# In the Bag!

### Summary

After learning the dollar value of filled coin bags, students calculate how many quarters are in a $1,000 bag. They then explain their problem-solving strategy using pictures, numbers, equations, and/or words.

### Coin Type(s)

- Cent
- Nickel
- Dime
- Quarter
- Half dollar

### Coin Program(s)

- Generic

### Objectives

To achieve the standard of whole number computation, students will:

- Construct number meanings through real-world experiences and the use of physical materials
- Understand our numeration system by relating counting, grouping, and place value concepts
- Interpret the multiple uses of numbers encountered in the real world
- Model, explain, and develop reasonable proficiency with basic facts and algorithms
- Use a variety of mental computation and estimation techniques
- Use calculators in appropriate computational situations
- Select and use computation techniques appropriate to specific problems and determine whether the results are reasonable

### Major Subject Area Connections

- Math

### Grades

- Third grade
- Fourth grade
- Fifth grade

### Class Time

**Sessions**: One

**Session Length**:
30-45 minutes

**Total Length**:
0-45 minutes

### Groupings

- Whole group
- Individual work

### Terms and Concepts

Money

### Materials

- Internet access
- H.I.P. Pocket Change's "Birth of a Coin" at www.usmint.gov/kids/cartoons/birthOfACoin/
- Paper
- Pencils
- Manipulatives, as needed

- Have the students review "Birth of a Coin" on the U.S. Mint's H.I.P. Pocket Change™ Web site. If needed, guide them to the appropriate page (www.usmint.gov/kids/cartoons/birthOfACoin/).
- Tell the students that new coins are checked for quality, counted, and put into bags at the Mint before they're sent to banks in the Federal Reserve system. Each bag of dimes, quarters, and half dollars holds $1,000; nickel bags hold $200; and one cent bags hold $50.
- Ask the students to determine how many coins are in a $1,000 bag of quarters. Have them explain their strategy for solving the problem using pictures, numbers, equations, and/or words.

### Enrichments/Extensions

Have more advanced students determine how many nickels are in a $200 bag.

Use class participation and presentations to determine whether the students were able to determine how many quarters are in a $1,000 bag and to explain their problem-solving strategies.

**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**: 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**: 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.