G8

Final Check for Understanding

(Teacher Checks Work)
Directions: Simplify the expression. Leave the solution in scientific notation.

1. (2 × 10¯1) × (3.2 × 104)

Solution:
6.4 × 103

2. (6.4 × 103) ÷ (4 × 102)

Solution:
1.6 × 101

Closure

Recap today’s lesson with one or more of the following questions:
MP2: What properties might we use to find a solution?
MP8: How would you prove that the solution is correct?

Copyright © Swun Math Grade 8 Unit 3 Lesson 5 C TE 246

Homework Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 5: Scientific Notation: Multiply & Divide

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

Vocabulary Steps

Multiplying in Scientific Notation 1. Check both numbers are in scientific
1. Multiply coefficients. notation.
2. Add exponents.
2. If multiplying-
(3 × 102) (5 × 104) = • Multiply coefficients.
3 × 5 = 15 • Add exponents.
102+4 = 106
15 × 106 3. If dividing-
1.5 × 107 • Divide coefficients.
• Subtract exponents.
Proper Scientific Form
4. Write in scientific notation.
Dividing in Scientific Notation

1. Divide coefficients.
2. Subtract exponents.

(15 × 106) ÷ (3 × 102) =

15 ÷3 = 5

106-2 = 104

5 × 104

Example # 1 Example # 2

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

(2.5 × 103) × (8 × 102) (9.5 × 103) ÷ (5 × 102)

Solution: Solution:
• Verify that each number is written in scientific notation. • Verify that each number is written in scientific notation.

• Use the commutative property to move your numbers • Change the division problem into a ratio.

around and be able to multiply the two lead numbers • 9.5 × 103

and the base ten together. 5 × 102
• (2.5 × 8) × (103 × 102)
• 20 × 103 + 2 • Use the commutative property to create two ratios.
• 20 × 105 Not in scientific notation. Need to change 20 to
• 9.5 × 103 → 9.5 × 103
2.0 5 × 102 5 102
• 2.0 × 106
Answer: 2.0 × 106 • 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

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

Homework

Unit 3 · Lesson 5: Scientific Notation: Multiply & Divide

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

1. (1.5 × 104) × (5 × 104) 2. (2.5 × 103) × (3.1 × 101)

3. (9.4 × 10-1) ÷ (4.7 × 10¯2) 4. (6.1 × 102) × (1.5 × 10¯2)

5. (5.6 × 10¯1) × (1 × 106) 6. (1.0 × 10¯3) ÷ (2.5 × 101)

Copyright © Swun Math Grade 8 Unit 3 Lesson 5 C TE 248

Answer Key

Homework

1. (1.5 × 104) × (5 × 104) 2. (2.5 × 103) × (3.1 × 101)
(1.5 × 5) × (104 × 104) (2.5 × 3.1) × (103 × 101)
7.5 × 104 + 4 7.75 × 103 + 1

Answer: 7.5 × 108 Answer: 7.75 × 104

3. (9.4 × 10-1) ÷ (4.7 × 10-2) 4. (6.1 × 102) × (1.5 × 10-2)
(6.1 × 1.5) × (102 × 10-2)
9.4 × 10−1 9.15 × 102 + (-2)
4.7 × 10−2
Answer: 9.15 × 100
9.4 × 10−1
4.7 10−2

2.0 × 10-1 – (-2)
Answer: 2 × 101

5. (5.6 × 10-1) × (1 × 106) 6. (1.0 × 10-3) ÷ (2.5 × 101)

(5.6 × 1) × (10-1 × 106) 1.0 × 10−3
5.6 × 10-1 + 6 2.5 × 101

Answer: 5.6 × 105 1.0 × 10−3
2.5 101

0.4 × 10-3 – 1

0.4 × 10-4  Not in scientific notation
Answer: 4 × 10-5

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

Notes

Copyright © Swun Math Grade 8 Unit 3 Lesson 5 C TE 250

Scientific Notation: Multiply MPs Applied MP
& Divide
* Embedded MP
Procedural Lesson
Grade 8 · Unit 3 · Lesson 6 12345678

MC: 8.EE.4 * ** * *

Problem of the Day Student Journal Pages

Objective: I will multiply or divide numbers in scientific notation. 138-143

Vocabulary Teacher Resources

Multiplying in Scientific Notation Considerations:

1. Multiply coefficients. Review the exponent rules for multiplication and
2. Add exponents. division. Students may also need to see how the
commutative and associative properties help simplify
(3 × 102) (5 × 104) = these problems.

3 × 5 = 15 Steps:
102+4 = 106
15 × 106 1. Check for numbers in scientific notation.
1.5 × 107 2. If multiplying-

Proper Scientific Form • Multiply coefficients.
• Add exponents.
Dividing in Scientific Notation 3. If dividing-
1. Divide coefficients. • Divide coefficients.
2. Subtract exponents. • Subtract exponents.
4. Write in scientific notation.
(15 × 106) ÷ (3 × 102) =
15 ÷3 = 5 Application of MPs:
106-2 = 104
5 × 104 MP6: Pay attention to precision; why is this an
important concept for this lesson?
In this lesson, it is important to pay attention to
precision because _____________________.

MP8: How would you prove that the solution is correct?
I can prove that my solution is correct by
changing ___________________________.

251 Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE

Input/Model

(Teacher Presents)

Directions: Simplify the expression. Write solution in scientific notation.
1. (1.2 × 102) × (0.8 × 103)

Solution:
• Verify that each number is written in scientific notation.
• (1.2 × 102) × (0.8 × 103) not in scientific notation.
• (1.2 × 102) × (8 × 102)

• (1.2 × 8) × (102 × 102)
• 9.6 × 102 + 2
• 9.6 × 104
Answer: 9.6 × 104

2. (2.5 × 102) ÷ (5 × 103)

Solution:

• Verify that each number is written in scientific notation.

• 2.5⋅102
5⋅103
102
• 2.5 ⋅ 103
5
102
• 0.5 ⋅ 103

• 0.5 ⋅ 102−3

• 0.5 × 10–1 not in scientific notation

• 5 × 10–2

Answer: 5 × 10–2

Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE 252

Structured Guided Practice

(A/B Partners Practice)
Directions: Simplify the expression. Write solution in scientific notation.

1. (0.04 × 10-2) × (4 × 103)

Solution:
1.6 × 100

2. (8.1 × 10-2) ÷ (3 × 10-4)

Solution:
2.7 × 10²

253 Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE

Final Check for Understanding

(Teacher Checks Work)
Directions: Simplify the expression. Write solution in scientific notation.

1. (0.5 × 10-1) × (9 × 101)

Solution:
4.5 × 100

2. (9 × 103) ÷ (2 × 101)

Solution: Grade 8 Unit 3 Lesson 6 P TE 254
4.5 × 102

Copyright © Swun Math

Student Practice Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 6: Scientific Notation:
Multiply & Divide

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

1. (3 × 104) × (0.7 × 102) 2. (2.5 × 102) ÷ (5 × 103)

Solution: Solution:
2.1 × 106 5 × 10-2

3. (6.6 × 103) ÷ (6 × 10-1) 4. (8.1 × 10-2) × (0.01 × 104)

Solution: Solution:
1.1 × 104 8.1 × 100

5. (5.2 × 10-3) × (2 × 10-1) 6. (7 × 10-1) ÷ (14 × 108)

Solution: Solution:
1.04 × 10-3 5 × 10-10

255 Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE

Challenge Problems �1.2×102�3
2. 1.2×103
Directions: Simplify the expression.
1. (1.2 × 103)2

Solution: Solution:
Distribute the outside exponent to both terms.
Distribute the outside exponent to both terms.
(1.2)2 × (103)2 (1.728 ÷ 1.2) × (106 - 3)
1.44 × (103 × 2) Answer: 1.44 × 103
Answer: 1.44 × 106

Extension Activity

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

* MP4: Apply mathematics in everyday life.

Using only the digits 1-9, create as many true equations as possible. For each equation, the
digits are only to be used once.

▭.▭ ▭ ▭.▭× 10³ × × 10³
× 10³ =

Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE 256

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: Pay attention to precision; why is this an important concept for this lesson?
MP8: How would you prove that the solution is correct?

257 Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE

Homework Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 6: Scientific Notation:
Multiply & Divide

Objective: I will multiply or divide numbers in scientific notation.

