorelearning.com/
Predict from trend lines
Contextualised data
Useful for demonstrating that trend lines are made of points (a property that many students do not
understand) and that prediction is from points on the trend line and not individual data points
(because individual data may suffer measurement error and random variation)
Plug-in required
►Select ►Browse Gizmos ►Grades 9-12 ►Data analysis and probability ►Analysing and
displaying data ►Solving using trend lines
44
Mathematics: Combined resource lists
3.4.6 Dat #(4)
Infoplease
http://www.infoplease.com/ipa/A0004372.html
Infant mortality and life expectancy for selected countries
Suggested tasks
Ask students to pose questions about the data, represent the data in order to answer their
questions, comment on any unusual or notable things about the data, and explain their results in
terms of their knowledge about the countries
A fuller investigation of this data and related datasets is suggested for 3AMAT
►Select ►Health and Social Statistics ►Infant mortality and life expectancy for selected countries
3.5.1 ; 3.5.2 ; 3.5.3 App
National Library of Virtual Manipulatives
http://nlvm.usu.edu/
Histogram and boxplot for own or provided data (decontextualised)
Change histogram interval width with slider
Select: box plot
►Select ►Data analysis and probability 9-12 ►Histogram ►Boxplot
3.5.2 ATe
NetMBA Business Knowledge Centre
http://www.netmba.com/
Advantages of boxplots
Note that box plots for the Mathematics course do not show outliers
►Statistics ►Boxplots
3.5.3 App
Statistics – Concepts and controversies
http://www.whfreeman.com/sccbridgepage/
Histograms for real data
Click and drag to change intervals
Discuss misleading graphs
►Click on textbook on the right ►Select ►Statistical applets ►One variable statistical calculator
Select ►Dataset ►Data ►Statistics ►Histogram ►Stemplot
3.5.3 App
Gizmos- Online Learning
http://www.explorelearning.com
Effect of changing histogram intervals
The applet displays a dot plot and histogram
Free use for 5 minutes
►Select ►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Analysing and displaying data ►Histograms
Mathematics: Combined resource lists
45
3.5.5 ; 3.5.7 Ate
App
International Association for Statistical Education
http://www.stat.auckland.ac.nz/
Ideas for teaching and testing standard deviation
►Select ►Hosting ►International Association for Statistical Education (IASE) ►Publications ►
SERJ ►Current issues and archives ►Volume 4, Number 1 ►Contents ►Bob Delmas and Yan
Liu ►pp. 60-63
Rice Virtual lab
http://onlinestatbook.com/
Applet that is relevant to the above
Add data by clicking on histogram. Statistics displayed at the side and on the graph
►Rice Virtual lab in Statistics ►Simulations and demonstrations ►Select: Mean and median
3.5.8 ; 3.5.9 Dat
Rice Virtual lab
http://onlinestatbook.com/
Generate response time data for comparison: centre, spread and skewness differ
Select: Comparing Distributions
Students generate response times by clicking on small and large squares—data shown as box
plots and histograms
Warn students that results are recorded after the first two trials, without any warning, and any
outliers on the box plots are plotted separately
►Rice Virtual lab in Statistics ►Simulations and demonstrations ►Select: Sampling distributions
3.5.8 ; 3.5.9 Qu
ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/
Comparison questions in an article that describes student responses to the questions
►Hosting ►International Association for Statistical Education (IASE) ►Publications ► SERJ
►Current issues and archives ►Volume 1, Number 2 December 2002 ►scroll down to Contents
►then go to Pfannkuch and Rubick’s article ►pp. 4-22
46
Mathematics: Combined resource lists
3.5.11 App
VESTAC
http://lstat.kuleuven.be/java/
Chance variation between samples: growing a sample (Applet takes a while to load)
►Select ►Basics ►Histogram and boxplot (upper right cell) ►check histogram (bottom right,)
click step ►walk or run to grow a random sample from a normal distribution (steps of 10 points)
Suggested activities:
Observe that
-the shape (or distribution) of data for small samples can differ from the distribution for the
population (the normal curve)
-the shape (or distribution) of sample data gets more like the shape of population as sample size
increases. What are the implications of this for inferring the mean, standard deviation, median,
quartiles, and IQR for a population?
►Check boxplot (bottom right) ►reset and step ►walk or run to grow a sample
Observe relative stability/instability of median, quartiles and extrema as sample grows. ►Select
►new window and grow two samples side-by side—very different numbers of points, then same
numbers of points
Discuss implications for comparison of same and different sized data sets
Does the display confirm your previous conclusions about the median, quartiles, and IQR? Which
is more stable--range or IQR—and what are the implications for inference?
Calculate a boxplot for a standard normal distribution and compare this with boxplots for small and
large samples. Write a summary about reliability when using samples to infer results for
populations
3BMAT
3.1.1 ASt
Cut the knot
http://www.cut-the-knot.org/index.shtml
Articles—correlation versus cause, sampling
First item covers correlation/cause and effect. Second item deals with sampling
►Select ►Table of Contents ►Probability ►Probability problems ►Scroll down to ►Misuse and
Misconception of Statistics ►Correlation and causation
3.1.2 ; 3.2.1 Appl
Sun site - University of Vienna
http://sunsite.univie.ac.at/
Correlation
►Spreadsheets in Mathematics, Statistics and Science Education ►Example spreadsheets and
projects ►Correlation visualised
Mathematics: Combined resource lists
47
3.1.1 ; 3.1.2 Dat
North Carolina School of Science and Mathematics
http://courses.ncssm.edu/math/
Animal gestation period, versus average longevity gives a weak positive relationship and what
about outlier s?
►Select ►Learning Material for teachers and students ►Scroll down to ►Data sets ► Gestation
period and average longevity
3.1.1 ; 3.1.2 Dat
Australian Bureau of Statistics
http://www.abs.gov.au/
Belly button height, height—strong positive relationship
The mean of the ratios for belly button height to height is close to the Golden Ratio
►Search ►CensusAtSchool Data ►Information ►Tables scroll down to the eight data set
3.1.3 ; 3.1.4 Dat #(5)
ATe
Journal of statistics education
http://www.amstat.org/
Carat weight of diamond stones, colour and clarity, price in Singapore $ —data for linear
regression and alternate models. Also an article associated with the dataset
►Publications ►Journals ►Journal of Statistics Education ►Data Archive ►Scroll down to
►diamond.dat and diamond.txt
3.1.3 ; 3.1.4 Dat
ASt
Journal of Statistics Education
http://www.amstat.org/
Article with historical dataset used in formulation of regression lines—diameter of mother and
daughter sweet pea seeds
►Publications ►Journals ►Journal of Statistics Education ►Search ►Stanton ►V9N3 Galton,
Pearson, and the Peas
The MacTutor History of Mathematics archive
http://www-history.mcs.st-and.ac.uk/
►Select ► Biographies ►Galton
3.1.3 App
NCTM resources
http://illuminations.nctm.org/
Properties of regression lines
Suggested teacher demonstration: Add points and ask students how the line is calculated Ask
which distances
When students have no more suggestions sketch a scatterplot with residuals then show the
following
Data points, regression line, residuals, squares and numerical expression for least squares are on
view
►Lessons ►Select 9-12 and Data ►Search ►Scroll to ►Least squares regression
Or
►Lessons ►Select 9-12 and Data ►Search ►Scroll to ►The regression line and correlation
48
Mathematics: Combined resource lists
