### Lesson Plan

# Scientific Notation: Exploring Expressions and Equations

Students will solve real-world problems using scientific notation.

Grades

6–8

### Objectives

**Students will:**

- Convert between different units of measure.
- Express very large or very small numbers in scientific notation.
- Compare very large or very small numbers using scientific notation.
- Perform operations with numbers expressed in scientific notation.

See standards below.

### Materials

- Digital Interactive Tool: “Launching Into Expressions and Equations” (optional)
- Interactive whiteboard OR computer/projector hookup (optional)
- Internet connection (optional)
- Computers for small groups and/or all students (optional)
- The Amazon in Perspective: Performing Operations With Numbers Expressed in Scientific Notation printable
- Answer Key for Adventures in Expressions and Equations

**Note:** The lesson includes both online and printable components but was designed to be a meaningful learning experience whether or not the online components are used.

### Lesson Directions

### INTRODUCTION TO NEW MATERIAL

**Step 1:** Tell students that they will be studying the world’s largest habitat, the ocean. Ask students:

- What are some of the threats to this habitat’s life-forms?
- What are some solutions for combating these threats?

Tell students that the National Oceanic and Atmospheric Association (a government agency) reports that, since 1996, 904 tons of debris have been removed from a Hawaiian conservation area. Remind students that 1 ton is equivalent to 2,000 pounds. Tell students that in order to convert tons to pounds, they can multiply the number of tons by the unit rate 2,000 pounds/1 ton:

**Note**: You might want to explain to students that, essentially, the left-hand expression is a division expression. Tons ÷ ton can be simplified to multiplying the expression by 1.

**Step 2:** Tell students that in 2014 alone, 57 tons of debris were removed. Ask students to calculate the number of pounds of debris removed in 2014. (114,000 pounds)

**Step 3:** Explain to students that when they encounter a very large or very small number it might be more efficient to write these numbers in scientific notation. Scientific notation is a way of writing numbers as an expression that multiplies a constant by a power of 10. These expressions can be used within equations, in written word problems, and even in conversation. It eliminates writing strings of many zeroes as placeholders in numbers with many digits.

**Step 4: **Model for students how to express numbers in scientific notation.

- Move the decimal point so that the number is greater than or equal to 1 and less than 10. Remember that the decimal of a whole number is always at the end of the number.
- Count the number of places the decimal moved.
- The scientific notation is the constant times 10 to the power of the number of times the decimal moved.
- For numbers greater than or equal to 1, the power of 10 is positive; for numbers less than 1, the power of 10 is negative.
- EXAMPLE:

1,808,000 = 1.808 x 10^{6}because 1.808 is greater than or equal to 1 but less than 10, and the decimal point moved 6 places from 1,808,000 to 1.808. - EXAMPLE:

0.009802 = 9.802 x 10^{–3}because 9.802 is greater than or equal to 1 but less than 10, and the decimal point moved 3 places from 0.009802 to 9.802.

**Step 5:** Tell students that, in 2014, it was estimated that 8 million metric tons of plastic trash enter the sea from land every year. A metric ton is about 2,200 pounds. Have students convert this measure from tons to pounds. Then have them express the amount in scientific notation (about 17,600,000,000; about 1.76 x 10^{10}).

**Step 6:** In 2016, *the Okeanos Explorer*, a ship for ocean exploration, encountered a pricklefish, which has a maximum length of 8.1 centimeters. There are 100 centimeters in a meter. How long is the maximum length of a pricklefish in meters? Have students express this in scientific notation:

**Step 7:** Have students use the following facts to practice representing numbers in scientific notation:

- The U.S. shoreline is more than 95,000 miles long. Express this in scientific notation. (9.5 x 10
^{4}miles) - If 1 mile is equivalent to 5,280 feet, how many feet long is the U.S. shoreline? Express this in scientific notation. (5.016 x 10
^{8}feet) - The Mariana Trench’s deepest point is 36,070 feet below sea level. Express this depth in scientific notation. (–3.607 x 10
^{4}feet) - Species of foraminifera live in Challenger Deep, the lowest part of the Mariana Trench. Foraminifera can range from 0.0001 meters to 0.2 meters in length. Express these lengths in scientific notation. (1.0 x 10
^{-4}meters; 2.0 x 10^{-1}meters)

**Step 8:** Tell students that many marine areas are government protected. One such area is Thunder Bay, which measures 4.48 x 10^{2} square miles. Papahanaumokuakea Marine National Monument in Hawaii is nearly 1.4 x 10^{5} square miles. About how much larger is Papahanaumokuakea Marine National Monument than Thunder Bay?

To find out, have students identify the standard form of 10^{2} and 10^{5} (100 and 100,000). Tell students to divide those two values. (100,000 ÷ 100 = 1,000, or 103). What do they notice about the answer? (10^{3} = 10^{5–2}) Then have students divide 1.4 by 4.48 (0.3125). So, Papahanaumokuakea Marine National Monument is 0.3125 x 103 times bigger than Thunder Bay. Adjust 0.3125 x 10^{3} since 0.3125 is less than 1: 3.125 x 10^{2}.

**
Step 9: **Tell students that in 2014 an Egyptian man named Ahmed Gabr broke the world record for the deepest SCUBA dive by diving about 1.09 x 10

^{3}feet deep into the Red Sea. An unmanned sub,

*Nereus*ROV (remotely operated vehicle), dove to about 3.2814 x 10

^{1}times deeper. About how deep did

*Nereus*ROV dive?

To determine the answer, have students identify the standard form of 10

^{3}and 10

^{1}(1,000 and 10). Tell students to multiply those two values (1,000 x 10 = 10,000, or 104). What do they notice about the answer? (10

^{4}= 10

^{3+1}) Then have students multiply 1.09 by 3.2814 (about 3.5767). So, the

*Nereus*ROV dove to about 3.5767 x 10

^{4}, or 35,767 feet deep.

### GUIDED PRACTICE and INDEPENDENT PRACTICE

**Step 10:** Mix and match from among these digital and printable materials below depending on your class’s needs and technological capabilities.

These engaging materials situate students in real-world scenarios of exploration—from an astronaut blasting off into space to a biologist swimming the Amazon River. This highlights the value of math in real-world situations and careers, in which expressions and equations are necessary tools for solving problems.

- Module 2 of the Digital Interactive Tool: Scientific Notation
- The Amazon in Perspective
**: Performing Operations With Numbers Expressed in Scientific Notation**

### Lesson Extensions

Have students research ocean missions from the recent past at ocean explorer site. Have students search for very large or very small figures that they can express in scientific notation within interesting facts about these oceanic missions. Have them write questions about expressing these figures in scientific notation, then swap the questions with a partner so that partners can “quiz” each other on what they’ve learned.

### Standards

**(CCSS and NCTM):**

**Grade 8:**Scientific notation, operations on scientific notation (**CCSS**8.EE.A.3 & 4)**Grades 6–8:**(**CCSS**MP1, 2, 4, 6 & 7);**NCTM**Algebra