G8

Unit 2 ∙ Constructed Response
Exponents

2. Examine the expression below.

a. Show how to simplify the expression using expanded form.

b. Simplify the expression using the properties of exponents.

Answer: ___________________ 196Grade 8 Unit 2 Constructed Response TE

Copyright © Swun Math

Unit 2 ∙ Constructed Response
Exponents

3.
a. Simplify the expression. Show your work in detailed and organized steps.

Answer: ___________________
b. Explain the properties of exponents used to help you solve 3a.

197 Copyright © Swun Math Grade 8 Unit 2 Constructed Response TE

Unit 2 ∙ Constructed Response Name: ____________________________
Exponents Date: ______________________________

Task 2: Square and Cube Roots

Directions: Read and solve each problem.

4. Cameron will install a new tile floor in his square-shaped room. The tiles are 1 ft 2 .
He needs a total of 225 tiles to cover the entire floor.

a. What information given helps you determine the length of each side of the living
room?

b. Find the length of each side of the living room. Show work.
Answer: ___________________

Copyright © Swun Math 198Grade 8 Unit 2 Constructed Response TE

Unit 2 ∙ Constructed Response
Exponents

5. Stan is buying a storage cube to hold food for his dogs. The cube has a volume of 64
ft 3. (Volume = l·w·h )

a. Find the dimensions of the storage container. Show your work in detailed and
organized steps.

Answer: ___________________

b. After clearing out a square-shaped storage room, Stan decides that he would like to
purchase more cubes to store supplies. The area of the storage room is 100 ft 2. What
are the length and width of the room? Show your work.

199 Copyright © Swun Math Grade 8 Unit 2 Constructed Response TE

Unit 2 ∙ Constructed Response Name: ____________________________
Exponents Date: ______________________________

Task 3: Zero & Negative Exponents

Directions: Read and solve each problem.
6.

a. Simplify the expression.

Answer: ___________________
b. Write the answer from 1a with positive exponents.

Answer: ___________________
7.

a. Simplify using the expanded form.

b. Simplify using the properties of exponents.

Copyright © Swun Math 200Grade 8 Unit 2 Constructed Response TE

Unit 2 ∙ Constructed Response Unit 1 ∙ Constructed
Exponents ResponseSCORING RUBRIC

TASK 1: Combining Exponents

# Answer/Exemplar Standard Points
1a. 7 11
8.EE.1 1

1b. Deana made two errors. The first error was multiplying the bases. 8.EE.1 1
The second error was multiplying the exponents, but they should 1
have been added. Deanna could decompose the problem to show
that 7 is being multiplied by itself 11 times, so the correct answer is
7 11 .

2a. 8.EE.1

2b. Add the exponents together. 8.EE.1 1

3a. 8.EE.1 1

3b. First, I used the power to power property to multiply the u in the 8.EE.1 1
denominator. Then I used the division of like bases property to
subtract the exponents and simplify the problem.

201 Copyright © Swun Math Grade 8 Unit 2 Constructed Response Rubric TE

Unit 2 ∙ Constructed Response Unit 1 ∙ Constructed
Exponents ResponseSCORING RUBRIC

TASK 2: Square and Cube Roots

# Answer/Exemplar Standard Points

4a. It is important to know that the living room floor is in the shape of 8.EE.2 1
a square and that the tiles are also in the shape of a square. There
is only 1 array for 225 that has the same length and width.

4b. 15 ft 8.EE.2 1

5a. 4 x 4 x 4 (feet); 8.EE.2 1

5b. 10 ft; 8.EE.2 1

TASK 3: Zero & Negative Exponents Standard Points

# Answer/Exemplar 8.EE.1 1
6a.
8.EE.1 1
6b.
8.EE.1 1
7a.

7b. 8.EE.1 1

Copyright © Swun Math 202Grade 8 Unit 2 Constructed Response Rubric TE

Grade 8

Unit 3: Scientific Notation

Table of Contents

Lesson # Lesson Type Lesson Title MC MP Applied Page

1C Scientific Notation 8.EE.3 6, 8 205

2P Scientific Notation 8.EE.3 6, 7 213

3C Scientific Notation: Add & Subtract 8.EE.4 1, 2 223

4P Scientific Notation: Add & Subtract 8.EE.4 2, 6 231

5C Scientific Notation: Multiply & Divide 8.EE.4 2, 8 243

6P Scientific Notation: Multiply & Divide 8.EE.4 6, 8 251

7P Scientific Notation: Mixed Practice 8.EE.4 1, 2 263

8 MT Scientific Notation 8.EE.4 275

 indicates a major standard; unmarked standards are additional or supporting

203 Copyright © Swun Math Grade 8 Unit 3 Table of Contents TE

Grade 8 • Unit 3
Table of Contents, continued

Constructed Response

Task Lesson Title MC Page

1 Scientific Notation 8.EE.3 279
8.EE.4 283

Constructed Response Scoring Guide

Materials Needed

Lesson Materials

1 Base-ten blocks (optional)

5-7 Calculators (optional)

 indicates a major standard; unmarked standards are additional or supporting

Copyright © Swun Math 204Grade 8 Unit 3 Table of Contents TE

Scientific Notation MPs Applied MP

Conceptual Lesson * Embedded MP
Grade 8 · Unit 3 · Lesson 1
12345 67 8
MC: 8.EE.3
*  *

Problem of the Day Student Journal Pages

114-117

Objective: I will convert numbers between standard form and scientific notation.

