Name:__________________________________________ Period:_________________

 

No Need to Count Your Pennies

 

Have you ever saved pennies, nickels or dimes?  If you have, you probably took them to the bank to exchange for dollars. Tellers at the bank don’t have to count each coin to determine how much money is there.  They use the properties of the coins instead.

 

A penny, nickel and dime each have a particular mass and thickness.  A roll of coins will have a certain mass and length depending on how many coins are in the roll.

 

Objective: To determine the # of pennies in an unknown roll without opening it and counting them. 

 

Unknown Roll #: _______________

 

Procedure:

  1. Using a balance, measure the mass of unknown roll to the nearest .01 gram. Record this mass in the data table.
  2. Measure the thickness of 1 coin, 2 coins, 3 coins, 4 coins, 6 coins, 10 coins, 15 coins, and 25 coins to the nearest .5 mm.  DO NOT measure the thickness of one coin and then multiply to find the other measurements.  Measure each set of coins. Measure the entire the length of the unknown row.  Record these values in the data table.

 

Data table:

Number of coins

Mass of  pennies (grams)

Mass of nickels (grams)

Thickness (mm)

1

2.47

4.85

 

2

4.98

9.84

 

3

7.51

14.78

 

4

10.56

19.76

 

6

16.04

29.75

 

10

27.95

49.81

 

15

41.70

74.96

 

25

68.35

119.98

 

row

 

X

 

 

 

Graphing:  Make a line graph with the mass information in the data table.

  1. Make a title for your graph including the independent and dependent variable.
  2. The number of coins should be on the x-axis. This axis should have a minimum of 42 coins because that is the most number of coins in the unknown rows.
  3. The mass of the coins should be on the y-axis.  This axis should have a minimum of the mass of your unknown row. Be sure to label each axis and give the graph a title.
  4. Plot the data for the # of coins vs. the mass of the pennies (except the mass of the unknown row) in blue colored pencil. Using a ruler, draw a “best fit” line through as many points as possible.
  5. Plot the data for the # of coins vs. the mass of the nickels in green colored pencil. Draw a “best fit” line.
  6. Make a key or legend for your graph.
  7. Find the mass of the unknown row on the y-axis.  Draw a horizontal line from this point across the paper in red until it intersects with your blue “best fit” line.
  8. To determine the number of coins in the unknown row, find the point where the red and blue lines intersect and trace it down to where it meet the x-axis.

 

What is the closest value for the # of coins? ____________________________________

 

Ask your teacher how many coins were actually in the row.  Write this number here. ______________________________________

 

Questions:

  1. Are all the pennies the same mass?  Explain your answer.

 

 

 

  1. Are all the pennies the same thickness?  Explain your answer.

 

 

 

 

  1. Was measuring the mass of the pennies accurate for determining the # of coins in the unknown row?