Purpose: Two exercises designed to show how to take data, find a function that best fits that data and use that function to predict values within the given data.
Exercise 1
Equipment: 
Plain (not peanut) M&M's (4050)
Styrofoam or plastic cups (1 for every 2 students)
Graph paper (1 for every 2 students) 
Procedure: 
In this exercise the number of the toss is the independent variable and the number of M&M's remaining face down is the dependent variable.
Each group of two students will: 

 Pour out the M&M's, count the number of candies, record
that number in the data table below for Toss #1, column A and return the candies to the cup.
 Pour out the M&M's and remove all the candies on which the M
is turned up. Count the remaining candies, record that number in
the data table, Toss #2, column A and return these to the cup. (Don't eat the M&M's yet! We might repeat this exercise.)
 Repeat #2 until no candies remain or until you find duds.
 Graph the data points on the graph paper. Toss #'s are x and column A are y.
 Repeat the exercise, recording the remaining candies number in
column B and column C. (Optional) Compare the graphs.

What kind of graph does the data resemble? Use the TI83 to graph your results and find the function that best fits the data points.

 Clear out the lists. STAT, EDIT, CLEAR L1, L2, L3 . . .
 Store the Toss #'s in L1. STAT, EDIT
 Store the data in column A in L2. STAT, EDIT, 2ND, QUIT
(If you repeat the exercise, store column B in L3 and so on.)
 Draw a scatterplot of the data. STAT PLOT, 1. Turn Plot 1 ON, select a TYPE (the first choice), XList : L1, YList: L2,
select a MARK. GRAPH, ZOOM, 9. This will plot your points
and set the scales appropriately to fit your data.
 Use technology to find an equation of best fit. STAT, CALC, 5, ( why #5?) ENTER. Write the equation y=ax^{2} + bx + c.
 To graph this curve we must enter an equation in the Y=.
Put cursor on Y1=. VARS, 5, EQ, 1, GRAPH.

Data Table
Toss #  M & M's remaining 
 A  B  C 
1    
2    
3    
4    
5    
6    
Exercise 2
Equipment: 
Tape measure or yardstick. Graph paper 
Procedure: 
In this excercise the measure of the length of the humerus is the
independent variable (x) and height is the dependent variable (y). 

 Measure the humerus and the height of at least six
classmates.
 Record the measurements in the data table below.
Humerus measures are x, corresponding height is y.
 Graph the coordinates on graph paper.
 What kind of graph best fits the data?

Use the TI83 to graph your results and find a function that best fits the data. Then use the function to predict other values with the given data.

 Clear out the lists. STAT, EDIT, CLEAR L1, L2, L3 . . .
 Store the humerus measurements in L1. STAT, EDIT
 Store the corresponding height measurements in L2. STAT, EDIT, 2ND, QUIT
 Graph a scatterplot of the data. STAT PLOT, 1. Turn
Plot 1 ON, select a TYPE (the first choice), XList: L1,
YList: L2, select a MARK. GRAPH, ZOOM, 9. This
will plot your points and set the scales appropriately
to fit your data.
 Use technology to find the graph that best fits the data.
STAT, CALC, 4, (why #4?). ENTER. Write the
equation y=ax + b.
 To graph this line we must enter an equation in the Y=.
Put cursor on Y1=. VARS, 5, EQ, 1, GRAPH.
 Use the graph or the equation to predict the height of a classmate whose humerus is 12 in. long or 15 in. long.

Data Table
Humerus  Height 
 
 
 
 
 
. . .  . . . 

Background: The Pythagoreans examined the arithmetic mean (a+b)/2, the geometric mean, and the harmonic mean; and the relationships among them. The mean is the sum of all the numbers divided by the number of the items in the set. This is the value often intended when the word “average” is used. Piaget’s research indicates that students cannot comprehend the concept of the mean until about age 12, when they become conservers and can consider two or more interrelated values simultaneously.
Purpose: To introduce and develop the concept of finding an average (mean).
Materials: Strips of construction paper, approximately 3 cm wide and longer than anyone’s foot; tape; scissors; meterstick.
Procedure 1:
 Distribute a paper strip to each student.
 Announce to the class: “Let’s find the average foot length in our class.”
 “Cut your paper strip so that it’s the same length as your foot.”
 “Now let’s tape all of our strips together.”
Questions to Ask and Answer:
 How can we find the average foot size?
 How many centimeters long is our big, long strip?
 How many people’s feet do we have?
 How many centimeters is that for the average foot?
Procedure 2:
 Cut the long strip into equal parts that stand for the average foot size in the class.
 Give one cut strip to each student.
Questions to Ask and Answer:
 Who has a foot that is about the size of the average foot?
 Is your foot shorter or longer than average?
 Suppose we all bought a pair of shoes in the average foot size, what would happen?
Conclusion:
(Total length of paper strip)/(number of strips) = Average foot size