Vocabulary Teacher Resources

Scientific Notation: a method to write very large Considerations:
numbers or very small numbers as the product of
a number between 1 and 10 and a power of 10 Students tend to struggle with standard form to scientific
notation with the exponent’s positive or negative value.
99 = 9.9 × 101 This lesson is focusing on asking the students questions
about the size of the original number to help them
Number Digits Power of 10 understand conceptually the positive and negative powers
of ten. Practice writing the scientific notation to standard
0.0000026 = 2.6 × 10-6 form to prove the exponent. Don’t focus as much on the
steps of moving right or left, but rather the idea of large and
small numbers and how powers of 10 work.

Steps:

Power of Ten: ten multiplied by itself the Standard to Scientific Notation
number of times indicated by the exponent
To build conceptual understanding, ask yourself these
To figure out power of 10, think “How many places questions:
does the decimal point move?”
1. Is the number a big or small number?
If number is 10 or greater, 2. Will the exponent be positive or negative?
move to the left = positive power
• Big number = positive power
If number is smaller than 1, • Small number = negative power
move to the right= negative power 3. Locate or place the decimal point.
4. Count the number of places the decimal will
move to create a number in the ones place.
This will be the power of ten.
5. Write an expression using scientific notation.

Scientific Notation to Standard Form:
1. If the exponent is positive, move to the right
(multiplication).
2. If the exponent is negative, move to the left
(division).
3. Make additional zeros for place value needed.

Application of MPs:

MP6: How do you know if the exponent will be a positive or a

negative?

I know that the exponent will be a positive/negative

because .

MP8: What patterns do you find in figuring out the power of 10?
The pattern I could see when figuring out the power of 10
was .

205 Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE

Input/Model

(Teacher Presents)

Directions: Convert the standard form into scientific notation.
1. 1,500,000

Solution:
• Step 1: Is the number a big number or small number? Big
• Step 2: Will the exponent be positive or negative? Positive
• Step 3: Where is the decimal point now? If there is no decimal point, add one to the right of the ones place.
• Step 4: Count the number of places to move the decimal so there is a digit in the ones place: 6

1500000
1 5 0 0 0 0 0.

The new number will be 1.5.
• Step 5: Rewrite the expression in scientific notation.

Answer: 1.5 × 106

2. 0.02623

Solution:
• Step 1: Is the number a big number or small number? Small
• Step 2: Will the exponent be positive or negative? Negative
• Step 3: Where is the decimal point now? It is between the zeros.
• Step 4: Count the number of places to move the decimal so there is a digit in the ones place: 2

0. 0 2 6 2 3
0. 0 2 6 2 3

• Your new number will be 2.623.
• Step 5: Rewrite the expression in scientific notation.

Answer: 2.623 × 10−2

3. Write the standard form: 2.623 × 102

Solution:
The exponent is positive, so move the decimal 2 places to the right.
Answer: 262.3
*Note the differences between #2 and #3 with the positive and negative exponents.

Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE 206

Structured Guided Practice

(A/B Partners Practice)
Directions: Convert the given number into scientific notation.

1. 27,300,000

Solution:
2.73 × 107

2. 0.00035

Solution:
3.5 × 10−4

3. Write the standard form: 2.73 × 10-7

Solution:
The exponent is negative, move the decimal 7 places to the left.
0.000000273

*Reflect on the differences between #1 and #3

207 Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE

Final Check for Understanding

(Teacher Checks Work)
Directions: Convert the given number into scientific notation.

1. 172,900,000

Solution:
1.729 × 108

2. 0.0000038

Solution:
3.8 × 10−6

3. Write the standard form: 3.8 × 106

Solution:
3,800,000

Closure

Recap today’s lesson with one or more of the following questions:
MP6: How do you know if the exponent will be a positive or a negative?
MP8: What patterns do you find in figuring out the power of 10?

Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE 208

Homework Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 1: Scientific Notation

Objective: I will convert numbers from standard form to scientific notation.

