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Area With Error
Purpose: To compare the area of each shape to the number of circular objects the shape can contain without going beyond the shape’s boundary and to determine if the relationship is linear, if so, to find the line of best fit and the equation for the line.

Materials Needed:
  • Peppermint Starlites *You may substitute any circular objects to cut costs.
  • Skittles
  • Mini M&Ms
  • Ruler
  • Blank Paper
Background Information: To find the formula for the area of each shape, refer to your textbook or other resource. The relative error is the difference between two specific answers. The percent error is the relative error divided by the correct answer times 100.

Length of Activity: You should allow at least three class periods working in groups of two.

Process:
  1. Trace 10 differently sized geometric shapes onto your blank paper.


  2. Find the area of each shape in units of centimeters to the nearest hundredth. Record each measurement in the charts.


  3. Fill each shape with peppermint starlites so that none of the candies go beyond the boundary. Record the number of peppermint starlites in the chart.


  4. Fill each shape with skittles so that none of the candies go beyond the boundary. Record the number of skittles in the chart.


  5. Fill each shape with mini M&Ms so that none of the candies go beyond the boundary. Record the number of mini M&Ms in the chart.


  6. Graph a scatter plot of the results of the PEPPERMINTS chart on a coordinate plane, draw the trend line, and determine the equation of the trend line.


  7. Graph a scatter plot of the results of the SKITTLES chart on a coordinate plane, draw the trend line, and determine the equation of the trend line.


  8. Graph a scatter plot of the results of the MINI M&Ms chart on a coordinate plane, draw the trend line, and determine the equation of the trend line.


Charts and Graphs:
             Peppermints                               Skittles                                          Mini M&Ms

Area#Area#Area#
      
      
      
      
      
      
      
      
      
      





Extension: Now that you have determined the equation of each trend line, we will now use the graphing calculator to determine the equation of the regression line for each chart of data to compare the accuracy of your equations.
  1. What window setting would work the best when graphing the data from the PEPPERMINTS chart?
  2. Why does this window seem to be the most appropriate setting?
  3. What is the equation of the regression line?


  4. What window setting would work best when graphing the data from the SKITTLES chart?
  5. Why does this window seem to be the most appropriate setting?
  6. What is the equation of the regression line?


  7. What window setting would work best when graphing the data from the MINI M&Ms chart?
  8. Why does this window seem to be the most appropriate setting?
  9. What is the equation of the regression line?


  10. Describe the meaning of the slope in each equation.
  11. If a shape has an area of 82.5 cm2:

    1. How many peppermints does your equation for the trend line determine should fit into the shape without going beyond the shape’s boundary?
    2. How many peppermints does your equation for the regression line determine should fit into the shape without going beyond the shape’s boundary?
    3. Assuming that the equation for the regression line is the correct equation, calculate the percent error on the number of peppermints?


    4. How many skittles does your equation for the trend line determine should fit into the shape without going beyond the shape’s boundary?
    5. How many skittles does your equation for the regression line determine should fit into the shape without going beyond the shape’s boundary?
    6. Assuming that the equation for the regression line is the correct equation, calculate the percent error on the number of skittles?


    7. How many mini M&Ms does your equation for the trend line determine should fit into the shape without going beyond the shape’s boundary?
    8. How many mini M&Ms does your equation for the regression line determine should fit into the shape without going beyond the shape’s boundary?
    9. Assuming that the equation for the regression line is the correct equation, calculate the percent error on the number of M&Ms?


    10. What is the pattern of the percent error and what does this tell us?



G Redden

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