Look at the game I just got for my birthday. It’s called...

Leap Frog.

I can’t wait to play it. But I wonder... how can I win the game?

Let’s read the directions to find out.

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Hmmm... The directions say the object of the game is to "leap" the frogs from one side of the pond to the other. Each time I spin a color on the spinner, that color frog gets to "leap" another step across the pond.

The first frog to get to the other side wins the game!

That sounds easy enough.

But look, there are
three different spinners.

Which one should I use to play the game?

wpe1B.gif (1717 bytes) wpe1F.gif (1740 bytes) wpe22.gif (1914 bytes)

Click on the spinner you would choose.

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NA01321_.WMF (18558 bytes)Well, if I’m going to play the game, I want to win.
So, I have to figure out
...
Which spinner should I use to WIN the game?
Click to choose the spinner I should use and explain why I should
use it. Type your reason in the box.
Click on each spinner to find out more.

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NA01320_.WMF (382124 bytes) One way to find out the answer is to design an experiment. 
Have you ever done an experiment in science or math before? What did you do?
Tell me about it.
Type your answer in the box.




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Well, I know that the first step to designing an experiment is to...
understand the problem.
So here’s how I see it...

To win the game,  I have to "leap" one frog to the other side of the pond on the game board.

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There are three different spinners. I can choose one. They look like this.

wpe1A.gif (1215 bytes)wpe20.gif (1282 bytes)wpe21.gif (1224 bytes)

There are three frogs. They look like this. I can choose one.

wpe27.gif (1470 bytes)wpe2A.gif (1370 bytes)wpe2B.gif (1370 bytes)

The question is…
Which spinner should I
use to win the game?
Do you understand
the problem?
Explain the problem in
your own words.
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The next step to designing an experiment is to figure out a plan. Let’s look at the spinners that came with the game and think about it, first.

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How many parts does this spinner have?

Is the spinner divided into equal parts?

How many parts does this spinner have?

Is the spinner divided into equal parts?

How many parts does this spinner have?

Is the spinner divided into equal parts?

 

 

 

 

 

 

 

 

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What would
you do to
figure this out?

Remember, we have to have a plan before we can start an experiment!
AN00817_.WMF (5062 bytes) Type your plan in the box.
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Here’s what I’m going to do. I’m going to write down everything I notice about each of the spinners on this tree. This will help me think through what I want to do.
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12 equal sections

Spinner 1

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wpe36.gif (899 bytes) 6 green sections

wpe1A.gif (1215 bytes)

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4 equal sections
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Spinner 2

wpe3F.gif (908 bytes)
wpe2D.gif (1095 bytes) wpe35.gif (899 bytes) 2 yellow sections

wpe21.gif (1224 bytes)

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3 equal sections

Spinner 3

wpe3D.gif (908 bytes)
wpe37.gif (899 bytes) 1 section of each color
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Click in the box
or boxes
next to the
observations
that you think
are important.
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Now what shall I do? Here are some possibilities I thought of…
Make a prediction about each spinner and then test the prediction by spinning. This is called guess and check.
Play the game by myself to find out which spinner helps me win the game.
Draw a picture to show the possibilities with each spinner.
Create a chart showing all of the possibilities with each spinner.
Record what happens when I spin the spinners and then look for patterns in the results.

Click next to
the plan you
would try.
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Now that I’ve thought about it, I think I know what I’m going to do now. First, let's guess how many wins each color will have with each spinner on this chart after 20 spins. Click to show the number of wins you think each color will have on each spinner.

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wpe24.gif (1215 bytes)

wpe27.gif (1282 bytes)

green       green      green      
yellow      yellow     yellow     
orange     orange    orange    
spinner total = 20 spinner total = 20 spinner total = 20
Check the box for each spinner if the predictions total 20 when added together.

Then I’m going to spin each spinner 20 times to check what happens. Finally, I’ll look back at what the data says and see if I can answer my question "Which spinner should I use to WIN the game?"

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Here's what happened when I spun this spinner 20 times.

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green
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yellow
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orange
wpe37.gif (978 bytes)

Click the lily pad path
for each frog to match
the number of times
that color was spun.

 

Which color
had the most
wins?

 

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Here's what happened when I spun this spinner 20 times.

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wpe2A.gif (3419 bytes)
wpe2C.gif (1677 bytes)




                                                  
wpe2B.gif (1370 bytes)
wpe2A.gif (1370 bytes)
wpe27.gif (1470 bytes)
wpe2B.gif (3404 bytes)
green
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yellow
wpe20.gif (969 bytes)
orange
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Click the lily pad path
for each frog to match
the number of times
that color was spun.

 

Which color
had the most
wins?

 

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Here's what happened when I spun this spinner 20 times.

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wpe2A.gif (3419 bytes)
wpe2C.gif (1677 bytes)  



                                          
wpe2B.gif (1370 bytes)
wpe2A.gif (1370 bytes)
wpe27.gif (1470 bytes)
wpe2B.gif (3404 bytes)
green
wpe2D.gif (977 bytes)
yellow
wpe2E.gif (920 bytes)
orange
wpe2F.gif (958 bytes)

Click the lily pad path
for each frog to match
the number of times
that color was spun.

 

Which color
had the most
wins?

 

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Let's look back at the experiment with this chart. Now can I answer my question,
"Which spinner should I use to win the game?"

wpe23.gif (1224 bytes)

wpe24.gif (1215 bytes)

wpe27.gif (1282 bytes)

green       7 green       5 green       9
yellow      5 yellow      8 yellow      5
orange     8 orange     7 orange     6
I think I can make a prediction, but I would need to do the experiment many more times before I could say for sure.

AN00817_.WMF (5062 bytes)What do
you think?

Click next to the
spinner you would
use to WIN the
game now and explain why in this box.
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You might have thought that designing and conducting an experiment only happens in science, but that’s not quite true. Mathematicians conduct experiments too, just like we did to find answers to our questions. Mathematicians’ questions are usually called problems.

Here are the steps I followed in my experiment.
Click to put them in order.
Figure out a plan.                  
Look back at what you did.  
Conduct the experiment.       
Understand the problem.      

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wpe31.gif (7411 bytes) Now that you know how to design an experiment, what are your questions about the spinners and playing "Leap Frog?"
How will you design your experiment to answer your questions? Now it’s your turn to try at your desk. Remember to follow the steps we learned.

 

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Click on the frog if you
need to see the problem
solving steps again.
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