Course: 8th Grade Math
DETAIL LESSON PLAN
Student Objective
8.EE.A.4
Perform operations (+, -, x, ÷) with numbers expressed in scientific notation. Some problems may include
one number written in standard form and the other in scientific notation such as 120 + 3 x 10⁴. Students may
also be asked to interpret scientific notation that has been generated by technology.
8.EE.A.3
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very
small quantities, and to express how many times as much one is than the other.
Calculator
No
Lesson
Lesson 3.2.4 – Replacement Lesson (Perform Operations in Scientific Notation)
Tonight’s Homework
Teacher selected
Bellwork
Teacher selected
Prior Knowledge
 Over the last few days we have been working with exponents and also learning about scientific notation.
Introduction
 Today, we will start with a step-by-step review of how to convert between standard form and scientific notation.
 Then we will move on to something new. We will learn to multiply, divide, add, and subtract two numbers written in scientific
notation.
 Let’s start our review with a real world example of how scientists rewrite numbers so that they are easier to use.
 Show brief PowerPoint:
Lesson 3.2.4 – Intro “Why Learn about Scientific Notation?”
Teacher Input
 Review bellwork
 Review homework
 Pass out student notes
 Complete Part 1 which is a review on converting between standard form and scientific notation. (20 minutes max)
 Complete Part 2 of the lesson.
 Allow students to complete “you try” problems throughout the lessons
 Extra problems are provided for student practice at the end of the lesson. Good practice for 8.EE.3 and 8.EE.4.
Assessment
Observe students as they work on you try problems and classwork.
Closure
1. In scientific notation, the first number is _______ ? Greater than or equal to 1, but less than 10.
2. The second number is always a power of ____. 10
3. Give me an example of a number correctly written in scientific notation. Answer will vary
4. 572,000,000 Which number does the decimal go after when writing a large number in scientific notation?
First whole number.
5.72
5. How do you determine the correct power of 10?
Count the number of jumps from the end until you get to the decimal.
6. What kind of exponent will really small numbers have in scientific notation.
Negative
Lesson Part 1
Let’s review how to convert
between...
Standard Form
Scientific Notation
.
.
.
Student Notes
Standard Form
Scientific Notation
Scientific Notation –
 It’s a short cut way of writing really big numbers and really small numbers.
 A number written in Scientific Notation is made up of 3 parts:
Writing a LARGE number in Scientific Notation
980,000,000
You try!
Write in Scientific Notation form:
6,300,000
= _________
_________
800,300
= _________
_________
Writing a SMALL number in Scientific Notation
0.000079
You try!
Write in Scientific Notation form:
0.00000056 =
_________
_________
.003001 =
_________
_________
Changing Scientific Notation back to Standard Form
8.88 x 10⁸
You Try!
Write in Standard Form:
5.9 x 10⁻⁸
1.69 x 10⁵
= _____________________
2.3 x 10⁻⁴
= _____________________
Lesson Part 2
Performing Operations with
Scientific Notation
Examples:
.
.
.
.
.
.
.
.
Student Notes
Operations with Scientific Notation
Multiplying
Multiplying in Scientific Notation
Step 1: Multiply the decimal numbers.
Step 2: Then add the exponents of the powers of 10.
Step 3: Place the new power of 10 with the decimal in scientific notation form.
Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first
digit and count the number of places the decimal moves.
If the decimal moves left, increase the exponent by the number of moves.
If the decimal moves right, decrease the exponent by the number of moves.
Example
(2.6 ×
)
(6.3 ×
)
Step 1: Multiply the decimal numbers.
.
.
Step 2: Add the exponents.
Step 3: Put the new decimal number with the new exponent in scientific notation form.
.
Step 4: IF the number is not in scientific form, you need to move the decimal so
that it is behind the first digit and count the number of places the decimal moves.
If the decimal moves left, increase the exponent by the number of moves.
If the decimal moves right, decrease the exponent by the number of moves.
In this case, the decimal point moves one place left, so add 1 to the exponent.
.
Guided Practice
a. (2.5 x
) × (3 x
You Try!
b. (4.4 x
) × (3.9 x
.
) = ___________
)=
___________
Operations with Scientific Notation
Dividing


Dividing in Scientific Notation
Step 1: Divide the decimal numbers.
Step 2: Then subtract the exponents of the powers of 10.
Step 3: Place the new power of 10 with the decimal in scientific notation form.
Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first
digit and count the number of places the decimal moves.
If the decimal moves left, increase the exponent by the number of moves.
If the decimal moves right, decrease the exponent by the number of moves.
Example (1.23 ×
)
(2.4 ×
)
Step 1: Divide the decimal numbers.
.
.
Step 2: Subtract the exponents.
Step 3: Put the new decimal number with the new exponent in scientific notation form.
.
Step 4: IF the number is not in scientific form, you need to move the decimal so
that it is behind the first digit and count the number of places the decimal moves.
If the decimal moves left, increase the exponent by the number of moves.
If the decimal moves right, decrease the exponent by the number of moves.
.
Guided Practice
a. (5.76
You Try!
b. (3
)
)
(8
(3.2
.
) =___________
) =___________
Operations with Scientific Notation
Adding or Subtracting
When you are asked to add or subtract two numbers expressed in scientific notation you
need to be a little more careful. Both powers of ten must be the same.
Adding or Subtracting in Scientific Notation
Step 1: If needed, use what you know about the below rule to make adjustments so that the powers of
ten are the same.
Step 2: Add or subtract the decimal numbers as asked.
Step 3: Place the power of 10 with the decimal in scientific notation form.
Step 4: IF the number is not in scientific form, you need to move the decimal so that it is behind the first
digit and count the number of places the decimal moves.
If the decimal moves left, increase the exponent by the number of moves.
If the decimal moves right, decrease the exponent by the number of moves.
Example (4.4 ×
)
(7.1 ×
)
Step 1: If needed, make adjustments so that the powers of ten are the same.
Both are the same.
No adjustments needed.
Step 2: Add or subtract the decimal numbers as asked.
.
.
.5
Step 4: Place the power of ten with the decimal in scientific notation form.
.
Step 4: IF the number is not in scientific form, you need to move the decimal so
that it is behind the first digit and count the number of places the decimal moves.
If the decimal moves left, increase the exponent by the number of moves.
If the decimal moves right, decrease the exponent by the number of moves.
.
.
Example (4.12 ×
)
(3.94 ×
)
Step 1: If needed, make adjustments so that the powers of ten are the same.
In this case they are not the same (
) so we must adjust one of them.
It doesn’t matter which one you adjust. I will change the
to a power of 4.
Step 2: Add or subtract the decimal numbers as asked.
.
.
Step 3: Put the new decimal number with the exponent in scientific notation form.
.
Step 4: IF the number is not in scientific form, you need to move the decimal so
that it is behind the first digit and count the number of places the decimal moves.
If the decimal moves left, increase the exponent by the number of moves.
If the decimal moves right, decrease the exponent by the number of moves.
.
Guided Practice
You Try!
Note: When subtracting, adjust the exponent which will not make your
coefficients negative!
a. (5.3 x
)
(2.2 x
)=
___________
b. (1.4 x
)
(4.6 x
)=
___________
Name: _______________
Period: ______
Operations with Scientific Notation
obj.
8.EE.A.3,
8.EE.A.4
Try These! Simplify each of the following.
Multiply
1)
.
.
Divide
2)
3)
.
A typical dwarf sperm whale, the planet’s smallest whale species, weighs about
pounds. A blue whale, the planet’s largest whale, might weigh .
pounds. How
many times heavier is the blue whale than the dwarf sperm whale?
Add or Subtract
4)
.
.
.
5)
.
Challenging!
6)
8)
7)
.
Michelle used a calculator to multiply the following numbers .
.
Her calculator displayed the answer below. What do you think her calculator is displaying?
1.44E24
Answer Key
Operations with Scientific Notation
obj.
8.EE.A.3,
8.EE.A.4
Try These! Simplify each of the following.
Multiply
1)
.
.
Answer:
.
Answer:
.
Divide
2)
3)
.
A typical dwarf sperm whale, the planet’s smallest whale species, weighs about
pounds. A blue whale, the planet’s largest whale, might weigh .
pounds. How
many times heavier is the blue whale than the dwarf sperm whale?
Answer:
.
times larger
Add or Subtract
4)
.
Answer:
.
.
5)
.
.
Answer:
.
7)
.
Challenging!
6)
Answer:
8)
or
.
Answer:
.
or
.
Michelle used a calculator to multiply the following numbers .
.
Her calculator displayed the answer below. What do you think her calculator is displaying?
1.44E24
Answer:
.