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# Quarter, Nickel, Dime…

### Summary

Students will systematically collect, organize and describe data, and will then make inferences and a convincing argument based on data analysis.

### Coin Type(s)

- Quarter

### Coin Program(s)

- 50 State Quarters

### Objectives

Students will systematically collect, organize and describe data, and will then make inferences and a convincing argument based on data analysis.

### Major Subject Area Connections

- Math

### Minor/supporting Subject Area Connections

- Science

### Grades

- Fourth grade
- Fifth grade
- Sixth grade

### Class Time

**Sessions**: Two

**Session Length**:
45-60 minutes

**Total Length**:
91-120 minutes

### Groupings

- Whole group
- Pairs

### Background Knowledge

Students should have a basic knowledge of:

- Coin values
- Creating an organized list
- Constructing and interpreting a bar graph
- Chance/probability

### Terms and Concepts

- Probability
- Statistics
- Data

### Materials

- Coin Cards handout
- Coin Graph worksheet
- Envelopes (1 per student)
- Chart paper
- Markers
- Tape

### Preparations

- Make copies of the Coin Cards handout (1 per pair).
- Make copies of the Coin Graph worksheet (1 per student).
- Create a class graph on chart paper that looks similar to the Coin Graph worksheet.

### Worksheets and Files

Lesson plan, worksheet(s), and rubric (if any) at www.usmint.gov/kids/teachers/lessonPlans/pdf/341.pdf.

**Session 1**

- Tell students that they will be working in pairs to play the game “Nickel, Quarter, and Dime.” The rules of the game are as follows: Each player has an envelope containing slips of paper featuring a nickel, a quarter and a dime. On the count of three, each player places one of the three papers randomly on the table. A quarter wins over a dime, a dime wins over a nickel, a nickel wins over a quarter.
- Divide the class into pairs. Give each pair a “Coin Graph” worksheet and a “Coin Cards” handout. Give each student an envelope.
- Instruct the students to cut out the coin cards and each place a picture of a nickel, a quarter, and a dime into their own envelope.
- Ask the students to decide who will be Player A and B and write their names on the appropriate line on the “Coin Graph” worksheet.
- Tell the students that after each round of the game, they will mark their “Coin Graph” worksheet to show who won that round. Students will mark any ties in athird column labeled “Ties.”
- Have each pair play the game 18 times.
- Ask the pairs to total the number of wins for each player on their worksheet in the appropriate blank.
- When the pairs finish, have each group note which column (for their rounds of play) contained the most “wins” (Player A, B, or Ties).
- Display a class graph. Instruct the winning student from each pair to record one mark in the appropriate column on this graph. In the event of a tie, have each student in the pair place a mark in their own graph column.
- After each group has recorded their information, have the class review the data collected, and make inferences about probability. Were the number of wins for Player A and Player B approximately the same after 18 rounds of play?

**Session 2**

- Ask students to work together (in their pairs) to answer the following questions. As you discuss the questions, discuss how they might approach answering them, and explain unknown vocabulary. Make an organized list of the possible outcomes for a round of play in this game. How many possible outcomes are there for each round of play? (9) How many of these outcomes would be wins for player A? (3)What is the probability that player A will win in any round? (3/9=1/3).

**Note**: Explain that probability means favorable outcomes/possible outcomes. How many of these outcomes would be wins for player B? (3) Find the probability that B will win in any round. (3/9) Do you think the game is fair? Do both players have an equal probability of winning in any round? (yes) - Review the answers as a class, and have the students predict what would happen if they continued playing the game. Students should mention that the results for players A and B should continue to stay fairly even.

### Differentiated Learning Options

Have students work with partners who can model the game.

### Enrichments/Extensions

- Create a class center where students can continue to test the results of this activity. Move the class chart into this center, and allow students to record the winners on the class chart.
- Alter the number of players or coins used in the activity to see how the results will change.
- Have the students conduct another exploration where they determine the probability of getting “heads” or “tails” when flipping a quarter.

Use the worksheets and class participation to assess whether the students have met the lesson objectives.

**Discipline**: Math

**Domain**: 4.MD Measurement and Data

**Grade(s)**:
Grade 4

**Cluster**: Represent and interpret data

**Standards**:

**4.MD.4.**Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

**Discipline**: Math

**Domain**: 4.MD Measurement and Data

**Grade(s)**:
Grade 4

**Cluster**: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

**Standards**:

**4.MD.1.**Know relative sizes of measurement units within one system of units including km, m, cm, kg, g, lb, oz, l, ml, hr, min and sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table.- For example, know that 1ft is 12 times as long as 1in. Express the length of a 4ft snake as 48in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

**4.MD.2.**Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.**4.MD.3.**Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

**Discipline**: Mathematics

**Domain**: All Problem Solving

**Cluster**: Instructional programs from kindergarten through grade 12 should enable all students to

**Grade(s)**:
Grades K–12

**Standards**:

- Build new mathematical knowledge through problem solving
- Solve problems that arise in mathematics and in other contexts
- Apply and adapt a variety of appropriate strategies to solve problems
- Monitor and reflect on the process of mathematical problem solving

**Discipline**: Mathematics

**Domain**: 3-5 Data Analysis and Probability

**Cluster**: Understand and apply basic concepts of probability.

**Grade(s)**:
Grades K–12

**Standards**:

In grades 3–5 all students should

- describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible;
- predict the probability of outcomes of simple experiments and test the predictions; and
- understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.

**Discipline**: Mathematics

**Domain**: 3-5 Data Analysis and Probability

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

**Grade(s)**:
Grades K–12

**Standards**:

In grades 3–5 all students should

- propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.