Semester 1 Topic 8 Level I

Task Name : Cat and Dog Task Level : I (Year 8)
Semester : 1 Topic : Chance VC Strand : Chance
Web Address :
Equipment Needed : A selection of six-sided, eight-sided, ten-sided and twelve-sided dice
Victorian Curriculum outcome : Identify complementary events and use the sum of probabilities to solve problems. Describe events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’. Represent events in two-way tables and Venn diagrams and solve related problems.
Task description : Students play “Cat and Dog” as an intro to this task. The rules are that two six-sided dice are rolled. If the difference between the two dice are 0, 1 or 2, the “Cat” (one of the players) gets a point. If the difference between the two dice are 3, 4 or 5, the “Dog” gets a point. They then use this unfair game to create their own game which is fair. The new game must have three options – cat gets a point, dog gets a point, and either neither gets a point or both get a point. They use a two way table to show the game is fair, and use a Venn Diagram to show the probability for all possible events (cat gets a point, cat doesn’t get a point, dog gets a point, dog doesn’t get a point, both get a point, neither get a point). Encourage students to use something other than two six-sided die for extra challenge.
Assessment options : Photograph of game with two way tables explaining the probability of each event as well as Venn Diagrams.

Teacher notes :

Extension: Students design a game of chance
Intro presentation: Design a game of chance
Design a game of chance rubric

Extra task: Play the game Higher or Lower: What is your strategy? What was your highest score?

Record the probabilities for one full game. For example:
Pr(<7) = 24/51 (A, 2, 3, 4, 5, 6 are all lower: 6 x 4 suits = 24 out of 51 cards left)
Pr(>4) = 35/50 (5, 6, 7, 8, 9, 10, J, Q, K are all higher: 9 x 4 suits ( – 1) = 35 out of 50 cards left)
Pr(<K) = 46/49 (all cards except other kings are lower so the game skips)
Pr(<8) = 26/48