# Nickel, Quarter and Dime

### Summary

Students will play a game to help them develop an appreciation for statistical methods as a powerful means for decision making.

### Coin Type(s)

- Nickel
- Dime
- Quarter

### Coin Program(s)

- Generic

### Objectives

- Students will systematically collect, organize and describe data.
- They will construct, read and interpret a graph.
- They will make inferences and a convincing argument based on data analysis.

### Major Subject Area Connections

- Math

### Grades

- Sixth grade
- Seventh grade
- Eighth grade

### Class Time

**Sessions**: One

**Session Length**:
45 minutes

**Total Length**:
0-45 minutes

### Groupings

- Pairs
- Individual work

### Terms and Concepts

- Coins
- Money
- Probability
- Problem solving
- Statistics

### Materials

- A currently circulating U.S. nickel, quarter and dime for each student
- Graph paper
- Colored pencils
- Paper
- Pencils

- Introduce the game "Nickel, Quarter and Dime" to the students. Explain the rules of the game: Each player has a nickel, a quarter and a dime. On the count of three, each player places one of the three coins on the table. A quarter wins over a dime, a dime wins over a nickel, and a nickel wins over a quarter.
- Divide the class into pairs and distribute the coins. Have each pair play the game 18 times and keep track of who wins.
- Have each pair construct a bar graph that shows the number of wins each player had.
- Help the students determine the range, mode and mean for their set of data.
- Compare the results as a class.
- To determine whether the game is fair or not, have the students answer the following questions:
- How many outcomes (combinations of coins) are possible? (9) Make a tree diagram of the possible outcomes (a win for A, for B or a tie).
- How many ways could player A win? (3)
- What is the probability that player A will win in any round? (3/9=1/3) Explain that probability means likelihood, arrived at by dividing favorable outcomes by possible outcomes.
- How many ways could player B win? (3)
- What is the probability that player B will win in any round? (3/9=1/3)
- Is the game fair? Do both players have an equal probability of winning in any round? (yes)
- Have the students write a paragraph explaining why or why not the game Nickel, Quarter and Dime is a fair game.

### Enrichments/Extensions

Have students create a game that is not fair. Have them describe the game and explain why the game is not fair.

Use the answers to the questions and their paragraph explaining whether the game is fair or not to assess whether the students have met the lesson objectives.

This lesson plan is not associated with any Common Core Standards.

**Discipline**: Mathematics

**Domain**: 6-8 Number and Operations

**Cluster**: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

**Grade(s)**:
Grades 6–8

**Standards**:

In grades 6–8 all students should

- work flexibly with fractions, decimals, and percents to solve problems;
- compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line;
- develop meaning for percents greater than 100 and less than 1;
- understand and use ratios and proportions to represent quantitative relationships;
- develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation;
- use factors, multiples, prime factorization, and relatively prime numbers to solve problems; and
- develop meaning for integers and represent and compare quantities with them.

**Discipline**: Mathematics

**Domain**: 6-8 Data Analysis and Probability

**Cluster**: Develop and evaluate inferences and predictions that are based on data.

**Grade(s)**:
Grades 6–8

**Standards**:

In grades 6–8 all students should

- use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken;
- make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit; and
- use conjectures to formulate new questions and plan new studies to answer them.

**Discipline**: Mathematics

**Domain**: 6-8 Data Analysis and Probability

**Cluster**: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

**Grade(s)**:
Grades 6–8

**Standards**:

In grades 6–8 all students should

- formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population; and
- select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

**Discipline**: Mathematics

**Domain**: 6-8 Data Analysis and Probability

**Cluster**: Select and use appropriate statistical methods to analyze data.

**Grade(s)**:
Grades 6–8

**Standards**:

In grades 6–8 all students should

- find, use, and interpret measures of center and spread, including mean and interquartile range; and
- discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

**Discipline**: Mathematics

**Domain**: 6-8 Number and Operations

**Cluster**: Compute fluently and make reasonable estimates.

**Grade(s)**:
Grades 6–8

**Standards**:

In grades 6–8 all students should

- select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods;
- develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use;
- develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results; and
- develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

**Discipline**: Mathematics

**Domain**: 6-8 Number and Operations

**Cluster**: Understand meanings of operations and how they relate to one another.

**Grade(s)**:
Grades 6–8

**Standards**:

In grades 6–8 all students should

- understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;
- use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals; and
- understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.