probability - tree diagrams
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Probability tree diagramsTRANSCRIPT
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.
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
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.
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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__________________________________ March 7, 2012Ms. Brown/Ms. Regan – Math
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? ___________
__________________________________ March 7, 2012Ms. Brown/Ms. Regan – Math
Block II: Probability – Tree DiagramsSWBAT use a tree diagram to make an organized list of all possible outcomes of an experiment.