Mathematics Grade 6

Strand: EXPRESSIONS AND EQUATIONS (6.EE) Standard 6.EE.1

This lesson will strengthen students' understanding of scientific notation.

*Number Notation Table**Planet Table*- 3 x 5 cards
- Stopwatch
*Number Cards*

Students were introduced to the concept of exponents in fifth grade.

* Scientific notation *is writing a number as the product of a number
(greater than or equal to 1 and less than 10) and a power of ten.
We use scientific notation because numbers can be hard to work with
when they have so many zeros. Scientists use scientific notation as a
simpler way to write these numbers.

1. Demonstrate a positive learning attitude toward mathematics.

2. Become mathematical problem solvers.

3. Reason mathematically.

Invitation to Learn

Mercury is about 35 million miles from the sun.

Have students estimate how long they think it would take to write 35 million numerically (35,000,000).

Write down estimation.

Have each student (or one student) write out 35,000,000. Time to see how long it takes.

Instructional Procedures

- Give each student a
*Number Notation Table*. - As a class (teacher directed), complete the first few lines together. Discuss what pattern can be seen.
- Have class finish chart individually or in groups. Discuss what pattern can be seen.
- Demonstrate how to change 35,000,000
(the distance Mercury is
from the sun) into scientific notation (3.5 x 10
^{7}). - Discuss how the number
was changed and compare the pattern
they discovered to the number. What is happening?
Students will most likely assume that the exponent matches the
number of zeroes. However, the exponent (power of ten) matches
the number of places the decimal point moves (e.g., 1,000 = 1 x
10
^{3}. The decimal moves three places to the left.). Change 3.5 x 10^{7}back to standard form. - Compare 1 x 10
^{7}to 3.5 x 10^{7}Emphasize again that the exponent (power of ten) matches the number of places the decimal point moves. - Give more examples as needed.

2.87 x 10^{2}= 287

3.982 x 10^{4}= 39,820

5.843 x 10^{5}= 584,300

1.457 x 10^{5}= 145,700

5.47 x 10^{6}= 5,470,000

38,700 = 3.87 x 10^{4}

16 billion = 1.6 x 10^{10}

2,137,000 = 2.137 x 10^{6}

493,000,000,000 = 4.93 x 10^{11}

4,382,000,000,000 = 4.382 x 10^{12} - Have each student (or one student) write out 35,000,000,
using
scientific notation (3.5 x 10
^{7}). Time to see how long it takes. (This shows that scientific notation is an efficient way to write large numbers.) - Give each student two 3 x 5 cards. Have each student
write a
self-selected (large) number in standard form on one card, and the
equivalent number in scientific notation on the second card.
Collect all the cards.
- To play the game, use half of the pairs of cards to play one round of the game (since you now have twice as many cards as students).
- Tape one card to each students back, making sure that you use both the standard and scientific notation form cards of each number selected.

Have students find the person with the equivalent number. They may attempt to identify the number by asking yes or no questions only. The round continues until all students have found their partner. You may want to play a second round using the remaining cards.

- Just as a positive exponent designates how many spaces the decimal moves to the left, a negative exponent denotes how many spaces a decimal moves to the right. Although the concept of negative exponents is not in the sixth grade core curriculum, the study of microorganisms could be used to introduce the concept.
- Use
*Number Cards*to create a human problem: Give a card to each student and have them stand to create a number (e.g., 2.87). Assign one student to be the decimal point. Have the decimal point move to the correct spot to form the number (2.87).

Family Connections

- Students time a family member writing a number both in standard form and scientific notation and record the difference.
- Students search for a large number in a newspaper article and write the number in scientific notation.

- Informal assessment includes observation of students
as they
complete the
*Number Notation Table*. Class discussion and discovery is another form of assessment. - Formal assessment includes completed
*Number Notation Tables*with correct scientific notation and standard forms.

Research Basis

Hatfield, M., Edwards, N., Bitter, G., & Morrow, J. (2000). *Mathematics
Methods for
Elementary and Middle School Teachers*. New York, NY. John Wiley & Sons
Inc.

This resource includes the NCTM Principles and Standards for School Mathematics 2000, as well as the newest NAEP data and findings from the TIMSS. The book emphasizes considerations regarding cultural diversity and includes a CD-ROM with vignettes of real classroom situations to help the reader study teaching practices as they occur naturally in the classroom.

Created: 02/27/2006

Updated: 02/05/2018

Updated: 02/05/2018