Vocabulary Steps

Multiplying in Scientific Notation 1. Check for numbers in scientific notation.
2. If multiplying-
1. Multiply coefficients.
2. Add exponents. • Multiply coefficients.
• Add exponents.
(3 × 102) (5 × 104) = 3. If dividing-
• Divide coefficients.
3 × 5 = 15 • Subtract exponents.
4. Write in scientific notation.
102+4 = 106

15 × 106

1.5 × 107
Proper Scientific Form

Dividing in Scientific Notation

1. Divide coefficients.
2. Subtract exponents.

(15 × 106) ÷ (3 × 102) =

15 ÷3 = 5
106-2 = 104

5 × 104

Example # 1 Example # 2

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

(1.2 × 102) × (0.8 × 103) (2.5 × 102) ÷ (5 × 103)

Solution: Solution:

• Verify that each number is written in scientific notation. • Verify that each number is written in scientific notation.
• (1.2 × 102) × (0.8 × 103) not in scientific notation.
• (1.2 × 102) × (8 × 102) • 2.5⋅102
5⋅103
• (1.2 × 8) × (102 × 102) 102
• 9.6 × 102 + 2 • 2.5 ⋅ 103
• 9.6 × 104 5
102
Answer: 9.6 × 104 • 0.5 ⋅ 103

• 0.5 ⋅ 102−3

• 0.5 × 10–1 not in scientific notation

• 5 × 10–2

Answer: 5 × 10–2

Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE 258

Homework

Unit 3 · Lesson 6: Scientific Notation:
Multiply & Divide

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

1. (1.2 × 103) × (1.3 × 10-1) 2. (1.25 × 102) ÷ (5 × 10-1)

3. (2.4 × 104) × (3.1 × 101) 4. (6.4 × 103) ÷ (4 × 104)

259 Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE

Homework 6. (1.3 × 10-5) × (6.2 × 10-2)

Unit 3 · Lesson 6: Scientific Notation:
Multiply & Divide

5. (6 × 10-1) ÷ (1.5 × 10-2)

Explain the steps you used to solve problem number _______.

______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE 260

Answer Key 2. 1.25⋅102 =
5⋅10−1
Extension Activity
1.25 102
Answers will vary. Sample responses: 5 10−1
1.3 × 10³ × 4 × 10³ = 5.2 × 10³
2.6 × 10³ × 3 × 10³ = 7.8 × 10³
3.4 × 10³ × 2 × 10³ = 6.8 × 10³

Homework

1. (1.2 × 1.3) × (103 × 10-1)
1.56 × 103 + (-1)
1.56 × 102

⋅

0.25 ⋅ 102
10−1

0.25 × 102 – (-1)

0.25 × 103

2.5 × 102
6.4⋅103
3. (2.4 × 3.1) × (104 × 101) 4. 4⋅104 =
7.44 × 104 + 1
7.44 × 105 6.4 103
4 104
⋅

1.6 ⋅ 103
104

1.6 × 103–4
1.6 × 10-1

5. 6. (1.3 × 6.2) × (10-5 × 10-2)
6 ⋅ 10−1 8.06 × 10-5 + -2
1.5 ⋅ 10−2 = 8.06 × 10-7

6 ⋅ 10−1
1.5 10−2

4 ⋅ 10−1
10−2
4 × 10-1– (-2)

4 × 101

261 Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE

Notes

Copyright © Swun Math Grade 8 Unit 3 Lesson 6 P TE 262

Scientific Notation: Mixed MPs Applied MP
Practice
* Embedded MP
Procedural Lesson
Grade 8 · Unit 3 · Lesson 7 12345678

MC: 8.EE.4 *  * * * *

Problem of the Day Student Journal Pages

144-149

Objective: I will multiply, divide, subtract, and add numbers in scientific notation.

