Creative Activities in Mathematics - Book 3

Problem-based learning is a powerful alternative to drill-and practice or skills-based learning, especially within maths, but it can be difficult to source rich materials that engage an entire class.

The Creative Activities in Mathematics series provides a wealth of investigations and open-ended active learning activities, designed to engage students with mathematics and develop their problemsolving, collaboration and mathematical skills.

Book Three provides nine different class activities suitable for students in lower and middle secondary school (Years 7 to 10), along with teaching notes and staged lesson plans. Each activity is a whole-class investigation with open-ended answers that takes a particular scenario and develops it over four levels. This enables it to be used both at different year levels and with students of differing ability in the same class. All activities are firmly rooted in the Australian Curriculum: Mathematics and linked to the content descriptors of the Number and Algebra, Measurement and Geometry, and Statistics and Probability strands.

Student materials

Download a full set of activity sheets that provide a framework for student responses. These can be printed or copied for use in class. This set also includes a number of extension activities for advanced students.

Download activity sheets

Additional online resources

Part 1: Number and Algebra

Chapter 2: The Tower of Hanoi

• Francois Édouard Lucas - http://www-history.mcs.st-andrews.ac.uk/Biographies/Lucas.html
• Tower of Hanoi simulation - http://www.towerofhanoi.org/
• Tower of Hanoi simulation - http://britton.disted.camosun....
• Tower of Hanoi simulation - http://www.mazeworks.com/hanoi...
• Scientific calculator - http://web2.0calc.com/

Chapter 3: Nim-like games

• The 21 game - http://en.wikipedia.org/wiki/Nim#The_21_game
• Nim history - http://www.archimedes-lab.org/game_nim/nim.html
• Nim - strategy game or scam? - http://h2g2.com/approved_entry/A20725760
• Win at Nim - http://www.archimedes-lab.org/How_to_Solve/Win_at_Nim.html

Part 2: Measurement and Geometry

Chapter 4: Hidden treasure

• The Story of Mathematics - http://www.storyofmathematics.com/
• Euclid - http://www.storyofmathematics.com/hellenistic_euclid.html
• GeoGebra - http://www.geogebra.org/cms/do...
• Compass and straight-edge constructions - http://schools-wikipedia.org/w...
• Circumcentre of a triangle - http://www.mathopenref.com/constcircumcenter.html
• Hexagons - http://mathworld.wolfram.com/Hexagon.html

Chapter 5: Tessellations

• Attack on the pentagon results in discovery of new mathematical tile - http://gu.com/p/4b9b3/sbl
• Penrose Tiles - http://mathworld.wolfram.com/PenroseTiles.html
• Polyominoes: A big word for a lot of fun - http://math.rice.edu/~lanius/L...
• Polyominoes and other animals - https://www.ics.uci.edu/~eppstein/junkyard/polyomino.html
• Pentominoes: An introduction - http://www.cimt.plymouth.ac.uk...
• About pentominoes - http://isomerdesign.com/Pentomino/
• Tetraominoes - http://www.cut-the-knot.org/blue/TetrominoFaultFree.shtml

Chapter 6: How high is a building?

• Basic clinometer from classroom materials - http://www.instructables.com/id/Basic-Clinometer-From-Classroom-Materials/
• Make a clinometer - http://www.wikihow.com/Make-a-Clinometer
• How to make a clinometer (video) - https://www.youtube.com/watch?v=GMLcU1Qknts
• Basic rangefinders - https://people.rit.edu/andpph/text-rangefinder-basic.html
• Make a simple rangefinder - http://www.ehow.com/how_7857303_make-simple-rangefinder-mirrors.html

Part 3: Statistics and Probability

Chapter 7: Greedy Pig

• Greedy Pig - http://nzmaths.co.nz/resource/greedy-pig-0
• Greedy Pig - http://nrich.maths.org/1258
• Game of Pig: Sixes - http://www.math.usu.edu/~schneit/CTIS/GreedyPig/
• Dice roller - http://www.roll-dice-online.com
• Dice roller - http://www.brockjones.com/dieroller/dice.htm
• Virtual dice - http://www.bgfl.org/bgfl/custo...

Chapter 8: Pascal's triangle

• Pascal's triangle - http://www.mathsisfun.com/pascals-triangle.html
• The hockey stick theorem - http://luckytoilet.wordpress.com/2010/10/22/the-hockey-stick-theorem-an-animated-proof/
• Pascal's triangle and its patterns - http://ptri1.tripod.com/
• Pascal's triangle (video)- https://www.youtube.com/watch?v=YUqHdxxdbyM
• Linking newspaper rings, Pascal's colours and poetry of math - http://mathmunch.org/tag/pascals-triangle/

Chapter 9: Monty Hall's problem

• Monty Hall's problem - http://en.wikipedia.org/wiki/Monty_Hall_problem
• Monty Hall's problem simulation - http://www.nytimes.com/2008/04/08/science/08monty.html?_r=0#
• Monty Hall's problem simulation - http://www.stayorswitch.com/
• Monty Hall's problem simulation - http://blossoms.mit.edu/legacy/monty-hall/index.htm
• Monty Hall's problem (video) - https://www.youtube.com/watch?v=OTosh1aZ5fs
• Monty Hall's problem (video) - https://www.youtube.com/watch?v=mhlc7peGlGg
• Bertrand's box paradox - http://www.datagenetics.com/blog/june72013/index.html
• Bertrand's box paradox - http://blog.zymergi.com/2013/06/bertrands-box-paradox.html
• Two envelopes problem - https://www.math.hmc.edu/funfa...
• Two envelopes problem - https://en.wikipedia.org/wiki/Two_envelopes_problem
• Two envelopes problem (video) - https://www.youtube.com/watch?v=6Odh-7Cz1d8
• Sleeping Beauty problem - http://en.wikipedia.org/wiki/Sleeping_Beauty_problem
• Sleeping Beauty problem - http://measureofdoubt.com/2011...
• Sleeping Beauty problem - http://stats.stackexchange.com/questions/41208/the-sleeping-beauty-paradox
• Sleeping Beauty problem (video) - https://www.youtube.com/watch?v=5Cqbf86jTro
• Sleeping Beauty problem (video) - https://www.youtube.com/watch?v=zL52lG6aNIY
• Three prisoners problem - https://en.wikipedia.org/wiki/Three_Prisoners_problem
• Monty Hall and three prisoners - http://www.mathrecreation.com/2009/03/monty-hall-and-three-prisoners.html
• Classic probability problems - http://probabilityblogger.blogspot.com.au/2012/05/classic-probability-problems-revisited.html
• The birthday paradox - http://betterexplained.com/articles/understanding-the-birthday-paradox/
• The birthday paradox - https://www.mathsisfun.com/data/probability-shared-birthday.html
• Boy or girl paradox - http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

Additional sites

• Maths 300 - http://www.maths300.esa.edu.au...
• NRICH - http://nrich.maths.org/
• NZ Maths - http://nzmaths.co.nz/
• AMSI TIMES (The Improving Mathematics Education in Schools) Modules - http://schools.amsi.org.au/times-modules/