The Penney Ante Game is a great activity that can be used in
the mathematics classroom to enrich the learning of students. There are multiple positive outcomes, as it is
mathematically rich in its promoting of higher order thinking through both collaborative
and discovery learning.
For the Penney Ante Game to be undertaken, an existing knowledge is required in the use of tree diagrams, sample space and calculation of probabilities. For this reason, it is most organic when situated in the context of a year 10 class - it is during Stage 5 that these topics are expected to be covered according to the syllabus. The extension content can also be beneficial for HSC students. Discussion of binary in Conway’s Algorithm (to calculate the odds of winning in this game of probability) will function optimally when students’ minds are able to think more abstractly through the use of number systems with a different base. In addition to this, there are other ways of calculating the odds of winning by using limiting sums, which would demonstrate a practical application for the year 12 content.
The Penney Ante is a great means of exploring mathematical and logical ideas. As the game is played, collaboration tacitly occurs among the students. For the game to function, there is a need assign roles to perform different tasks and to communicate with one another. As rounds of the game progress, students discover patterns and recognise the need to come up with strategies to best their peers. Healthy competition, implicit in the game, creates a natural incentive to form tactics in order to win. As this happens, students are learning to think mathematically and logically on a higher level.
Your students would be missing out if they didn’t play the Penney Ante! Follow the links below for an overview of how the Penney Ante Game can be implemented in your classroom.
For the Penney Ante Game to be undertaken, an existing knowledge is required in the use of tree diagrams, sample space and calculation of probabilities. For this reason, it is most organic when situated in the context of a year 10 class - it is during Stage 5 that these topics are expected to be covered according to the syllabus. The extension content can also be beneficial for HSC students. Discussion of binary in Conway’s Algorithm (to calculate the odds of winning in this game of probability) will function optimally when students’ minds are able to think more abstractly through the use of number systems with a different base. In addition to this, there are other ways of calculating the odds of winning by using limiting sums, which would demonstrate a practical application for the year 12 content.
The Penney Ante is a great means of exploring mathematical and logical ideas. As the game is played, collaboration tacitly occurs among the students. For the game to function, there is a need assign roles to perform different tasks and to communicate with one another. As rounds of the game progress, students discover patterns and recognise the need to come up with strategies to best their peers. Healthy competition, implicit in the game, creates a natural incentive to form tactics in order to win. As this happens, students are learning to think mathematically and logically on a higher level.
Your students would be missing out if they didn’t play the Penney Ante! Follow the links below for an overview of how the Penney Ante Game can be implemented in your classroom.
Sample SpaceWe're dealing with a sequence of three (3) coin tosses. First, we must know our sample space.
|
The GameHere you will find the rules for the Penney Ante Game.
|
Winning StrategyI thought coin tosses were fair? How could this game possibly have a strategy?
|
Conway's AlgorithmFor those after an explanation of the probabilities in this game, Conway's Algorithm is for you.
|
Estimated TimelineOver a 20 minute period, here is an approximate timeline for the activity.
|