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What is the Mass of a Coin?
Objective: Students will determine the mass of different coins (or different sized washers) without actually massing the coins individually.   

Previous Knowledge: Students should be able to set up and solve a system of 3 equations and 3 variables.  

Time Required: 1 day.  

Group Size: 6.  

Materials:
  • 4 film containers per group
  • Collection of 3 different types of coins (or 3 different sizes of washers)
  • Triple beam balance (or other type of balance)
Procedure:
  1. Before class, the instructor will fill 3 containers per group with various amounts of the three coins/washers. 
  2. When students enter, one container will be handed out to each pair of students.  Each pair must mass their container of coins/washers and come to a consensus on the measurement.  Each group should record the masses in the table below.
  3. One pair in each group should mass an empty container.  Put the result in the table below.
  4. Subtract out the mass of the empty container from each measurement so that you have the actual mass of the coins/washers alone.
  5. Count each type of coin/washer in each container and put the results in the table below.

     Container #1Container #2Container #3Empty Container
    Total Mass in grams    
    Mass of Coins/Washers   ---------------
    Number of Pennies   ---------------
    Number of Nickels   ---------------
    Number of Dimes    ---------------

  6. Transform your data into a system of 3 equations and 3 variables.  Let x = mass of a penny (or small washer), y = mass of a nickel (or medium washer), and z = mass of a dime (or large washer).  Each equation should be modeled as follows:
  7. Once each container’s contents are transformed into an equation, use the matrix capabilities of a graphing calculator to solve the system of equations to determine the mass of each type of coin/washer.  *Link to Lessons/Matrices/Solving Equation with Matrices* (Or students may solve the system of equations using elimination.)
  8. Check your answers by massing each type of coin/washer and comparing it to your solutions.



K Dodd

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