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:
- 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)
- Before class, the instructor will fill 3 containers per group with various amounts of the three coins/washers.
- 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.
- One pair in each group should mass an empty container. Put the result in the table below.
- Subtract out the mass of the empty container from each measurement so that you have the actual mass of the coins/washers alone.
- Count each type of coin/washer in each container and put the results in the table below.
| ||Container #1||Container #2||Container #3||Empty Container|
|Total Mass in grams|| || || || |
|Mass of Coins/Washers|| || || ||---------------|
|Number of Pennies|| || || ||---------------|
|Number of Nickels|| || || ||---------------|
|Number of Dimes || || || ||---------------|
- 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:
- 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.)
- Check your answers by massing each type of coin/washer and comparing it to your solutions.