Summary Questions

1. Do your results seem reasonable?  Explain.
2. What patterns do you see?
3. Do you think you would get the same results for any circle?
4. Calculate the circumferences of the circles you have been working with by using the formulas c = pd and c = 2 p r.
5. How do the computed values for circumference compare to the values in the table you just completed?

Activity 2:  Graphing Relationships

•  Activity 1 (Student Copy) you previously completed
•  graph paper ruled 4 squares to the inch
•  ruler
•  calculator

Plot the points represented by the first and third rows from the table in Activity 1 (diameter and circumference) on your graph.  For example, if you measured an object that was 10 cm in diameter and had a circumference of 32 cm, you need to find 10 on the x-axis (labeled diameter) and 32 on the y-axis (labeled circumference).  Go up from the 10 until you are across from the 32 and make a point.  Use this method to find points on the graph that represent each of the objects in your table.

Take a ruler and draw a line that connects the points as closely as possible.  You should have only one line with about half the points on each side.

Pick any two new points on your line.  One point will be higher than the other.  Make a triangle by drawing a line straight down from the top point and a second line going right from the bottom point.  Determine the length of each of the lines you just drew.  Now divide the vertical (up and down) length by the horizontal (across) length.  Record your answer.

Try this three more times using other pairs of points on your line.  You have just computed the slope of a line (the change in the y direction divided by the change in the x direction).  Record your answers.

1. What would happen if you measured other objects and plotted the diameter and circumference on the graph?  Would the points be on or near the line you have drawn?
2. Write a statement that explains the numbers you found in Part C and why those numbers make sense.