AlgebraLab

Heavy Candy

By K Mathis


Objective: Students will weigh M and M’s and count the number of M and M’s.  Using their data, they will write an equation predicting the weight of M and M’s from the number.



Note: Activity can be changed to use any quantity that can be counted and weighed. Non-food alternatives could include: beads, counting chips, centimeter cubes.



Prior Knowledge:
  • Linear regression equation
  • Meaning of the slope
  • Meaning of the y-intercept
Materials:
  • Large bags of M and M’s or an alternative material listed above
  • Styrofoam cups, 1 for each group
  • Triple-beam balance, 1 for each group
  • 3-oz paper cups, one for each student
  • Paper plates or paper towels for each student

Group Size: 4-6 students



Time Frame:
  • Background:  10 minutes
  • Distributing and weighing samples :  20 minutes
  • Plotting points and calculating a linear regression equation:  10 minutes
  • Follow-up questions: 10 minutes
  • Clean-up:  10 minutes
Procedure:
  1. Before weighing the M and M’s, the styrofoam cup must be weighed empty, and this weight recorded. This weight will be subtracted from the total weight each time a student weighs their M and M’s.


  2. Each person in the group will fill his/her paper cup with M and M’s.One at a time, the student will pour his/her cup of M and M’s into the Styrofoam cup and weigh it. Record the net weight (Total weight – weight of cup). The student will then pour the M and M’s back into his/her cup or on the paper plate or paper towel.


  3. Count the number of M and M’s. Each student should make sure the recorder correct records his/her sample number and weight.


  4. Assign a recorder to make the table of values to be recorded shown below.



    Student Name Total Number
    of M and M's         		Net Weight
    of M and M's
       
       
       
       
       
       


Student Worksheet and Conclusions
  1. Make a scatterplot of the data, putting number of M and M’s on the horizontal axis and their net weight on the vertical axis. Label the axes with uniform scales.



  2. Using a straightedge, draw a trend line on your data that you feel best fits the data.


  3. Identify two grid points on your trend line (do NOT use data points). Write down their coordinates:

    4. Point 1: (    ,    )
    Point 2: (    ,    )

  4. Find the slope of your trend line.


  5. Write the equation of your trend line.


  6. What is the y-intercept of your trend line? Do you get the same answer looking at the graph as you do using your equation? What does this number represent?  Does this make sense?


  7. Using your equation, predict the weight of 1000 M and M’s.


  8. What is the meaning of the slope of your trend line? Describe this rate of change in words.

Extension: Each student in your group probably has a different slope and y-intercept for his/her equation of the trend line, and therefore, has made different predictions for the weight of 1000 M and M’s. Describe a way that you could combine the information of your team members to create a better trend line equation.