Maria Bessler
Math Lesson: Scientific Notation (5th Grade)
MATERIALS:
 Copy of pre/post test on scientific notation (two copies per student)
 Astronomy Picture of the Day "Scale of the Universe-Interactive"
http://apod.nasa.gov/apod/ap120312.html
 Teacher reference: http://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html
 Website that converts numbers to scientific notation:
http://www.mathsisfun.com/numbers/scientific-notation.html
 Website to practice and check scientific notation: http://janus.astro.umd.edu/cgibin/astro/scinote.pl
 Examples of scientific notation:
http://mrsgrotheer.weebly.com/uploads/8/3/8/9/8389616/scientificnotationwks
4website.pdf
ESSENTIAL QUESTIONS:
 Why do we use scientific notation?
 When is scientific notation helpful, and when is it unhelpful?
KEY CONCEPTS:
 identifying the pattern found in scientific notation
 applying when to use scientific notation
 deductive reasoning and critical thinking
OBJECTIVES:
In this lesson, students will:
 SOL Computation and Estimation (Focus: Multistep Applications and Order of
Operations)
5.5 The student will
a) find the sum, difference, product, and quotient of two numbers expressed as
decimals through thousandths (divisors with only one nonzero digit); and
b) create and solve single-step and multistep practical problems involving decimals.
 SOL Computation and Estimation (Focus: Applications of Operations with
Rational Numbers)
6.7 The student will solve single-step and multistep practical problems involving
addition, subtraction, multiplication, and division of decimals.
 SOL Number and Number Sense (Focus: Proportional Reasoning )
7.1 The student will
a) investigate and describe the concept of negative exponents for powers of ten;
b) determine scientific notation for numbers greater than zero;
c) compare and order fractions, decimals, percents, and numbers written in
scientific notation;
 convert large and small numbers between standard and scientific notation
Vocabulary/Themes:
 scientific notation, integer, expression, equation, standard notation
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Maria Bessler
PROCEDURES:
TEACHER NOTES:
Introduction/Hook: What is a power of 10? What does
is look like in real life? Visit the Astronomy Picture of the
Day website, date March 12, to view the "Scale of the
Universe" through the powers of 10:
http://apod.nasa.gov/apod/ap120312.html
Pre-test students on scientific
notation prior to the lesson, and
adjust content accordingly.
Learning Activities:
What did you notice about the items on the scale?
[Ranged from very large to very small]
What happened to the power of 10 in the corner of the
screen as we zoomed in and out?
[The exponent was negative for small items and
positive for large items]
Can you write out the number two billion, nine hundred
million?
Now, I would like you to write out the number seven
octillion. (Hint: it has 27 zeros. )
Now let's put seven octillion into the calculator and add
fifteen trillion to it!
Is this a convenient way of writing these numbers? No!
We can't fit these numbers into a calculator this way.
There is a better method, a "shorthand", a way of taking
notes on numbers: scientific notation, often used by
scientists. We use the powers of ten to write a
mathematical expression that represents the number.
This works well for numbers that are very large or very
small and take a long time to write out in standard form
(also called standard notation).
Two billion becomes 2.9 x 10^9
Seven octillion becomes 7 x 10^27
Fifteen trillion becomes 1.5 x 10^13
Scientific notation takes a very long number to write out,
and simplifies it into two factors: an integer or decimal
between 0 and 10 (positive or negative), and a power of
10.
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Scientific notation-when a
number is expressed as a
product of a decimal/integer and
a power of 10. Used when
numbers are too large or too
small to be written conveniently
in decimal/ standard form. (2.3 x
10^4)
Integer-a whole number
(positive or negative)
Expression-combination of
symbols (5 x 4)
Equation-math statement
showing equality between two
sets of expressions (5 x 4 = 20)
Standard notation-when a
number is expressed in standard
form. (23000)
Note: 10^0 = 1
Underlined part is called the
significant part of the number.
Maria Bessler
Take students to the website:
http://www.chem.tamu.edu/class/fyp/mathrev/mrscnot.html to view some examples of scientific notation.
Have students identify that the pattern for converting
numbers between standard and scientific notation.
If a number in scientific notation has a negative
exponent, it is a number less than zero and you need to
move the decimal point to the left as many places as the
number of the exponent.
Example: 4.234 x 10^-3 =
0.004234
If a number in scientific notation has a positive exponent,
it is a number greater than zero and you need to move
the decimal point to the right as many places as the
number of the exponent.
Example: 7.293 x 10^6 =
7293000
Have students practice putting numbers into scientific
notation, and converting them back to standard
notation.
Numbers close to zero can be put in scientific notation,
but this takes longer than necessary. Scientific notation
is most helpful when working with very large or very
small numbers.
Interest Center: Allow several students at a time to visit
the APOD "Scale of the Universe" website via classroom
computers to interact with the simulation and 'explore
the universe.' Have them share their findings with the
class.
Grouping: Students will be grouped in a whole-class
grouping for direct instruction on scientific notation
since it is a new concept for all students, according to
the pretest. Students will work and take notes in small
groups of 3-6 at their working tables, and a 4 computers
are available for students to explore the scientific
notation-related websites shown to them in this lesson.
Debriefing: Post-test on scientific notation (same as
pre-test). Collect and review answers together as a
class.
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Examples: 3 = 3 x 10^0
528 = 5.28 x 10^2
0.009 = 9 x 10^-3
Maria Bessler
Homework: (Optional) Look for very large or very
small numbers in the newspaper, on the Internet, etc.
and practice converting them to scientific notation.
Differentiation for:
ELL
Twice-Exceptional
Highly Gifted
Differentiation:
Choice:
Resources:
Products:
Tiered questions/assignments:
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Allow student to visit website
http://janus.astro.umd.edu/cgibin/astro/scinote.pl to do
practice problems and be able to
check the work.