This lesson begins with the essential question: How can you use an organized list to find the total number of possible outcomes of an experiment?
We'll review the terms sample space and organize list. Then I will model how to use an organized list.
When doing the examples, I tell students that part of being organized is to be systematic. For example, when listing numbers list them in numerical order. When listing letters, list them in alphabetical order. This helps us to keep track of our work. Using an organized list is an example of mathematical practice 5 - use appropriate tools strategically.
There are two examples. Each example has an additional check for understanding problem.
Students may work in pairs on this set of problems. The problems start with simple and progress to slightly more complicated examples. I never make an organized list of more than two events; trees are much better for that.
Problems like GP3 and GP5 can be a bit confusing for students. There is only one object - either a coin or a die - that is being flipped or rolled twice. Sometimes students do not realize their list should be pairs of outcomes.
See the example:
Now my students get the opportunity to how successful they will be solving problems on their own. The problems are similar to the guided problem solving problems.
Students may have a problem with figuring out how to list the different songs on problem 4. I might suggest R1, R2, R3, etc for rap song 1, rap song 2, rap song 3, and so on.
Students may have a hard time visualizing question #5. If they are familiar with bar/tape diagrams you may suggest they use one to figure out how many WIN and LOSE sections exist.
The extension asks students to identify probabilities after creating a list of all possible outcomes. The focus of the lesson is to learn how to use an organized list well but it is not usually much of a stretch to ask students to identify the probabilities of events.
The students will take a brief exit ticket. It is designed to see whether or not students can make and read an organized list. Note: it does not matter whether students list the coin flip first or the spinner first; either way is fine with me.
It is important that they have all 10 outcomes listed and can answer the questions to follow based on that list.
A students should be able to correctly do 4 out of 5 problems to show they have mastered the lesson objective.