Probability - Tree Diagrams

Tree Diagrams

Teacher: Brown and Regan Time: 100 minSubject: Math Grade: SeventhUnit: Probability Date: 3-7-12Standard:

Aims: Does the AIM align with the Essentials of Great Instruction? How does this AIM connect to the one preceding it and the one following it? (Is there a clear sequential, scaffolded connection?)

SWBAT show all possible outcomes of an experiment by creating a tree diagram.SWBAT use a tree diagram to make an organized list of all possible outcomes of an experiment.Exit Ticket Key Points (Why)

1) Tara spins each of the spinners below one time. What are the total possible outcomes for spinning the two spinners? Draw a tree diagram to display all possible outcomes of this experiment.

2) The deli offers a lunch special for $5.25. The special includes a sandwich, a side, and a beverage. The choices are below:Sandwich Side DrinkTurkey Fries WaterRoast Beef

Chips Soda

Veggie Salad

Create a TREE DIAGRAM:

List all possible combinations:

How many combinations are there? ___________

In life, we have lots of choices and decisions to make. Tree diagrams are a counting technique; they are an organized way for us to identify all possible outcomes.

Counting techniques exist for finding the number of possible combinations. The outcomes of an event can be represented pictorially using a tree diagram or an organized list.

In this lesson, you will learn how to find all the possible outcomes of a compound event by drawing a tree diagram.

Key Points (What) Key Points (How/CFS) Counting techniques exist for finding the

total number of possible combinations for a given experiment or situation.

The number of outcomes can be represented pictorially by using a tree diagram or an organized list.

To make sure we have accounted for all possible combinations in an organized list, we

Read and annotate to determine how many single experiments are in the question.

Identify the sample space for each single experiment.

Draw a tree diagram to show all the possible choices. Be sure to label each level of the tree diagram.

make a tree diagram. Sample space refers to all of the possible

outcomes/combinations for a given experiment or situation.

o Example: When tossing a number cube, all of the sample space is: 1, 2, 3, 4, 5, 6.

Individual combinations or results of experiments are known as events or outcomes.

o Example: Tossing a 6 on a number cube.

Compound experiments are a combination of two or more single experiments.

o Example: Tossing a number cube and then flipping a coin.

Vocabulary: Potential Misunderstandings Event Outcome Sample Space Tree Diagram Compound Event

Students may have difficulty identifying the levels of an experiment.

__________________________________ March 7, 2012Ms. Brown/Ms. Regan – Math

Probability: Tree DiagramsSWBAT show all possible outcomes of an experiment by creating a tree diagram.

Warm-UpThe sample space for tossing a coin is: heads, tails.

List the sample space for tossing a number cube: ___, ___, ___, ___, ___, ___

Example OneWhat are all the possible outcomes of spinning a three section spinner and then flipping a coin? Draw a tree diagram to display all possible outcomes.

Katharine Brown, 03/05/12,

You are already familiar with the concept of sample space, or the set of all the possible outcomes of an experiment.Quickly review the sample space for the cube.Frame:Today is the first day of our next unit… Probability. Together we will explore the idea of chance, which mathematicians represent as a number between 0 and 1, inclusive.In this lesson, you will learn how to find all the possible outcomes of a compound event by drawing a tree diagram.In life, we have lots of choices and decisions to make. Tree diagrams are a counting technique; they are an organized way for us to identify all possible outcomes.Counting techniques exist for finding the number of possible combinations. The outcomes of an event can be represented pictorially using a tree diagram or an organized list.


What are the two simple experiments that create this two-part experiment?What is the sample space for the spinner?What is the sample space for the coin?Label the first level of the experiment “Spinner.” List the possible outcomes for the spinner.After I spin the spinner, the next level of the experiment is the coin toss. Label it.If the spinner landed on one, what could happen when I toss the coin?Continue until the tree diagram is complete.This tree diagram show the sample space for this compound event. Turn and talk: What is sample space?Listen for kids who talk about all the possible outcomes of an experiment.What is a compound event?

Key Points:Sample __ __ __ __ __ refers to all of the

possible outcomes/combinations for a

given experiment or situation.

Example: When tossing a number cube, all

of the sample space is: 1, 2, 3, 4, 5, 6.

Individual combinations or results of

experiments are known as __ __ __ __ __ __

or outcomes.

Example: Tossing a 6 on a number cube.

Compound experiments are a combination

of two or more __ __ __ __ __ __

experiments.

Example: Tossing a number cube and then

flipping a coin.

Tree diagrams display the sample space of compound experiments.

Example TwoThe students on the school spirit committee are selling pennants. The table below shows the different colors, sizes, and designs. What are all of the possible choices for pennants?

School PennantsColor Size DesignRed Small Pole

Green Large Rivets


This “experiment” is more of a real life situation. What are the three different decisions you would have to make to determine which pennant you will buy?These single decisions are simple experiments. When we choose color, size, and design, these are simple experiments.What is the sample space for color? Size? Design? (Circle the sample space on the page and label it sample space.)What can we use for the first level of the experiment? After we choose a color, we will choose the pennant size. Finally, the design.


simple


If I do the experiment of tossing the six-sided number cube, an event or outcome of that experiment could be the cube landing on the number 6.


events


Show a number cube. Cubes have six faces. It could land on any of the six faces!


space

Steps Read and annotate to determine how many single experiments are in the question. Identify the sample space for each single experiment. Draw a tree diagram to show all the possible choices. Be sure to label each level of

the tree diagram.

Everybody WritesExplain how you would create a tree diagram to show all the possible outcomes for the following experiment:

Part A: Flip a coinPart B: Roll a number cube

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Independent Practice1) Students can choose one sandwich, one fruit, and one drink for their school lunch.

Create a tree diagram to show all possible combinations.


The top quality student response I am looking for:To create a tree diagram for this compound experiment, first I would identify the sample space for each part of the experiment. Then, I would begin the tree diagram by writing the possibilities for flipping a coin. Finally, I would finish the tree diagram by adding a level for the number cube and listing the possible outcomes beneath the possibilities for the coin.

2) Spinner A has red, blue, green, and yellow sections. Spinner B has purple, pink, and gold sections. Make a tree diagram to find the total possible outcomes if Dennis spins each spinner once.

3) Mr. Pettaway is handing out materials for P.E class. Each student gets a flag and a jersey. The flags that Mr. Pettaway is handing out come in three different colors: blue, red and green. The jerseys come in 2 different colors: yellow or purple.

4) At the Dairy Queen, you can make your own sundae. The choices are below.Dairy Queen Sundae Options

Ice Cream Topping #1 Topping #2Vanilla Hot Fudge Rainbow SprinklesChocolate Caramel Whipped CreamStrawberry

5) Why do we display information in tree diagrams?

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Exit Ticket: Probability – Tree DiagramsSWBAT show all possible outcomes of an experiment by creating a tree diagram.SWBAT use a tree diagram to make an organized list of all possible outcomes of an experiment.Mastered It! Almost Not Yet

1) Tara spins each of the spinners below one time. What are the total possible outcomes for spinning the two spinners? Draw a tree diagram to display all possible outcomes of this experiment.

Turn me over. More on the back

2) The deli offers a lunch special for $5.25. The special includes a sandwich, a side, and a beverage. The choices are below:

Sandwich

Side Drink

Turkey Fries Water

Roast Beef

Chips Soda

Veggie Salad

Create a TREE DIAGRAM:

List all possible combinations:

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________

How many combinations are there? ___________


Block II: Probability – Tree DiagramsSWBAT use a tree diagram to make an organized list of all possible outcomes of an experiment.

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Probability - Tree Diagrams