PE02311_.WMF (28244 bytes) I am going to have a birthday party.   I have to know two things...

how many guests are coming
AND
how many guests will be boys or girls

This is so I can buy party favors and plan fun games.                                           

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Click here to help with the party planning.

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SO00790_.WMF (42168 bytes) That means I have to conduct an experiment

AND

predict who will come to the party before I really know.

That could be a problem I need you to help me solve.  Do you remember the problem-solving steps?

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Click here to review the steps for problem solving.

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Let's see. 
Do you understand the problem?

Write the problem in your own words here.

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Now that you understand the problem, you can help me solve it. 
What's the next step to solve this problem?
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Click on the picture if you need a hint about the next problem-solving step.

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If we need to make a plan to solve the problem, then we should probably start with a prediction.

How many people will come to the party?   My family says I can invite my four best friends. Two of them are boys and two are girls. Each friend can invite two of their friends. And don't forget to count me!

How many of the guests will be boys?
Click on the boy to check your prediction.

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How many of the guests will be girls?
Click on the girl to check your prediction.

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Were all of your predictions correct?

Yes. If your predictions were correct, this next step will help you learn another way to solve more difficult problems.

No. If not, that's probably because it's hard to make a  prediction when you don't know all of the facts.  It's also hard to predict without a plan. 

Let's use a picture, like a tree diagram to help us plan for solving the problem.









 

Here is a real tree diagram.wpe6.jpg (4793 bytes)

It shows the total number of people coming to the party.

What is the total number?
Type your answer in the box.
 



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I can bring four friends. Rosa and Amal are girls. John and Josť are boys. Click on the picture for another hint.
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Tree diagrams can also show possible combinations.
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The first branch shows Rosa's first choice. The last branch shows Rosa's second choice. FD00300_.WMF (18892 bytes)

 


If you follow the branches of the tree diagram, these are Rosa's possible combinations...
 boy, girl
 boy,   boy
girl
girl,

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This tree diagram can also help you solve the problem by showing all of the possible combinations we just figured out.
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How many does Rosa have?



In our experiment, the possible combinations are the different pairs of boys or girls who might come to the party.
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If there are four possible combinations or pairs Rosa can invite to the party, what are the possible combinations for Amal?

Remember, Amal might invite boys or girls.
Click to choose the possible combinations in the chart below.
First Person invited Second Person invited
boy
girl
girl

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Click on the picture to check Amal's possible combinations.
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Let's look at Amal's branch on the tree diagram. Can you place the possible combinations for Amal on the tree diagram below?

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DD00113_.WMF (10614 bytes) Type all of the combinations in the box to complete Amal's tree diagram.

Remember to follow the pattern set by Rosa.
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John's combinations are the same as Amal's, but he is ready to decide which two of his four friends to invite.
John used his tree diagram to show all of the possible outcomes or ways he can invite his two friends on this list.
If Jamal and Minh are boys and Claire and Natasia are girls, 
How many different pairs are there?
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Type the number in the box and click the Check Me! button.
HINT: Repeating pairs are the same color, count them only once.

Jamal,

Claire

Jamal,

Natasia

Jamal,

Minh

Minh,

Jamal

Minh,

Claire

Minh,

Natasia

Claire,

Jamal

Claire,

Minh

Claire,

Natasia

Natasia,

Jamal

Natasia,

Minh

Natasia,

Claire
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Now use John's tree diagram to chart his possible outcomes. Claire, Natasia (girls), Minh, and Jamal (boys) are John's friends.Click on the arrows to show John's different possible outcomes.

First Friend

Second Friend
Jamal
Natasia
Natasia
Claire
Natasia


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Click here to check.
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Now it's time to help Josť see all of his possible outcomes.  He has four friends too.  Use the tree diagram at the right. Click to show a possible outcome on each row. Click on the picture to make sure you have all six possible outcomes.

Girl Girl Boy Boy
Van Kate Brad Jake
Van Kate Brad Jake
Van Kate Brad Jake
Van Kate Brad Jake
Van Kate Brad Jake
Van Kate Brad Jake


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Well, we solved the problem of how many people are coming to my party using a tree diagram. We still need to solve the problem of how many girls or boys are coming.

Let's see if you learned anything about how to use tree diagrams.
A tree diagram can help you
display possible combinations and outcomes.
predict events.
solve problems.
"see" a problem more clearly.
Click on the words tree diagram to check.

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Click here to go to the next lesson on planning the party!

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