Vocabulary Steps

Scientific Notation: a method to write very large Standard to Scientific Notation
numbers or very small numbers as the product of
a number between 1 and 10 and a power of 10 Ask yourself these questions:
1. Is the number a big or small number?
Power of Ten: ten multiplied by itself the 2. Will the exponent be positive or negative?
number of times indicated by the exponent • Big number = positive power
• Small number = negative power
To figure out power of 10, think “How many places 3. Locate or place the decimal point.
does the decimal point move?” 4. Count the number of places the decimal will
If number is 10 or greater, move to create a number in the ones place.
move to the left = positive power This will be the power of ten.
If number is smaller than 1, 5. Write an expression using scientific notation.

move to the right= negative power Scientific Notation to Standard Form:
1. If the exponent is positive, move to the right
(multiplication).
2. If the exponent is negative, move to the left
(division).
3. Make additional zeros for place value needed.

209 Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE

Homework

Unit 3 · Lesson 1: Scientific Notation

Example # 1 Example # 2

Directions: Convert the given number into scientific notation.

1,500,000 0.02623

Solution: Solution:
• Find the appropriate place for the decimal point, • Find the appropriate place for the decimal point so that there

so that there is a digit in the ones place value. is a digit in the ones place value.
• 1500000 • 0. 0 2 6 2 3
• If there is no decimal point add one to the right of • Notice this time there is a decimal.
• 0. 0 2 6 2 3
the ones place value in order not to change the
value of the original number. • Your new number will be 2.623.
• 1 5 0 0 0 0 0. • The exponent is negative because the original number is

• Your new number will be 1.5. smaller than 2.623.
• The exponent is positive because the original • Rewrite the expression in scientific notation.

number is larger than 1.5. Answer: 2.623× 10−2
• Rewrite the expression in scientific notation.

Answer: 1.5 ×106

Write the standard form: 2.623 × 102

Solution:
The exponent is positive, so move the decimal 2 places to the right.
Answer: 262.3
*Note the differences between #2 and #3 with the positive and negative exponents.

Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE 210

Homework

Unit 3 · Lesson 1: Scientific Notation

Directions: Convert the given number into scientific notation or standard form.

1. 1.53 × 105 2. 2.6 × 107

3. 0.00009801 4. 0.001026
5. 0.000075 6. 147,000,000,000

211 Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE

Answer Key 2. 26,000,000

Homework 4. 0.001026
1.026
1. 153,000 1.026 × 10-3

3. 0.00009801 6. 147,000,000,000
9.801 1.47
9.801 × 10-5 1.47 × 1011

5. 0.000075
7.5
7.5 × 10-5

Copyright © Swun Math Grade 8 Unit 3 Lesson 1 C TE 212

Scientific Notation MPs Applied MP

Procedural Lesson * Embedded MP
Grade 8 · Unit 3 · Lesson 2
12345678
MC: 8.EE.3
* ** *  *

Problem of the Day Student Journal Pages

118-123

Objective: I will use the scientific notation to write very large and very small numbers.

Vocabulary Teacher Resources

Scientific Notation: a method to write very Considerations:
large numbers or very small numbers as the Review powers of 10 by creating a class chart.
product of a number between 1 and 10 and a
power of 10 Explain which way to move the decimal depending on the
exponent. Write the number out in expanded form to prove.
99 = 9.9 × 101 Have students use an arrow to mark the decimal places to
avoid careless errors. Use the × symbol for multiplication in
Power of Ten: ten multiplied by itself the this lesson.
number of times indicated by the
exponent Students must understand that moving the decimal left or
right is the same as multiplying it by 10x.
To figure out power of 10, think “How many
places does the decimal point move?” Steps:
1. Ask yourself, “Is my number big or small?”
If number is 10 or greater,
move to the left = positive power • Big number = positive power
• Small number = negative power
If number is less than 1, 2. Move the decimal point so that you have a number
move to the right = negative power between 1 and 10.
3. Count how many times you moved the decimal to
determine the power.
4. Write expression using scientific notation.

Meaning Value Scientific Notation to Standard Form:

104 10·10·10·10 10,000

103 10·10·10 1000 1. If the exponent is positive, move to the right
(multiplication).
102 10·10 100
2. If the exponent is negative, move to the left
101 10 10 (division).

100 1 1 3. Make additional zeros for place value needed.

10-1 1 0.1
10

10-2 1 ⋅ 1 0.01 Application of MPs:
10 10

10-3 1 ⋅ 1 · 1 0.001 MP6: How do you know if the exponent will be + or - ?
10 10 10

10-4 1 ⋅ 1 · 1 ⋅ 1 0.0001 I know that the exponent will be a positive/negative
10 10 10 10
because .

MP7: What connection do you find between the exponent

and the value of the power of 10?

The connection I see between the exponent and the

value is .

213 Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE

Input/Model

(Teacher Presents)

Directions: Read and solve.
1. The news report had 40,000,000 people watching. What is that number in scientific
notation?

Solution:
• The decimal needs to be between the 4 and 0.
• This means that the decimal needs to be moved 7 places to the left: 4.0
• The new number is less than the original number. The exponent needs to be a positive.

Answer: 4 × 107

Directions: Read and solve.

