Grabbing CDs
Systematically count outcomes
Compare the likelihood of events
Devise and use problem solving strategies to explore situations mathematically (systematic list, draw a picture, use equipment).
This is a counting then comparing problem. The counting can be done in many ways. The comparing is always the easy part.
Problem
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?
Teaching Sequence
- 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.
Solution
I’ll do this with a picture that could represent equipment. The students could make ‘paper’ CDs as their equipment. I have to see how many ways there are of choosing two CDs form the collection.
From the picture I can see that there are 28 ways of taking two CDs from Rangi collection.
There are just 10 ways for Paul 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.
| Attachment | Size |
|---|---|
| GrabbingCDs.pdf | 61.08 KB |
| GrabbingCDsMaori.pdf | 82.47 KB |
Similar Resources
Make the Highest Total
theoretically and experimentally examine the probabilities of games of chance
devise and use problem solving strategies to explore situations mathematically (be systematic, use a table).
Coin Shake-Up
Predict the likelihood of an event based on data collected
Use a systematic approach to find all possible outcomes
Effectively plan mathematical exploration
Lara's Equiprobable Dice I
Find certain probabilities relating to rolling two dice
Devise and use problem solving strategies to explore situations mathematically (be systematic)
Another Dartboard
Predict probabilities of an event involving area
Make deductions from probabilities
Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, look for patterns, draw a diagram, make a table, think, use algebra).
Dressing In The Dark
Work systematically to identify all the possible outcomes.
Describe events using everyday language.
