This lesson will strengthen students' understanding of scientific notation.
Background for Teachers
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.
Intended Learning Outcomes
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.
- 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 107).
- 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
103. The decimal moves three places to the left.). Change 3.5 x 107 back
to standard form.
- Compare 1 x 107 to 3.5 x 107
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 102 = 287
3.982 x 104 = 39,820
5.843 x 105 = 584,300
1.457 x 105 = 145,700
5.47 x 106 = 5,470,000
38,700 = 3.87 x 104
16 billion = 1.6 x 1010
2,137,000 = 2.137 x 106
493,000,000,000 = 4.93 x 1011
4,382,000,000,000 = 4.382 x 1012
- Have each student (or one student) write out 35,000,000,
scientific notation (3.5 x 107). Time to see how long it takes.
(This shows that scientific notation is an efficient way to write
- Give each student two 3 x 5 cards. Have each student
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
- Tape one card to each students back, making sure that
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
- 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
- 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
- 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
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
Hatfield, M., Edwards, N., Bitter, G., & Morrow, J. (2000). Mathematics
Elementary and Middle School Teachers. New York, NY. John Wiley & Sons
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.