2. The chemist found 6.8 × 10–8 traces of chlorine in the water. What is the number in
standard notation?

Solution: 1
108
• Since the power of 10 is negative, divide by a base of 10. 10−8 =

• Divide 6.8 by 100,000,000.

• This means move the decimal to the left. Add zeros if spaces are needed.

• 6.8 × 10–8 = 0.000000068

Answer: 0.000000068

Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE 214

Structured Guided Practice

(A/B Partners Practice)
Directions: Convert the given number into scientific notation.

1. The diameter of a bacteria cell was measured to be 0.00059 of a millimeter.

Solution:
5.9 × 10–4

Directions: Convert the given number into standard notation.
2. The distance from the Earth to the Sun is calculated to be 1 × 108.

Solution:
100,000,000

215 Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Convert each number either to standard or scientific notation.
1. 1,590

Solution: Grade 8 Unit 3 Lesson 2 P TE 216
1.59 × 103

2. 3 × 103

Solution:
3,000

Copyright © Swun Math

Student Practice Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 2: Scientific Notation

Directions: Convert each number either to standard or scientific notation.

1. 327,000 2. 3.2 × 104

Solution: Solution:
3.27 32,000
3.27 × 105
4. 4 × 10–5
3. 0.0000025

Solution: Solution:
2.5 0.00004
2.5 × 10-6
6. 0.0095
5. 9.8 × 10–2

Solution: Solution:
0.098
9.5
9.5 × 10-3

217 Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE

Challenge Problems

Directions: Solve.

1. Bryan needs to convert the following 2. When using a calculator to find the
number 10532017 into scientific notation. number of sand particles in a cup,
His work is listed below: Johnny’s scientific calculator read
5.344e6. When converting this number
10,532,017 into scientific notation, we would write
10.532017 × 106 5.344 × 106.

Is he correct? Explain.

Convert these calculator’s readings to
scientific notation.

a) 6.72e–4
b) 3.291e9

Solution: Solution:
Incorrect; solution is 1.0532017 × 107 a) 6.72 × 10–4
b) 3.291 × 109

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.

*MP4: Apply mathematics in everyday life.

Work with a partner to find ways scientific notation is used in the real-world. Find at least 5
examples. What pattern do you notice about the powers of ten?

Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE 218

Closure

Reaching Consensus
*MP3: Do you agree or disagree with your classmate? Why or why not?

Student Presentations
*MP1: What steps in the process are you most confident about?
*MP6: Explain how you might show that your solution answers the problem.

Closure

Recap today’s lesson with one or more of the following questions:
MP6: How do you know if the exponent will be a positive or a negative?
MP7: What connection do you find between the exponent and the value of the

power of 10?

219 Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE

Homework Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 2: Scientific Notation

Objective: I will use the scientific notation to write very large and very small numbers.

Vocabulary Steps

Scientific Notation: a method to write very large 1. Ask yourself, “Is my number big or small?”
numbers or very small numbers as the product of • Big number = positive power
a number between 1 and 10 and a power of 10 • Small number = negative power

99 = 9.9 × 101 2. Move the decimal point so that you have a
number between 1 and 10.
Power of Ten: ten multiplied by itself the
number of times indicated by the exponent 3. Count how many times you moved the
decimal to determine the power.

4. Write expression using scientific notation.

To figure out power of 10, think “How many places does the decimal Scientific Notation to Standard Form:
point move?”
1. If the exponent is positive, move to the right
If number is 10 or greater, (multiplication).
move to the left = positive power
2. If the exponent is negative, move to the left
If number is less than 1, (division).
move to the right = negative power
3. Make additional zeros for place value needed.

Example # 1 Example # 2

Directions: Convert number into scientific notation. Directions: Convert number into standard notation.

The news report had 40,000,000 people watching. The chemist found 6.8 × 10–8 traces of chlorine in the water.

Solution: Solution:
• The decimal needs to be between the 4 and 0.
• This means that the decimal needs to be moved 7 places to the • Since the power of 10 is negative, divide by a base of 10. 10−8 =
1
left: 4.0 108
• The new number is less than the original number. The
• Divide 6.8 by 100,000,000.
exponent needs to be a positive.
• This means move the decimal to the left. Add zeros if spaces
Answer: 4 × 107
are needed.

• 6.8 × 10–8 = 0.000000068

Answer: 0.000000068

Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE 220

Homework

Unit 3 · Lesson 2: Scientific Notation

Directions: Convert each number either to standard or scientific notation.

1. 0.089 2. 5,000,000

3. 1 × 10–7 4. 2.3 × 10–5

5. 7.098 × 105 6. 405,698

Explain the steps you used to solve problem number _______.

______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

221 Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE

Answer Key

Extension Activity

Answers may vary. Sample response: The number of grains of sand, astronomers measure distances in space,
doctors measure size of blood cells, etc…
The pattern is that smaller items are negative powers of ten, and larger numbers are positive powers of ten.

