In this problem students should be encouraged to draw combinations, make a systematic list or table, or use equipment to show that they have explored all the possibilities.
The solution shows a systematic approach.
Rangi is in a hurry to get off to a party. He grabs two CDs from his CD rack. If he has 5 Kickin' CDs and 3 Now CDs, is he more likely to have grabbed a pair of Kickin' CDs or one of each?
- Introduce the problem using models of the 8 CD's. Get students to take turns randomly selecting 2 CD's (with eyes shut or by covering the CD rack). After several turns ask the students to make statements about what they have observed.
- Pose the problem. Check that the students understand that they need to find all the ways of selecting 2 CD's from the rack of 8.
- As the students work on the problem in pairs ask questions that require them to explain how they are counting outcomes and how they know they will find ALL the possible ways.
- Encourage the students to record their solution in ways to convince others that they are correct.
- Share written records. Discuss the different approaches (list, pictures)
Extension to the problem
Write a CD problem where the answer is equally likely.
Regardless of their choice of strategy to solve this problem, students should demonstrate that they have explored all possibilities.
In this diagram the 5 Kickin' CDs are shown with white circles (1, 2, 3, 4, 5) and the 3 Now CDs are shown with black circles (1, 2, 3).
There are 28 ways of taking two CDs from Rangi collection.
There are just 10 ways for Rangi to have grabbed a pair of Kickin' CDs and 15 ways to have grabbed one Now and one Kickin'. So he is more likely to have taken a mixture of Kickin' and Now to the party.