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The Statistics of Coins

Main Subject Area: Mathematics

Additional Subjects: Mathematics

Duration of Lesson:  90 minutes

Keywords:

• Calculation
• Cent
• Circulation
• Coins
• Penny
• Percent

Brief Description:

Students will use skills of observation, recording, and calculation to provide an overview of years of cents (pennies) in circulation in the local area.

National Standard(s):

• Number and Operations
• Data Analysis and Probability

Additional Subject Area Standard(s):

Objectives:

Students will use skills of observation, recording, and calculation to provide an overview of years of cents (pennies) in circulation in the local area.

Materials (online):

Materials (offline):

Pennies

Lined paper

Graph paper

Calculators (if necessary)

Coins Used in Lesson:

Currently circulating U.S. cents (pennies)

Grade Level(s):   6-8  

Procedures (online):

Procedures (offline):

1. Divide students into pairs.

2. Supply each pair with a set of ten coins.

3. Instruct students to record the years marked on each cent (penny).

4. Distribute graph paper and instruct each group to create a bar graph showing the number of coins represented by each year. 5. Looking at their own graph, instruct students to determine the percentage of the total coins represented by the mode (the most frequently occurring year) in their data. Model this activity for the students.

6. Using their own data, also have students calculate the percentage of the total coins represented by each year recorded.

7. Ask students to speculate as to whether they believe their percentages would be close to those represented by the class as a whole.

8. Collect class data. This will include the number of groups involved in the activity as well as the number of coins represented by each year.

9.Students will each create a graph showing the class’ data, and will compare the mode of the class graph with the mode on their own graph. Are they the same?

10. Looking at just the class graph, instruct students calculate the percentage of the total coins that represent the mode.

11. Using the class data, ask students to calculate the percentages for each year recorded.

12. As a class, discuss how the information they discovered compared with what they expected.

Assessment / Evaluation:

Students will be given hypothetical situations; such as if they would be given a sack with 100 cents (pennies), what would be the probability they would withdraw a coin with a specific year on it.

Differentiated Learning Options:

Vary the number of coins given to each group.

Have students try this same activity using coins of different denominations. See if there are any trends that they notice among the different coin denominations.