Homework 2. 5,000,000
5.0
1. 0.089 5 × 106
8.9
8.9 × 10-2 4. 2.3 × 10-5
0.000023
3. 1 × 10-7
0.0000001 6. 405,698
4.05698
5. 7.098 × 105 4.05698 × 105
709,800

Copyright © Swun Math Grade 8 Unit 3 Lesson 2 P TE 222

Scientific Notation: MPs Applied MP
Add & Subtract
* Embedded MP
Conceptual Lesson
Grade 8 · Unit 3 · Lesson 3 12345678

MC: 8.EE.4 *  *

Problem of the Day Student Journal Pages

Objective: I will add and subtract numbers in scientific notation. 124-127

Vocabulary Teacher Resources

Adding & Subtracting Scientific Notation Considerations:

(4.342 × 10²) + (3.871 × 10³) = Refer to the previous lesson on scientific
notation and how to change the powers of ten.
Convert to same power: Some students might prefer to change numbers
(4.342 × 10²) + (38.71 × 10²) to standard form, add or subtract to identify the
solution and then convert the solution back to
Add decimals: standard notation. This lesson will focus on the
4.342 + 38.71 = 43.052 concept of adding and subtracting with scientific
notation, while the next lesson will focus on the
Bring down exponent: additional step of converting the exponents to
43.052 × 10² = the same power.

Proper Scientific Form Steps:
4.3052 × 10³ 1. Add or subtract the number (decimal).
2. Bring down the exponent on the ten.

Application of MPs:

MP1: How would you describe what you are trying to
find?
I am trying to find the sum or the difference of
_____________________.

MP2: What properties might we use to find a
solution?
A property that we might use to find a
solution can be the ____________________.

223 Copyright © Swun Math Grade 8 Unit 3 Lesson 3 C TE

Input/Model

(Teacher Presents)

Directions: Simplify. Write the sum or the difference in scientific notation.

1. (2.75 × 103) + (9.1 × 103) 2. (6.6 × 10–5 )– (3.5 × 10–5)

Solution: Solution:

• Since the powers of ten are the same, use the • Since the powers of ten are the same, use the

distributive property to combine the lead numbers distributive property to combine the lead numbers

and add them. and add them.
• 2.75 × 103 + 9.1 × 103 • 6.6 × 10-5 – 3.5 × 10-5
• (2.75 + 9.1) × 103 Add first (parentheses) • (6.6 – 3.5) × 10-5 Subtract first (parentheses).
• 11.85 × 103  Not in Scientific Notation • 3.1 × 10-5
• Answer: 3.1 × 10-5
• 11.85 needs to change to 1.185 for Scientific
or
Notation
• Answer: 1.185 × 104 • Convert to standard form:

or • 0.000066 – 0.000035= 0.000031

• Convert to standard form: • Convert solution 0.000031 into Scientific Notation

• 2750 + 9100 = 11,850 form.
Answer: 3.1 × 10–5
• Convert solution 11,850 into Scientific Notation

form.
Answer: 1.185 × 104

Copyright © Swun Math Grade 8 Unit 3 Lesson 3 C TE 224

Structured Guided Practice

(A/B Partners Practice)

Directions: Simplify. Write the sum or the difference in scientific notation.

1. (1.03 × 10–2) + (8.87 × 10–2) 2. (5.44 × 104) – (1.2 × 104)

Solution: Solution:
• 1.03 × 10-2 + 8.87 × 10-2 • 5.44 × 104 – 1.2 × 104
• (1.03 + 8.87) × 10-2 • (5.44 – 1.2) × 104
• 9.9 × 10-2 • 4.24 × 104
• Answer: 9.9 × 10-2 • Answer: 4.24 × 104

or or
• Convert to standard form:
• Convert to standard form: • 54,400 – 12,000 = 42,400
• 0.0103 + 0.0887 = 0.0990 • Convert 42,400 into Scientific Notation form.
• Convert 0.099 into Scientific Notation form. Answer: 4.24 × 104
Answer: 9.90 × 10–2
Grade 8 Unit 3 Lesson 3 C TE
225 Copyright © Swun Math

Final Check for Understanding

(Teacher Checks Work)

Directions: Simplify. Write the sum or the difference in scientific notation.

1. (4.3 × 102) + (5.1 × 102) 2. (3.63 × 106) – (1.71 × 106)

Solution: Solution:
9.4 × 102 1.92 × 106

Closure

Recap today’s lesson with one or more of the following questions:

MP1: How would you describe what you are trying to find?
MP2: What properties might we use to find a solution?

Copyright © Swun Math Grade 8 Unit 3 Lesson 3 C TE 226

Homework Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 3: Scientific Notation:
Add & Subtract

Objective: I will to add and subtract numbers in scientific notation.