3.1.5 ; 3.2.3 ; 3.2.4 App
Calfornia State University
http://www.math.csusb.edu/
Add data to scatterplot, trend line and residual plot appear
Good for showing residuals for data that does not fit a linear model
California State University San Bernardino Mathematics department
Search CSUSB ►Stanton ►Professor Charles Stanton, Dept. Math CSUSB ►Probability and
Statistics Demos ►Linear Regression
3.1.5 Dat
Quantitative Environmental Learning Project
http://www.seattlecentral.org/qelp/Data.html
Scatterplots both linear and exponential set out in a matrix
Can also be accessed Maths Topics
►Select ►Maths Topics ► Exponential Scatter plots ►Data Set #056 tree ring widths in a
Douglas fir
or
►Data Set #071 Raging river discharge
3.2.4 App
Shodor
http://www.shodor.org//
A National resource for computational science
Guessing alternative models by eye
Modelling—enter data without brackets, enter function with coefficients e.g. 1*x^2+0, sliders
appear for changing the coefficients
►Activities & Lessons ►Interactivate ►Learners Tools ►Statistics. ►Multi-Function Data Flyer
3.2.1 App
Rice Virtual Lab in Statistics
Estimate r for given datasets—for possible student use
http://onlinestatbook.com/
►Rice Virtual lab in Statistics ►Simulations and demonstrations ►Select ►Regression by eye
3.2.2 ; 3.2.7 Dat
StatLib
http://lib.stat.cmu.edu/
Data, Software and News from the Statistics Community
Linear trend: IQ, Brain size for ten sets of twins
Consider cause/correlation, and the limitation that the sample is small
►Select ►Get data ►Main download area ►Data Archive ►Datasets Archive ►Index of
Datasets Archive ►IQ Brain size
Mathematics: Combined resource lists
49
3.2.4 Dat
Journal Of Statistics Education
http://www.amstat.org/publications/jse/
Outlier, linear regression
►Data Archive ► Select: cigarettes.dat and cigarettes.txt
3.2.4 Dat #(4)
Australian Bureau of Meteorology
http://www.bom.gov.au/climate/ Weather data
►Climate Data Online
3.2.4 Dat
StatLib
http://lib.stat.cmu.edu/
Data, Software and News from the Statistics Community
Linear regression: The data contain a trend as well as outliers,
►Select ►Get data ►Main download area ►Data Archive ►Datasets Archive ►Index of
Datasets Archive ►Balloon”
3.2.7 ATe
Teaching Statistics
http://www.rsscse.org.uk/ts/
This is an International journal for teachers
Article on variation between samples of bivariate data considered on pages 2-3
►Scroll down to ►Getting the best from teaching statistics ►Section 2 ►Exploring sampling
3.2.7 App XL
VESTAC
http://lstat.kuleuven.be/java/
Illustrates random variation in trend lines for samples
►Regression ►Histograms of slope and intercept.
(Applet takes a while to load)
3CMAT
3.1.1 Qu
Centre for Innovation for Mathematics Teaching
http://www.cimt.plymouth.ac.uk/default.htm
Combinations: How many patterns are available in Braille
►Select ► Resources ►CMIT Resources ►Topical applications of Mathematics ►Braille
50
Mathematics: Combined resource lists
3.1.3 App Article
Stanford University – Susan Holmes
http://www-stat.stanford.edu/~susan/surprise/
The birthday problem simulation software generates random dates and matches birthdays on the
same day
►Projects ►Probability by surprise ►The birthday problem aplet.
3.1.3
PUMAS
http://pumas.jpl.nasa.gov/
Online Journal of Maths and Science examples of Pre-College education.
