## Using Our Site

### Summary

Students will estimate and calculate the sum of very large numbers. Students will understand the concept of exponential growth.

• Quarter

### Coin Program(s)

• 50 State Quarters

### Objectives

• Students will estimate and calculate the sum of very large numbers.
• Students will understand the concept of exponential growth.

### Major Subject Area Connections

• Language Arts
• Math

### Class Time

Sessions: One
Session Length: 45-60 minutes
Total Length: 0-45 minutes

### Groupings

• Whole group
• Pairs
• Individual work

### Terms and Concepts

• One million
• Estimation
• Exponential growth

### Materials

• The King’s Chessboard, by David Birch (optional)
• Large calendar (optional)
• A Million or Double? work page (page 4)
• Double Your Money work page (page 5)
• Calculators (optional)
• Pencil and paper

### Preparations

• Make copies of the “A Million or Double?” work page (page 4) and the “Double Your Money” work page (page 5).
• Gather calculators, one per student or partner group (optional).
• Read over The King’s Chessboard (optional).

### Worksheets and Files

Lesson plan, worksheet(s), and rubric (if any) at www.usmint.gov/kids/teachers/lessonPlans/pdf/348.pdf.

1. Begin a discussion about one million by asking students questions, such as “How much is one million?” “Do you consider one million a large number?” “Can you think of a number larger than one million?”
2. Hand out the “Million or Double?” work page (page 4). Make sure students understand the alternative offer (Option 1: one million dollars. Option 2: a cent on the first day, two on the second, with the amount doubling and accumulating each day for one month.)
3. When all students have finished the work page, reconvene and record each student’s decision on chart paper. If a copy of The King’s Chessboard is available, begin reading the book. You may wish to stop part way through and ask if anyone would like to change their answer. If a copy of the book is not available, begin demonstrating the concept on a calendar or on a grid drawn on the board. Enter a “1” on the first day, a “2” on the second, “4” on the third, and continue doubling the number on each consecutive day for one week. Total the results.
4. Once students understand the concept, tell students that they will be working on problem solving to determine how much money a person who selected “Option 2” would have at the end of three weeks. Hand out the “Double Your Money” work page (page 5) and go over the instructions. Invite students to begin working. When all have finished the work page, discuss the results.
5. Discuss the concept of doubling and exponential growth. Engage students in a discussion about how the amount of money became enormous so fast, and why, assessing the level of understanding from student responses.

### Enrichments/Extensions

Calculate how much money you would have if you exchanged cents for quarters for an entire month.

Engage students in a discussion about how the amount of money became enormous so fast, and why, assessing the level of understanding from student responses.

There are no related resources for this lesson plan.

Discipline: Math
Domain: 4.MD Measurement and Data
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
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 Number and Operations
Cluster: Compute fluently and make reasonable estimates.
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: All Reasoning and Proof
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Standards:

• Recognize reasoning and proof as fundamental aspects of mathematics
• Make and investigate mathematical conjectures
• Develop and evaluate mathematical arguments and proofs
• Select and use various types of reasoning and methods of proof