Vocabulary Steps

Adding & Subtracting Scientific Notation 1. Add or subtract the number (decimal).
2. Bring down the exponent on the ten.
(4.342 × 10²) + (3.871 × 10³) =
*Another option is to convert to standard form
Convert to same power: and subtract.
(4.342 × 10²) + (38.71 × 10²)

Add decimals:
4.342 + 38.71 = 43.052

Bring down exponent:
43.052 × 10² =

Proper Scientific Form
4.3052 × 10³

Example # 1 Example # 2
Directions: Simplify. Write solution in scientific notation.
(6.6 × 10–5) – (3.5 × 10–5)
(2.75 × 103) + (9.1 × 103)

Solution: Solution:

• Since the powers of ten are the same, use the • Since the powers of ten are the same, use the

distributive property to combine the lead numbers distributive property to combine the lead numbers

and add them. and add them.
• 2.75 × 103 + 9.1 × 103 • 6.6 × 10-5 – 3.5 × 10-5
• (2.75 + 9.1) × 103 Add first (parentheses). • (6.6 – 3.5) × 10-5 Subtract first (parentheses).
• 11.85 × 103  Not in Scientific Notation • 3.1 × 10-5
• Answer: 3.1 × 10-5
• 11.85 needs to change to 1.185 for Scientific
or
Notation
• Answer: 1.185 × 104 • Convert to standard form:

or • 0.000066 – 0.000035= 0.000031

• Convert to standard form: • Convert solution 0.000031 into Scientific Notation
• 2750 + 9100 = 11,850 form.

• Convert solution 11,850 into Scientific Notation Answer: 3.1 × 10–5

form.
Answer: 1.185 × 104

227 Copyright © Swun Math Grade 8 Unit 3 Lesson 3 C TE

Homework

Unit 3 · Lesson 3: Scientific Notation:
Add & Subtract

Directions: Simplify. Write the sum or the difference in scientific notation.

1. (1.389 × 104) + (3.56 × 104) 2. (9.61 × 10-3) – (4.68 × 10-3)

3. (4.2 × 10-2) – (2.66 × 10-2) 4. (3.56 × 105) – (1.6 × 105)

5. (1.53 × 103) + (1.379 × 103) 6. (4.65 × 102) – (3.65 × 102)

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Answer Key 2. 9.61 × 10-3 – 4.68 × 10-3
(9.61 – 4.68) × 10-3
Homework Answer: 4.93 × 10-3

1. 1.389 × 104 + 3.56 × 104 4. 3.56 × 105 – 1.6 × 105
(1.389 + 3.56) × 104 (3.56 – 1.6) × 105
Answer: 4.949 × 104 Answer: 1.96 × 105

3. 4.2 × 10-2 – 2.66 × 10-2 6. 4.65 × 102 – 3.65 × 102
(4.2 – 2.66) × 10-2 (4.65 – 3.65) × 102
Answer: 1.54 × 10-2 Answer: 102

5. 1.53 × 103 + 1.379 × 103
(1.53 + 1.379) × 103
Answer: 2.909 × 103

229 Copyright © Swun Math Grade 8 Unit 3 Lesson 3 C TE

Notes

Copyright © Swun Math Grade 8 Unit 3 Lesson 3 C TE 230

Scientific Notation: MPs Applied MP
Add & Subtract
* Embedded MP
Procedural Lesson
Grade 8 · Unit 3 · Lesson 4 12345678

MC: 8.EE.4 *  * * * *

Problem of the Day Student Journal Pages

Objective: I will add or subtract numbers in scientific notation. 128-133

Vocabulary Teacher Resources

Adding & Subtracting in Scientific Notation Considerations:

(4.342 × 10²) + (3.871 × 10³) = Look carefully at the problem first to see if the
exponents have the same power. The important
Convert to same power: thing to remember about adding or subtracting
(4.342 × 10²) + (38.71 × 10²) scientific notation is that the exponents MUST
BE THE SAME. If the exponents are not the
Add decimals: same, it is necessary to convert to the same
4.342 + 38.71 = 43.052 power. Practice converting decimals separately
as needed. Be sure to remind students to express
Bring down exponent: the answer in proper scientific notation.
43.052 × 10² =

Proper Scientific Form Steps:
4.3052 × 10³ 1. Convert exponents to the same power of
10 (if needed).
2. Add or subtract the number (decimal).
3. Bring down the exponent on the ten.
4. Write in proper form.

Application of MPs:

MP2: What properties might we use to find a
solution?
A property that we might use to find a
solution can be the ____________________.

MP6: Pay attention to precision; why is this an
important concept for this lesson?
It is important to pay attention to precision
since I am _________________________.

