# A Fraction of the Cost

### Summary

Students will use various coin denominations to explore the concept of fractions.

### Coin Type(s)

- Quarter

### Coin Program(s)

- 50 State Quarters

### Objectives

Students will use various coin denominations to explore the concept of fractions.

### Major Subject Area Connections

- Math

### Grades

- Second grade
- Third grade

### Class Time

**Sessions**: Two

**Session Length**:
30-45 minutes

**Total Length**:
46-90 minutes

### Groupings

- Whole group
- Pairs

### Background Knowledge

Students should have a basic knowledge of:

- Equal parts of a whole
- Coins and their value

### Terms and Concepts

- Fractions
- Coins
- Nickel
- Dime
- Quarter
- Half dollar
- Dollar

### Materials

- “Coin Value Spinner” handout
- “Fraction Circles” worksheets
- Scissors
- Brads (to assemble spinner) (1 per pair)

### Preparations

- Make copies of the “Fraction Circles” worksheet (1 per student).
- Make copies of the “Coin Value Spinner” handout (1 per pair).

### Worksheets and Files

Lesson plan, worksheet(s), and rubric (if any) at www.usmint.gov/kids/teachers/lessonPlans/pdf/287.pdf.

**Session 1**

- Distribute the “Fraction Circles” worksheets to each student.
- Review with the students the value of each coin, from the nickel to the dollar. Write each coin’s value on the board as it is discussed.
- Explain to students that coins and their values can be expressed as fractions. Since “cents” are units that make up a dollar, the portion of one whole dollar that any coin represents can be written as a fraction. For example, five cents is equal to 5/100.
- Referencing the fraction circles, hold up the whole circle and compare it to one dollar. Ask the students to locate the image of the dollar coin and cut it out. On the back, direct them to write this coin’s value.
- Hold up the image of a half dollar and ask the students to locate and point to this coin on their worksheet. Ask the students to cut out the image of the coin and write its value on the back.
- Ask students how many fifty-cent coins are needed to make one whole dollar. On the back of the half-dollar image, direct the students to write the fraction represented by this coin.
- Ask the students to locate and cut out the circle that shows this fraction. On each of the coin halves, the students should write “50¢.”
- Repeat steps 5 through 7 for each of the other coins.

**Session 2**

- Instruct the students to cut their fraction circles into the pie shapes that represent the particular fraction (the halves fraction circle will be in two parts, etc.). Tell them to make piles for the four different types of fractions as they cut.
- Place students in pairs. Model the instructions to the game:
- Students will assemble the “Coin Value Spinner.”
- The object of the activity is to see who can create a whole unit or $1.00 first.
- Students place their whole circle in front of them and take turns spinning the coin value spinner.
- They then place the corresponding fraction piece onto their whole piece if they can. Players should trade for equal fraction parts—2 dimes (two one-tenths) and a nickel (a twentieth) for a quarter (a fourth), 2 quarters (fourths) for a half dollar (a half), etc.
- The next player then spins and repeats the process detailed above.
- Students take turns spinning, and the first person to create a whole unit or full dollar wins.

### Differentiated Learning Options

- For an optional activity players start with a whole unit ($1.00) and subtract the amount that they roll. This forces them to trade in larger fractions for smaller ones (1/2 for 5/10.) This may be more appropriate for fourth graders.
- Student can also estimate and then check how many different combinations can make a whole unit ($1.00.)

### Enrichments/Extensions

Divide the class into two teams and alternate asking fraction-related math questions (decide whether students can work as a group or can only answer if it’s their turn) allowing them to use the chalkboard to figure the problem. When a team gets an answer correct, they can spin/roll and add to their team’s fraction circle. Make sure that “trading down” becomes a part of the process: if a team fails to do so, the other team gets the turn.

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**: 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**: Math

**Domain**: 2.OA Operations and Algebraic Thinking

**Grade(s)**:
Grade 4

**Cluster**: Represent and solve problems involving addition and subtraction.

**Standards**:

**2.OA.1.**Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, eg, by using drawings and equations with a symbol for the unknown number to represent the problem.

**Discipline**: Math

**Domain**: 2.OA Operations and Algebraic Thinking

**Grade(s)**:
Grade 4

**Cluster**: Add and subtract within 20

**Standards**:

- 2.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, eg, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

**Discipline**: Math

**Domain**: 3.NF Number and Operations: Fractions

**Grade(s)**:
Grade 4

**Cluster**: Develop understanding of fractions as numbers

**Standards**:

- 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- 3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
- Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

- 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- Recognize and generate simple equivalent fractions, eg, 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, eg, by using a visual fraction model
- Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
- Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, eg, by using a visual fraction model

**Discipline**: Mathematics

**Domain**: 3-5 Number and Operations

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

**Grade(s)**:
Grades 3–5

**Standards**:

In grades 3–5 all students should

- develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50;
- develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
- develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;
- develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
- use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; and
- select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

**Discipline**: Mathematics

**Domain**: 3-5 Number and Operations

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

**Grade(s)**:
Grades 3–5

**Standards**:

In grades 3–5 all students should

- understand various meanings of multiplication and division;
- understand the effects of multiplying and dividing whole numbers;
- identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems; and
- understand and use properties of operations, such as the distributivity of multiplication over addition.

**Discipline**: Mathematics

**Domain**: All Problem Solving

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

**Grade(s)**:
Grades 3–5

**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**: All Representation

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

**Grade(s)**:
Grades 3–5

**Standards**:

- Create and use representations to organize, record, and communicate mathematical ideas
- Select, apply, and translate among mathematical representations to solve problems
- Use representations to model and interpret physical, social, and mathematical phenomena

**Discipline**: Mathematics

**Domain**: 3-5 Number and Operations

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

**Grade(s)**:
Grades 3–5

**Standards**:

In grades 3–5 all students should

- understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
- recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
- develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
- use models, benchmarks, and equivalent forms to judge the size of fractions;
- recognize and generate equivalent forms of commonly used fractions, decimals, and percents;
- explore numbers less than 0 by extending the number line and through familiar applications; and
- describe classes of numbers according to characteristics such as the nature of their factors.