Birthday problem
The task, ‘Matching Birthdays’ would be suitable for 3CMAT §3.2.1, §3.2.2
It uses independence and multiplication properties to explore the possibility of people, in a group of
n people, having matching birthdays
►Search on ►Matching Birthdays ►Scroll down
3.1.3 ; 3.1.7 Dat #(4)
Australian Bureau of Meteorology –
http://www.bom.gov.au/climate/
Weather data
►Climate Data Online
3.1.4 ATe
Teaching Statistics
http://www.rsscse.org.uk/ts/gtb/contents.html
An International journal for teachers
Article on conditional probability
►Scroll down to ►Getting the best from teaching statistics ►Section 1 ►Find ►Understanding
conditional probability
3.1.3 ; 3.1.4 Qu
Dartmouth University
http://www.dartmouth.edu/~chance/
Text with questions
►Select ►a GNU book (left panel), GNU version in pdf (second paragraph)
p. 150 conditional probability, probability laws, central limit theorem
3.1.6 ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/
History of Mathematics—distributions
►Select ►Publications ►Scroll on left to Dissertations ►2004 Arthur Bakker ►Full version
►Distributions p. 74
Mathematics: Combined resource lists
51
3.1.6 ATe
International Association for Statistical Education
http://www.stat.auckland.ac.nz/~iase/
Article on teaching spread/variability
►Publications ►SERJ ►Archive of past issues ►Volume 4, Number 1 ►Joan Garfield and Dani
Ben-Zvi
3.1.6 App
Calfornia State University
http://www.math.csusb.edu/
Sum of dice simulation
Choose number of dice and number of trials
Choose ‘Rollem’ to run the simulation
Shows experimental and theoretical frequency
Could ask students to explain the displays for two dice with varying numbers of trials
►Search ►Stanton ►Charles Stanton’s home page ►Java Demos for Probability and Statistics
►Introduction to probability models
3.1.7 App
Gizmos- Online Learning
http://www.explorelearning.com
Binomial distribution with sliders for n and p
Ask students to explain the changes
►Select►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Probability ►Binomial probabilities ►Free use for five minutes
Waldomaths
http://www.waldomaths.com/
►Select►16-19 ►Binomial + Normal
3.1.7; Ate #(5)
Teaching Statistics
http://www.rsscse-edu.org.uk/tsj/
An International journal for teachers
Articles on capture/recapture
A practical study of the capture/recapture method of estimating population size
►Scroll down to ►The best from teaching statistics ►Statistics in the classroom ►Practical and
project work ►BAC Dudley ‘A practical study of the capture/recapture method of studying
population size’
Also
http://www.rsscse-edu.org.uk/tsj/
►Scroll down to ►Getting the best from teaching statistics ►Section 4 ►’How many fish in the
pond?’
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Mathematics: Combined resource lists
3.1.7 App#(5)
Gizmos- Online Learning
http://www.explorelearning.com
Capture/Recapture and the binomial distribution
Choose number tagged, number recaptured
Displays number and % that are tagged among those recaptured
Dynamic display of fish and actual total
Are the results what you would expect by chance?
Free use for 5 minutes
To save time, print screen dump to explain setup to students
►Select ►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Inferences and predictions ►Estimating population size
3.1.7 App
Gizmos- Online Learning
http://www.explorelearning.com
Probability of landing in specified area of dart board—binomial distribution
Free use for five minutes
Conduct multiple trials, record results. Are the results what you would expect by chance?
►Select ►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Probability ►Geometric Probability ►Run Activity A or B
3.1.8 App
Calfornia State University
http://www.math.csusb.edu/
Probabilities for a normal distribution
Calculates probabilities and displays them on the graph with a very clear display
►Search CUSUB for Stanton ►Charles Stanton’s home page ►Probability and Statistics Demos
►Normal Distribution
3.2.4 App
Gizmos- Online Learning
http://www.explorelearning.com
Sampling from distributions
Free use for 5 minutes
Draw a distribution, grow a sample
Shows sample distribution and mean value
►Select ►Browse Mathematics Gizmos ►Grade 9-12 ►Data analysis and probability
►Inferences and predictions ►Populations and samples
Qu
ARTIST
https://app.gen.umn.edu/artist/index.html
Multiple choice questions
Easy to use and lots of questions
Free registration
►Select ►Item database [Assessment builder] Enter email address and password, submit
►Select ►create a new test ►Fill in details, submit ►Access the database by topic
Mathematics: Combined resource lists
53
3DMAT
3.2.1 Dat
Seattle College – QELP
http://www.seattlecentral.edu/
Normally distributed data
►Search ►QELP►QELP Data page ►Math topics ►Histograms ►
►Dataset#057 Normally distributed wing-lengths (of houseflies)
►Dataset#059 Normal distribution of wheat yields
3.2.1 Dat
StatSci
http://www.statsci.org/index.html
Skewed data: Test fit with a normal distribution
►Select ►Teaching ►Data sets ►Ready for teaching ►OzDASL ►A first course in statistics
►Kiama Blowhole eruptions
Time between eruptions of the geyser
Pomona
http://www.economics.pomona.edu/StatSite/eclectic.html
►Scroll down to Old Semi Faithful
Australian Bureau of Statistics
http://www.abs.gov.au/
The left hand and right hand response times are skewed. Explain why.