231 Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE

Input/Model

(Teacher Presents)

Directions: Simplify the expression. Write solution in scientific notation.
1. (9.37 × 10-7 ) – (1.421 × 10-7)

Solution: Grade 8 Unit 3 Lesson 4 P TE 232
• (9.37 – 1.421) × 10-7
• 7.949 × 10-7
Answer: 7.949 × 10-7

2. (5.312 × 101) + (6.421 × 102)

Solution:
• 5.312 × 101 + 6.421 × 101 × 101
• 5.312 × 101 + 64.21 × 101
• (5.312 + 64.21) × 101
• 69.522 × 101  not in scientific notation.

• 6.9522 × 102

Copyright © Swun Math

Structured Guided Practice

(A/B Partners Practice)

Directions: Simplify the expression. Write solution in scientific notation.
1. (9.69 × 106) – (7.5 × 106)

Solution:
2.19 × 106

2. (6.78 × 104) + (7.24 × 105)

Solution:
7.918 × 105

233 Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Simplify the expression. Write solution in scientific notation.
1. (1.065 × 10-2) – (1.05 × 10-2)

Solution:
1.5 × 10-4

2. (5.4 × 105) + (2.6 × 106)

Solution: Grade 8 Unit 3 Lesson 4 P TE 234
3.14 × 106

Copyright © Swun Math

Student Practice Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 4: Scientific Notation: Add & Subtract

Directions: Simplify the expression. Write solution in scientific notation.

1. (5.3 × 10-1) – (4.7 × 10-1) 2. (9.55 × 10-3) + (1.02 × 10-4)

Solution: Solution:
6 × 10-2 9.652 × 10-3

3. (4.5 × 104) – (1.2 × 104) 4. (2.32 × 102) + (1.62 × 103)

Solution: Solution:
3.3 × 104 1.852 × 103

5. (1.24 × 105) + (5.76 × 104) 6. (4.5 × 10-6) – (3.6 × 10-6)

Solution: Solution:
1.816 × 105 9 × 10-7

235 Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE

Challenge Problems

Directions: Solve.

1. Jim argues that there is no way a 2. What value of x will satisfy the equation?
scientific notation number can be added Check your answer.
with a whole number. Is Jim correct?
Explain. + 1.52 × 102 = 3.24 × 102

Solution: Solution:
• Incorrect
• Answers will vary. Sample response: Every whole • Identify what needs to be moved to the right side

number can be converted into scientific notation; of the equation.
therefore, every scientific notation number can be • + (1.52 × 102) = 3.24 × 102
added with a whole number. This can occur by • = 3.24 × 102 – (1.52 × 102)
changing the whole number into scientific • = (3.24 – 1.52) × 102
notation. • = 1.72 × 102

Answer: 1.72 × 102

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.
* MP4: Apply mathematics in everyday life.

Decide if each statement below is true or false.

True False

1. The perimeter of a triangle with a side length of 4.7 × 103 will be 14.1 × 109.

2. The payroll of the professional baseball team was 9.2 × 106. The payroll of the

football team was 8.4 × 105. The baseball team has a $8,360,000 higher payroll.

3. The news program had 1.5 × 104 viewers on Monday. On Tuesday, they had 2.4 ×

104 viewers. The total viewers for both days is 3.9 × 104.

Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE 236

Closure

Reaching Consensus
*MP3: Do you agree or disagree with your classmate? Why or why not?

Student Presentations
*MP1: What steps in the process are you most confident about?
*MP6: Explain how you might show that your solution answers the problem.

Closure

Recap today’s lesson with one or more of the following questions:
MP2: What properties might we use to find a solution?
MP6: Pay attention to precision; why is this an important concept for this lesson?

237 Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE

Homework Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 4: Scientific Notation: Add & Subtract

Objective: I will add or subtract numbers in scientific notation.

Vocabulary Steps

Adding & Subtracting Scientific Notation 1. Convert exponents to the same power of 10 (if
needed).
(4.342 × 10²) + (3.871 × 10³) =
2. Add or subtract the number (decimal).
Convert to same power: 3. Bring down the exponent on the ten.
(4.342 × 10²) + (38.71 × 10²) 4. Write in proper form.

Add decimals:
4.342 + 38.71 = 43.052

Bring down exponent:
43.052 × 10² =

Proper Scientific Form
4.3052 × 10³

Example # 1 Example # 2

Directions: Simplify the expression. Write the solution in scientific notation.

(9.37 × 10-7) – (1.421 × 10-7) (5.312 × 101) + (6.421 × 102)

Solution: Solution:
• (9.37 – 1.421) × 10-7 • 5.312 × 101 + 6.421 × 101 × 101
• 7.949 × 10-7
• 5.312 × 101 + 64.21 × 101
Answer: 7.949 × 10-7 • (5.312 + 64.21) × 101
• 69.522 × 101  not written in scientific notation.

Answer: 6.9522 × 102

Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE 238

Homework

Unit 3 · Lesson 4: Scientific Notation: Add & Subtract

Directions: Simplify the expression. Write solution in scientific notation.

1. (2.3 × 10-4) – (1.5 × 10-4) 2. (2.5 × 103) + (7.9 × 103)

3. (9.5 × 103) + (4.3 × 104) 4. (1.01 × 103) + (6.5 × 104)

239 Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE

Homework

Unit 2 · Lesson 4: Scientific Notation: Add & Subtract

5. (7.9 × 10-6) – (6.5 × 10-6) 6. (9.2 × 10-1) – (7.9 × 10-1)

Explain the steps you used to solve problem number _______.

______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE 240

Answer Key 2. 2.5 × 103 + 7.9 × 103
(2.5 + 7.9) × 103
Extension Activity 10.4 × 103  Not in scientific notation
1.04 × 104
1. False
2. True 4. 1.01 × 103 + 6.5 × 104
3. True 1.01 × 103 + 6.5 × 101 × 103

Homework 1.01 × 103 + 65.0 × 103
66.01 × 103  Not in scientific notation
1. 2.3 × 10-4 – 1.5 × 10-4 6.601 × 104 L
(2.3 – 1.5) × 10-4
0.8 × 10-4  Not in scientific notation 6. 9.2 × 10-1 – 7.9 × 10-1
8.0 × 10-5 (9.2 – 7.9) × 10-1
1.3 × 10-1
3. 9.5 × 103 + 4.3 × 104
9.5 × 103 + 4.3 × 101 × 103

9.5 × 103 + 43.0 × 103
52.5 × 103  Not in scientific notation
5.25 × 104

5. 7.9 × 10-6 – 6.5 × 10-6
(7.9 – 6.5) × 10-6
1.4 × 10-6

0.8 × 10-4

241 Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE

Notes

Copyright © Swun Math Grade 8 Unit 3 Lesson 4 P TE 242

Scientific Notation: Multiply MPs Applied MP
& Divide
* Embedded MP
Conceptual Lesson
Grade 8 · Unit 3 · Lesson 5 12345678

MC: 8.EE.4 * *

Problem of the Day Student Journal Pages

Objective: I will multiply or divide numbers expressed in scientific notation. 134-137

Vocabulary Teacher Resources

Multiplying in Scientific Notation Considerations:

1. Multiply coefficients. Review exponent rules for multiplication and
2. Add exponents. division; show expanded notation. Refer to previous
lessons about scientific notation to change the
(3 × 102) (5 × 104) = powers of ten. Show students how the expressions
can also be multiplied by changing both numbers out
3 × 5 = 15 of scientific notation. Use calculators to check work.

102+4 = 106 Keeping the powers of ten separate makes the
equation substantially easier and manageable
15 × 106 without a calculator.

Moving the decimal and making the powers of ten the
same will not make the problem easier to simplify.

1.5 × 107 Steps:

Proper Scientific Form 1. Check for numbers in scientific notation.
2. If multiplying-
Dividing in Scientific Notation
1. Divide coefficients. • Multiply coefficients.
2. Subtract exponents. • Add exponents.
3. If dividing-
(15 × 106) ÷ (3 × 102) = • Divide coefficients.
• Subtract exponents.
4. Write in scientific notation.

15 ÷3 = 5 Application of MPs:
106-2 = 104
 MP2: What properties might we use to find a
5 × 104
solution?

A property that we might use to find a

solution can be the ____________.

 MP8: How would you prove that the solution is

correct?

I can prove that my solution is correct by

changing .

243 Copyright © Swun Math Grade 8 Unit 3 Lesson 5 C TE

Input/Model

(Teacher Presents)

Directions: Simplify the expression. Leave the solution in scientific notation.
1. (2.5 × 103) × (8 × 102)

Solution:

• Verify that each number is written in scientific notation.
• Use the commutative property to move numbers and multiply the two lead numbers and the base ten

together.
• (2.5 × 8) × (103 × 102)
• 20 × 103 + 2
• 20 × 105 Not in scientific notation. Need to change 20 to 2.0.
• 2.0 × 106
Answer: 2.0 × 106

2. (9.5 × 103) ÷ (5 × 102)

Solution:

• Verify that each number is written in scientific notation.

• Change the division problem into a ratio.

• 9.5⋅103
5⋅102

• Use the commutative property to create two ratios.

• 9.5 ⋅ 103
5 102

• Simplify the first ratio by dividing 9.5 by 5.

• 1.9 ⋅ 103
102

Use the rules for multiplying/dividing exponents.

• 1.9 × 103 – 2

• 1.9 × 101

Answer: 1.9 × 101

Copyright © Swun Math Grade 8 Unit 3 Lesson 5 C TE 244

Structured Guided Practice

(A/B Partners Practice)

Directions: Simplify the expression. Leave the solution in scientific notation.
1. (3 × 104) × (2.4 × 10¯2)

Solution:
7.2 × 102

2. (4.2 × 105) ÷ (1.2 × 102)

Solution:
3.5 × 103

245 Copyright © Swun Math Grade 8 Unit 3 Lesson 5 C TE