**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:**- 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.