Select ►Education ►Quick links ►Census At School Data ►Questionnaire ►scroll down to see
‘Table of left and right hand reaction times’
3.2.1 ASt
StatSci
http://www.statsci.org/
Report on air safety—binomial distribution
►Select ►Teaching ►Data sets ►Ready for teaching ►OzDASL ►A first course in statistics
►Independence and counting ►Air safety
3.2.3 Dat #(4)
Australian Bureau of Meteorology - Weather data
http://www.bom.gov.au/
►Climate ►Data services ►Climate data online
54
Mathematics: Combined resource lists
3.2.3 ATe
West Kentucky University – David Neal
http://www.wku.edu/
Articles on the sign test
►Search ►David Neal ►Statistical Inference on the TI 89
David Lane
http://davidmlane.com/
►Select ►Hyperstat Online ►Contents Chapter 17 ►Sign test
3.3.1 ; 3.4.1 ATe
Teaching Statistics
http://www.rsscse.org.uk/ts/
An International journal for teachers
Article on a normal distribution made with beads and uses of the resource in teaching ‘A’ useful
display of a normal population
The Best of teaching Statistics ►Scroll down to ►Visual and other aids ►RW Jernigan ‘A’ useful
display of a Normal population”
3.3.1 App
VESTAC
http://lstat.kuleuven.be/java/
Chance variation between samples—growing a sample
Note that outliers are plotted beyond the ends of the whiskers
►Observe relative stability/instability of median ►quartiles and extrema as sample grows ►Select
►new window and grow two samples side-by side—same then very different numbers of points
Also discuss implications for comparison of same and different sized data sets.
►Select ►Basics ►Histogram and boxplot (upper right cell) ►check histogram and boxplot-‘both’
(bottom right,) click step (Applet takes a while to load) ►walk or run to grow a random sample from
a normal distribution (steps of 10 points)
3.3.2 App
VESTAC
http://lstat.kuleuven.be/java/
Central Limit Theorem--distribution of sample means
Each sample is displayed on top graph, in turn, and the mean value is added to the bottom graph
Change parameters in Settings and Rescale
Animated, graphs sample, mean of sample, one other statistic that is selected
Generates distributions of the means for normal, uniform and other populations
►Select ►Basics ►Distribution of mean ►top right cell for sampling from a normal distribution
(Applet takes a while to load) ►bottom right cell to sample from a binomial distribution
Rice Virtual Lab
http://onlinestatbook.com/
Distribution of sample means simulation (good but small display)
►Scroll to Rice Virtual Lab in Statistics ►Simulations and demonstrations ►Sampling
distributions ►Read the Instructions ►Click Begin (on left) to activate applet
Mathematics: Combined resource lists
55
3.3.2 Activity
App
Rossman & Chance
http://www.rossmanchance.com/
Class activity in which students sample coins
Applet to interpret after the activity
Select ►Java applets ►Sampling Pennies
3.4.1 ; 3.4.2 ; 3.4.3 App
VESTAC
http://lstat.kuleuven.be/java/
Confidence Interval for sample means
(Applet takes a while to load)
►Select ►Tests ►Confidence interval for the mean
W H Freeman
http://www.whfreeman.com/sccbridgepage/
►Select ►right hand version of the text ►Statistical Applets ►Confidence intervals
California State University Mathematics Department
http://www.math.csusb.edu/
Samples (n=20) from a normal distribution. Choose level of confidence
►Select ►Search CSUB ►Charles Stanton ►Charles Stanton’s home page ►Probability and
Statistics Demos ►Confidence intervals for the mean
3
Qu
College Board
http://apcentral.collegeboard.com/
US Advanced Placement examinations
Free enrolment
►Home ►AP Courses and Exams (on the left) ►Exam Questions (on the right) ►Statistics (in
table) ►Scroll down to Free Response Questions and Scoring Guidelines
3
Qu
ARTIST
https://app.gen.umn.edu/artist/index.html
Multiple choice questions
Free registration
►Select ►Item database [Assessment builder] ►Enter email address and password and submit
►Select ►Create a new test ►Fill in details and submit. Access the database by topic.
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Mathematics: Combined resource lists