# How Much is a Million?

This lesson focuses students on the concept of 1,000,000. It allows students to see first hand the sheer size of 1 million while at the same time providing them with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice. This activity uses rice to develop thinking skills about how much a million truly is. I have done a similar activity using small paper clips.

### Standards & Objectives

Academic standards
CCSS.Math.Content.6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.
CCSS.Math.Content.6.EE.B.5
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or...
CCSS.Math.Content.6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can...
CCSS.Math.Content.6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all...
CCSS.Math.Content.6.EE.B.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that...
CCSS.Math.Content.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one...
CCSS.Math.Content.6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge...
CCSS.Math.Content.6.G.A.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures....
CCSS.Math.Content.7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
CCSS.Math.Content.7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between...
CCSS.Math.Content.7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles,...
CCSS.Math.Content.8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
GLE 0606.1.1
Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0606.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0606.1.3
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0606.3.1
Write and solve two-step equations and inequalities.
GLE 0606.3.2
Interpret and represent algebraic relationships with variables in expressions, simple equations and inequalities.
GLE 0606.3.3
Extend order of operations to include grouping symbols and exponents.
GLE 0606.3.4
Use expressions, equations and formulas to solve problems.
GLE 0606.3.5
Use multiple representations including symbolic algebra to model and/or solve contextual problems that involve linear relationships.
GLE 0606.4.3
Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and develop strategies to find the area of composite shapes.
GLE 0606.4.4
Develop and use formulas for surface area and volume of 3-dimensional figures.
GLE 0706.3.7
Use mathematical models involving linear equations to analyze real-world phenomena.
GLE 0706.3.8
Use a variety of strategies to efficiently solve linear equations and inequalities.
SPI 0606.3.1
Represent on a number line the solution of a linear inequality.
SPI 0606.3.2
Use order of operations and parentheses to simplify expressions and solve problems.
SPI 0606.3.3
Write equations that correspond to given situations or represent a given mathematical relationship.
SPI 0606.3.5
Translate between verbal expressions/sentences and algebraic expressions/equations.
SPI 0606.4.4
Calculate with circumferences and areas of circles.
SPI 0606.4.5
Determine the surface area and volume of prisms, pyramids and cylinders.
SPI 0606.4.6
Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.
SPI 0706.3.1
Evaluate algebraic expressions involving rational values for coefficients and/or variables.
SPI 0706.3.6
Solve linear equations with rational coefficients symbolically or graphically.
SPI 0706.3.7
Translate between verbal and symbolic representations of real-world phenomena involving linear equations.
SPI 0706.3.8
Solve contextual problems involving two-step linear equations.
SPI 0706.3.9
Solve linear inequalities in one variable with rational coefficients symbolically or graphically.
TSS.Math.6.EE.A.2
Write, read, and evaluate expressions in which variables stand for numbers.
TSS.Math.6.EE.B.5
Understand solving an equation or inequality is carried out by determining if any of the values from a given set make the equation or inequality true. Use...
TSS.Math.6.EE.B.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an...
TSS.Math.6.EE.B.7
Solve real-world and mathematical problems by writing and solving onestep equations of the form x + p = q and px = q for cases in which p, q, and x are all...
TSS.Math.6.EE.B.8
Interpret and write an inequality of the form x > c or x
TSS.Math.6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another.
TSS.Math.6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and...
TSS.Math.6.G.A.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these...
TSS.Math.7.EE.B.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
TSS.Math.7.G.B.3
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the...
TSS.Math.7.G.B.5
Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles,...
TSS.Math.8.G.C.7
Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.

Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.

Learning objectives:

Learning Objectives:

By the end of this lesson, students will:

• Find the weight of rice needed to make up 1,000,000 grains of rice.
• Learn how to extrapolate from a smaller group of data to a larger conclusion.
• Solve proportions.
Essential and guiding questions:

Questions for Students:

• About how many pounds (kilograms) of rice does it take to make 1 million grains of rice? Explain how you got your answer?
• How exact is your answer? Explain your reasoning.
• Explain and show what you could do to make your answer more precise.
• Explain how you could use a sampling technique to estimate the number of people who are watching a football game.

### Lesson Variations

Blooms taxonomy level:
Understanding
Extension suggestions:

Extensions:

• Environmental Science: Parts per million (ppm) is a common unit of measurement for pollutants. The concept of ppm can be difficult for students to visualize. The Environmental Protection Agency lists acceptable levels of different pollutants. One such pollutant is mercury. The EPA states that 1 ppm of mercury is an acceptable level. To demonstrate this to students, take 1 grain of rice from a pile of 1 million grains. Use a marker and color this grain black and then put the grain back into the bucket. This is truly 1 ppm. Students can take turns looking to see if they can find the 1 dark colored grain of rice. Then place the bucket of rice on a table and allow students to search during off times during the day.
• Social Science: How much does something cost? How much is our school district's annual budget? If each grain of rice was a dollar, how many pounds of rice would it take to equal that amount? How many pounds of rice will be “spent” in a year?
• Consider an making an example out of the national debt. How much is the debt? How fast is it growing?

### Helpful Hints

Materials:

• Small cups (1 per group of 2 or 3 students)
• 1 larger cup or glass jar
• Rice
• Poster Paper (optional)
• Balance – either a beam balance or a inexpensive postal scale
• Calculator (optional)

Contributors: