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Power Up: Using Scientific Notation

Introductory Activities
Learning Activities
Culminating Activity
Cross-curricular Extensions
Extension activities

Introductory Activities

Review decimal notation by logging onto the Converting fractions to decimals website. Provide students with a FOCUS FOR MEDIA INTERACTION by asking students to determine which numerical place they might find the number 8 in the number 432.567108? (The eight would be found in the millionths place in the preceding number. Explain to students that the term decimal has as its root dec- which means ten. Explain to students that decimal notation is a base-10 system that changes numbers either by multiplying or dividing by factors of 10.)

Check for student understanding by asking students to determine which number is found in each of the remaining numerical place"holders". (Each integer has an associated value based on the number 10; the 4 is in the 100s place. The 3 is in the 10s place. The 2 is in the ones place; the 5 in the tenths place, the 6 in the hundredths place, the 7 in the thousandths place, the 1 in the ten-thousandths place, the 0 is in the hundred-thousandths place and the 8 in the millionths place).

Create a number line. On a large writing space draw a horizontal line with arrowheads on each end similar to the one shown below. At the midpoint of the line, mark a point for zero. At equal intervals to the right of the zero, add additional points. At equal intervals to the left of the zero, add additional points.

Ask students to identify the placement of each of the following integers on the number line: -3, -2, -1, 1, 2, 3. (The negative integers should be placed to the left of the zero place with the –1 closest to 0, followed by –2 and –3. The positive integers should be placed to the right of the zero with 1 closest to the o, followed by 2 and 3.)

Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to recall from the previous website the"place value" of the zero on the number line shown. (Explain to students that the number line system is a model for using numbers. When combined with the concepts associated with decimals—base-10 numbers—the number line becomes an important frame of reference for different models in mathematics.)

Provide students with additional practice by providing real-life examples of positive and negative integers. Ask them to consider on which side of the zero they might find a variety of different numbers.

 Real-life examples of negative numbers Example Meaning Account balance \$-2.75 Overpayment: Customer paid over total amount due Checking account: Account deficient by \$2.75 Weather -5° C Temperature is 5 degrees below 0°C Treadmill Incline grade -9 Exercise machine is simulating the action of walking down a hill with a 9% decline (about 16°)

Learning Activities

Identify a rationale for using other ways besides decimals to express numbers. Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to record the distance between Earth and the Sun. LOG onto The Zany World of Basic Math, Module 6: Working with Decimals; segment 6,"Scientific Notation" using Video on Demand (prior registration required). Click on the streaming icon for high-speed playback or download for slower connection speeds. PLAY the segment by clicking on the triangular radio button located under the screen. PAUSE the segment using the radio button left of the play button when the narrator states the distance between Earth and the Sun. You will see a blue screen with an arrow between an Earth icon and a Sun icon. Write the answer on a large instructional writing space. (The distance between Earth and the Sun is approximately 144 billion meters.)

Ask a student to place an asterisk (*) after the ones place in the number 144 billion (144 000 000 000) on the large instructional writing space. (1*44 000 000 000). Distribute the"Number line paradigm" handout. Ask students to describe how the asterisk and the zero are similar. Ask students to write an example for each number type shown on the handout. (Answers will vary but an example of a negative number is –35 (a negative number is a number less than zero); an example of a negative number with a magnitude less than 1 is –0.005; a positive number with a magnitude less than 0.005; a positive number with a magnitude greater than 1 is 927.)

Discover scientific notation. Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to define scientific notation. PLAY segment from the beginning by clicking on the solid square then by clicking on the triangular radio button under the screen. PAUSE segment when the image of Earth and the Sun appears on the screen. (Scientific notation is a power of ten system where a very large or very small number is represented by a number between 1 and 9.999 multiplied by 10 expressed to an integral power.)

On the large instructional writing space, write down the three parts of any number expressed in scientific notation:
1. Coefficient between 1 and 9.999 which represents the magnitude of a number
2. Multiplier, always 10
3. Exponent (Power of 10); if the actual value of the number has a magnitude greater than 1, the power of ten is positive. If the actual value of the number has a magnitude less than 1, the power of ten is negative.

FAST FORWARD the downloaded segment to the"Amnesia Alert" (2:01-2:15). Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to complete the statement:"To use scientific notation for large numbers the exponent …" (The number is positive.)

: Identify additional contexts for scientific notation. Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to identify at least two uses of scientific notation in real life calculations. LOG onto the Institute for Energy and Environmental Research website. (On the site there are several examples of use of scientific notation: reporting volumes of radioactive waste—note the magnitudes of the numbers are represented in the last column; size of atomic particles, astronomical distances.)

Check for student understanding by asking them to name the three parts of a number written in scientific notation. (Coefficient between 1 and 9.999, a multiplier which is always 10 and an exponent/power on the ten which determines the number of spaces moved and the direction in which a decimal is moved to represent the actual value of a number.) Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to review the information provided on the Institute for Energy and Environmental Research site.

Culminating Activity

Divide class into four large groups. Distribute the"Working with Decimals" handout and advise students to record their responses at station III on a separate sheet of paper for collection and review. All students will circulate through all four groups round-robin style. Give each group 7 minutes at each station. Ask students to record their web-based scores from stations I and IV on their answer sheet with their other responses. Circulate around the room to check for student understanding and to monitor student progress.

 Station I Widener University: Scientific notation Decimal notation conversion drills http://science.widener.edu/svb/tutorial/scinotcsn7.html Station II "Working with Decimals" handout (pages 3 and 4 of Viewing Guide) #1-4. Upon completion students can review decimal calculations and rounding. Station III GED Connection: Mathematics (2001) Cathy Fillmore Hoyt, PBS LiteracyLink, pages 259 (#13-#19), 267 (#12), 268 (#19) Station IV AAA Math: Scientific notation drill (timed) http://www.aaamath.com/ dec71i-dec2sci.html

Explain to students that calculators are often equipped to handle calculations involving scientific notation. Check for student understanding by asking them the mathematical name/operation/function for"power of ten". (Exponentiation is the function associated with the"power of ten".) Provide students with a FOCUS FOR MEDIA INTERACTION by asking them to identify the button they think might be used to represent power of ten on a calculator. LOG onto the Online scientific calculator. (Answers will vary; there are two buttons associated with"power of ten": LOG and EXP. The INV button when pushed simultaneously with the LOG button, accesses the 10x function on the calculator. To be used for scientific notation, a student must first type in a coefficient before typing INV+LOG followed by the number for the exponent. The second (preferred) method for expressing a number in scientific notation using a calculator requires a student to hit the coefficient followed by the EXP button and the exponent.)

 Number Method I Method II 0.000612 6.12 + INV + LOG + +/- 4 6.12 + EXP + +/- 4 42 000 000 000 000 4.2 + INV + LOG + 13 4.2 + EXP + 13

Review the answers to the worksheets from Step 1 using the online calculator. Use Method II above to enter student responses then hit Enter. The answer provided on the calculator should match the original question from the"Working with decimals worksheet" #1-4.

Cross-Curricular Extensions

Visit the PBS LiteracyLink companion website (Registration required) at
http://www.pbs.org/literacy/index.html to become more familiar with the GED Math Test. Practice taking tests after reviewing concepts in math, science, language arts and social studies.

Science
Practice writing numbers in scientific notation using real data provided by science. Gather examples of the use of scientific notation in science using nuclide data or astronomical distances.

Extension activities

GED Connection Program 38: Introduction to Algebra (Broadcast date: February 12, 2004); Watch an additional presentation of uses of scientific notation and decimals in this program.

Scientific notation worksheet
http://www.ieer.org/clssroom/scidrill.html
Review and practice conversion between decimal and scientific notation after printing a copy of this worksheet.