Scientific Notation

Unit Objective: This unit is designed to introduce the concept of scientific notation, how it is used for large and small numbers, and how to multiply and divide using scientific notation. Although the activities were written for an Algebra 1 course, they could easily be adapted for other courses.

Activity 1: Planet Size Activity

Objective: Students will review the order of the planets from nearest to farthest from the sun and compare the size of the planets using scientific notation.

Wyoming Standards:     Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.
Sci 1.9-Students develop an understanding of scientific content through inquiry.
Sci 2.2-Students use inquiry to conduct scientific investigations.

Materials Needed: Marble, walnut, golf ball, raisin, acorn, basketball, soccer ball, softball, small grapefruit, kidney bean, post-it pads.

Time: 10 minutes

Directions: Write the name of each planet on a post-it note before class. Have one student volunteer to go to the board and arrange the planets in order from nearest to furthest from the sun. The student is encouraged to get help from his or her classmates. Once the order is complete briefly discuss the distances, mentioning that the Earth is approximately 93 million miles (150 million kilometers) from the sun. Leave the post-it notes on the board in order for later in the activity.

Have the students break into small groups. The students will try to make a model of the solar system using the items listed in the materials list. Let them know the sun is represented by a ball 9 feet across. You may want to measure out 9 feet on the board. Each group will try to determine which common item corresponds by size with the actual planets. For example, the largest planet (Jupiter) will correspond with the largest object (basketball).

Next have the student volunteer (or a new volunteer) try to match the common objects with the correct planet. Again the student is encouraged to get help from his or her classmates. Once the group believes it has the correct order you can give them the solution:

Mercury-marble
Venus-walnut
Earth-golf ball
Mars-acorn
Saturn-soccer ball
Uranus-softball
Neptune-small grapefruit
Pluto-kidney bean

Activity 2: Solar System Table

Objective: The students will use scientific notation with positive exponents to represent large numbers. For this activity the numbers will be the distance from the sun and the diameter of the planet.

Wyoming Standards:     Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.
Sci 1.9-Students develop an understanding of scientific content through inquiry.
Sci 2.2-Students use inquiry to conduct scientific investigations.

Materials Needed: Copy of table

Time: 10 minutes

Directions: Write the following on the board:

Planet            Distance (from Sun)                Diameter
Mercury        57,910,000 km                4,800 km

Make sure you leave extra space behind the distance and the diameter to allow enough room for the scientific notation values.

Show how to change the distance into scientific notation. Use the diameter as a second example. When finished with the examples have the students copy the values for Mercury on their own paper. Next have the students convert each of the distances and diameters into scientific notation.

To quickly check for understanding you can let the students try Venus and Earth. After a few minutes go over those numbers together.

Solution:
Mercury        5.7x107                    4.8x103
Venus        1.082x108                    1.21x104
Earth            1.496x108                    1.275x104
Mars            2.2794x108                6.8x103
Jupiter        7.7833x108                1.428x105
Saturn        1.4294x109                1.2066x105
Uranus        2.87099x109                5.18x104
Neptune        4.5043x109                4.95x104
Pluto            5.91352x109                3x103

Planet          Distance (from Sun)            Diameter
Mercury            57,910,000 km...0.39 A.U.        4,800 km
Venus        108,200,000 km...0.72 A.U.        12,100 km
Earth                149,600,000 km...1.00 A.U.        12,750 km
Mars                227,940,000 km...1.50 A.U.        6,800 km
Jupiter        778,330,000 km...5.20 A.U.        142,800 km
Saturn        1,429,400,000 km...9.50 A.U.    120,660 km
Uranus        2,870,990,000 km...19.20 A.U.    51,800 km
Neptune            4,504,300,000 km...30.10 A.U.    49,500 km
Pluto                5,913,520,000 km...39.50 A.U.    3,000 km

Activity 3: Deep Space Light Bulb Demonstration

Objective: The students will use scientific notation with negative exponents to represent small numbers.

Wyoming Standards:     Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.
Sci 1.9-Students develop an understanding of scientific content through inquiry.
Sci 2.2-Students use inquiry to conduct scientific investigations.

Materials Needed: Computer with web access and projector

Time: 5 minutes

Directions: Go to http://spaceplace.nasa.gov/en/kids/dsn_fact1.shtml and read through the web page as a group. Toward the bottom of the page have the students look closely at:

“the spacecraft signal delivers only 0.000000000000000003 watts of power to the 70-meter antenna.”
(note: there are seventeen zeroes between the decimal point and the 3)

Emphasize that scientific measurements can be quite large like the distance to a planet but can also be quite small. Either way the numbers are very difficult to work with in normal notation. Explain how to change small numbers into scientific notation using negative exponents.

Go ahead and finish the demonstration on the web page and proceed to Activity 4.

Activity 4: Scientific Notation Worksheet 1

Objective: The students will use scientific notation with positive and negative exponents to represent  numbers. The students will also convert numbers in scientific notation back to normal notation.

Wyoming Standards:     Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.

Materials Needed: Worksheet 1(labeled as “15. Scientific Notation” at the web site. It is saved as a pdf file called 'WORK10.pdf')

Time: 5 minutes

Directions: Show the students how to change from scientific notation to normal notation. Although they have not formally seen the process they may have already figured it out on their own.

Activity 5: Electromagnetic Spectrum Discussion

Objective: The students will use scientific notation with positive and negative exponents to compare the wavelengths of different types of waves.

Wyoming Standards:     Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.
Sci 2.2-Students use inquiry to conduct scientific investigations.

Materials Needed: Handout with electromagnetic spectrum

Time: 5 minutes

Directions: Have the students look at a copy of the electromagnetic spectrum (I prefer the first one for the students). Point out where waves 1 m (100 m) long are on the sketch. Emphasize how each mark on the scale represents a change of 10 times larger or 10 times smaller. Show where kilometers and millimeters are found. It is also helpful to have the students write in common items that are the same size as the numbers on the scale. Some samples are on the second link. You may also introduce terms such as micrometer, nanometer, and picometer.

Activity 6: Scientific Notation Worksheet 3 & 2

Objective: The students will multiply and divide scientific notation numbers with positive and negative exponents. A calculator is not necessary.

Wyoming Standards:     Math 1.1-Students represent and apply real numbers in a variety of forms.
Math 1.2-Students apply the structure and properties of the real number system.

Materials Needed: Worksheets 3 & 2(worksheet 3 is labeled as “17. Scientific Notation” at the web site. It is saved as a pdf file called 'WORK12.pdf' and worksheet 2 is labeled as “16. Scientific Notation” at the web site. It is saved as a pdf file called 'WORK11.pdf' )

Time: 10 minutes

Directions: (Note: notice the students will do Worksheet 3 before Worksheet 2. This is because multiplying will be easier to do than division with scientific notation)

Use the example on Worksheet 3 to show how to multiply scientific notation numbers. You can compare the process to multiplying with normal form to show how much easier scientific notation is to use. Emphasize the front numbers are multiplied and the exponents are added.

After the students complete Worksheet 3, show how to divide scientific notation numbers. Emphasize the front numbers are divided and the exponents are subtracted. Compare and contrast the methods for multiplication and division. A Venn diagram or a short two-column list will work well.