Ice Cubes

 

Purpose:

• To develop an understanding of mean and see what happens to the mean when a number is added.

Number of students:

• 2

Materials needed:

• cubes or squares of paper
• 2 - 8 ½ x 11 pieces of paper

Note :  If you are using paper for the cubes, then either that set of paper or the 8 ½ x 11 paper needs to be colored.
 

What you need to know before you start:

• The mean is often called the average.  If parts of some numbers in your data could be moved to other numbers so that they were all evened out, then that evened-out number would be the mean.

Example: 

 

Directions:

1. Place the 8 ½ x 11 pieces of paper with the long way across.  Fold it into thirds and cut it.
   
    
   
   These pieces of paper are now the “drinking glasses” and the cubes are the ice cubes in the drink.
• Use the “ice cubes” and the “glasses” to solve the problems.
• Put out the same number of glasses as there are numbers listed.
• Record your work in the chart under each question.
2. a. Put these numbers of ice cubes on the glasses.  (There are 4 numbers, so you should have 4 glasses.)
   
   5, 2, 6, 3
   
   
    
• Now move some of them around so that as many glasses as possible have the same number of ice cubes.
   

Total Number of Ice Cubes	Number of Glasses	Mean

1. b. Now you add another glass with 9 ice cubes.  Share out the ice cubes.
    

Total Number of Ice Cubes	Number of Glasses	Mean

1. c.  Suppose the fifth glass only had 4 ice cubes.  Share them out again.

Total Number of Ice Cubes	Number of Glasses	Mean

1. a. Put these numbers of ice cubes on your glasses.  (There are 5 numbers, so you should have 5 glasses.)

1, 1, 1, 1, 26

• Now move some of them around so that as many glasses as possible have the same number of ice cubes.
   

Total Number of Ice Cubes	Number of Glasses	Mean

b.  Now you add another glass with 12 ice cubes.  Share out the ice cubes.

Total Number of Ice Cubes	Number of Glasses	Mean

 

c.  Suppose the sixth glass only had 6 ice cubes.  Share them out again.

Total Number of Ice Cubes	Number of Glasses	Mean

 

1. Discuss this question with your partner.
    

"What do you have to do to make the mean number of ice cubes stay the same when you add another glass? "

 

1. There are 3 glasses with this number of ice cubes:

1, 2, 3  

Add a fourth glass with ice cubes so that the mean is 3.

Draw a picture of what your solution looks like.

 

 

 

 

How many ice cubes did you add?  ____________