Mathematics/Physics

How do You Stack Up? Revisited

Objective(s):

• Students will estimate the number of pennies, nickels, dimes and quarters in plastic bags.
• Students will build stacks of each type of coin.
• Students will find the thickness of a penny, nickel, dime and quarter after measuring their stacks.
• Students will measure to the nearest millimeter using a ruler.
• Students will determine how many coins of each type will fit in tubes of different lengths.

Materials Needed:

Approximately 100 of each type of coin, quarter, nickel, dime and penny. (Save up your pocket change for about 3 months and it should be enough.)
4 large plastic bags to put the coins in
4 different size tubes to fit each type of coin
Calculators
Chalk
Rulers

Strategy:

As a an introductory activity, keep the coins in the plastic bags spread out and have the class guess which bag has the most coins. (You will have counted the coins already so you know the answer.) Give the student with the correct answer a small prize such as a Susan B. Anthony dollar coin.

Next, divide the class into four groups – call them the pennies, nickels, dimes, and quarters groups. Have each group stack their coins in piles so they can measure the height of each pile. After they measure each pile, have them record the height of each pile and how many of each coin are in the pile on the board. Then ask "How can we find the thickness of just one of each of these coins?" The students should answer "Divide the height of the stack by the number of coins." Have them do the calculations and then record the thickness of each coin on the board and compare answers. If there is a large discrepancy in the answers, an error in measurement or in calculation could have occurred. Ask them to compare their answers to the government determined thickness published by our government and printed here:

Penny 1.57 mm
Nickel 1.98 mm
Dime 1.35 mm
Quarter 1.75 mm

Have them find the average of their calculated thickness values for each kind of coin for the final activity. Collect the bags of coins from the students. Then, pass out a tube to each group. Using a ruler and a calculator only, each group should tell you how many coins are needed to fill the tube. After they tell you their calculated answer, give them that number of actual of coins to see if their answers agree. If they do match, great! If they do not, perhaps an error was made. If the difference is only 1 or 2 coins, that is okay too.

Performance Assessment:

A wonderful way to assess the students’ understanding of this concept is to ask them to imagine a stack of coins $1000 high. How many nickels, pennies quarters, and dimes would that be? How tall would each stack be in mm, cm and m? Then give the following statistics as a comparison: a basketball player is 2m tall, the ceiling of most buildings is 4m, the height of a ten story building is 40m, and the height of Sears Tower is 440m. How tall would each of these things be in nickels, dimes, quarters, and pennies?

References:

Page, David and Philip Wagreich. Manuevers with Nickels and Numbers. Dale Seymour Publications, 1990.