# A Fraction of the Cost

## Summary

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

## Objectives

• Students will identify coins as parts of a dollar.
• Students will use coins to start to combine fractions.

• Math

• 3rd
• 4th

## Class Time

• Total Time: 46-90 minutes

## Background Knowledge

Students should have a basic knowledge of:
• Equal parts of a whole
• Coins and their value

## Lesson Steps

### Discuss Coins as Fractions

1. Distribute the "Fraction Circles" pages of the A Fraction of the Cost worksheet to each student.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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¢."
8. Repeat steps 5 through 7 for each of the other coins.

### Cut Fractions and Play Coin Spinner Game

1. 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.
2. Place students in pairs. Model the instructions to the game:
• Students will assemble the "Coin Value Spinner" found in the A Fraction of the Cost worksheets.
• 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

• 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.
• 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.)

## Assess

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

## Common Core Standards

CCSS.MATH.CONTENT.3.NF.A.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. CCSS.MATH.CONTENT.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. CCSS.MATH.CONTENT.3.NF.A.3.A Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

## National Standards

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.