Determine Outcomes Using Tree Diagrams

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Objective

SWBAT find the total possible outcomes of 2 or more events by drawing a tree diagram

Big Idea

Tree diagrams are a great way to see the outcomes of 2 or more events

Introduction

10 minutes

This lesson begins with the essential question:  How can you use a tree diagram to find the total number of possible outcomes of an experiment?  

We'll review the terms sample space and tree diagram.  Then I will model how to draw a tree diagram.

There are two examples.  I will draw one of the examples with the branches extending out to the right.  The other example will have branches extending down.  I'll explain that either method is fine.  

Once the tree diagram is drawn I will ask students to identify certain outcomes.  For example 1, I may ask:  How many outcomes show Heads and 2; Heads and an even number;  Tails and 7.  This is my check for understanding that students understand how to interpret the tree diagram. 

Guided Problem Solving

15 minutes

Students may work in pairs on this set of problems.  As students are working I will walk the room and provide help as needed.  Mostly this will involve making sure students can accurately represent the outcomes of the event in a tree diagram and that students can interpret the outcomes.  

On problems like GP1, look out for a common error that appears like this.   Students need to know that every branch node should have branches extending from them to show the next set of possible outcomes.

 

 

 

Independent Problem Solving

20 minutes

Students now will have three problems to solve on their own.  These are very similar to the previous set of problems.  I have also asked students to identify the probability of various events.  Again watch out for the common error where students do not have a new branch coming out of every node.  

If this problem persists, it can sometimes help to label the various levels of the tree.  The labels for problem 1 could be "flip 1", "flip 2", "flip 3", "flip 4".

Here is an image of how that might appear.

Exit Ticket

5 minutes

Students will now take an exit ticket.   Students may ask which spinner should be listed first.  I may only answer "Do you think it will change the outcomes?".  

Four correct answers out of five will be the criterion for a successful exit ticket.  If a students is able to do the first two parts I will know they have the fundamentals of a tree diagram.  

Question 3 is easy to miss if students rush through finding the sums of 7.  I'll remind them to be especially diligent with this problem.   The same is true with question 5.