Vocabulary Teacher Resources

Adding & Subtracting in Scientific Notation Considerations:

(4.342 × 10²) + (3.871 × 10³) = Have students refer to previous lessons and apply the
strategies used to simplify expressions in scientific
Convert to same power: method through multiplication and division. Have
(4.342 × 10²) + (38.71 × 10²) students pay attention to precision since they will be
applying various steps. Calculators should be used for
Add decimals: checking their work. For students that continue to
4.342 + 38.71 = 43.052 struggle with the strategies, remind them that they
can also simplify the expressions by changing both
Bring down exponent: numbers out of scientific notation.
43.052 × 10² =
Steps:
Proper Scientific Form 1. Check the operation you are using first.
4.3052 × 10³ 2. If adding or subtracting, convert to the
same exponent.
Multiplying in Scientific Notation 3. Work with coefficients.
1. Multiply coefficients. (Use commutative/associative properties)
2. Add exponents. 4. Work with exponents. (Use exponent rules)
5. Convert answer to proper scientific form.
(3 × 102) ⋅ (5 × 104) =
Application of MPs:
3 × 5 = 15
MP1: How would you describe what you are trying to
102+4 = 106 find?
I am trying to find the sum or the difference of
15 × 106= 1.5 × 107 ____________________________.

Proper Scientific Form MP2: What properties might we use to find a
solution?
Dividing in Scientific Notation A property that we might use to find a
1. Divide coefficients. solution can be the __________________.
2. Subtract exponents.

(15 × 106) ÷ (3 × 102) =

15
3 =5
106−2 = 104

5 × 104

263 Copyright © Swun Math Grade 8 Unit 3 Lesson 7 P TE

Input/Model

(Teacher Presents)

Directions: Simplify the expression. Write solution in scientific notation.
1. (3.6 × 109) + (0.7 × 1010)

Solution:
• Change (0.7 × 1010) into the correct form of scientific notation (7 × 109)
• (3.6 × 109) + (7 × 109)
• (3.6 + 7) × 109
• 10.6 × 109 Rewrite in scientific notation.
• 1.06 × 1010
Answer: 1.06 × 1010

2. (1.3 × 101) × (1.2 × 1010)

Solution: 264Grade 8 Unit 3 Lesson 7 P TE
• (1.3 × 1.2) × (101 × 1010)
• 1.56 × 101 + 10
• 1.56 × 1011
Answer: 1.56 × 1011

Copyright © Swun Math

Structured Guided Practice

(A/B Partners Practice)
Directions: Simplify the expression. Write solution in scientific notation.

1. (0.61 × 10-5) – (4 × 10-6)

Solution:
2.1 × 10-6

2. (5.4 × 1010) ÷ (1.5 × 10-7)

Solution:
3.6 × 1017

265 Copyright © Swun Math Grade 8 Unit 3 Lesson 7 P TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Simplify the expression. Write solution in scientific notation.
1. (15.3 × 102) + (6 × 104)

Solution: 266Grade 8 Unit 3 Lesson 7 P TE
6.153 × 104

2. (6.48 × 10-3) ÷ (5.4 × 104)

Solution:
1.2 × 10-7

Copyright © Swun Math

Student Practice Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 7: Scientific Notation:
Mixed Practice

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

1. (5.4 × 103)2 2. (2.7 × 10-1) ÷ (0.3 × 103)

Solution: Solution:
2.916 × 107 9 × 10-4

3. (1.34 × 10-2) + (7 × 10-2) 4. (1325 × 10-5) – (0.12 × 10-1)

Solution: Solution:
8.34 × 10-2 1.25 × 10-3

5. (3.2 × 10-2) × (6.7 × 102) 6. 2.5 billion + 1.8 million

Solution: Solution:
2.144 × 101 2501.8 × 106 (not in scientific notation)
2.5018 × 109
267 Copyright © Swun Math
Grade 8 Unit 3 Lesson 7 P TE

Challenge Problems

Directions: Solve. You will notice that these are longer and more complex, but still follow the
same patterns as the previous ones.

1. (2.15 × 1010) ÷ (4 × 107) – (4.6 × 102) 2. (3.3 × 103) × (4.1 × 105) + (7.6 × 108)

Solution:

• (2.15 × 1010) ÷ (4 × 107) – (4.6 × 102)

• 2.15⋅1010 − (4.6 ⋅ 102) Solution:
4⋅107 • (3.3 × 103) × (4.1 × 105) + (7.6 × 108)
1010 • (3.3 × 4.1) × (103 × 105) + (7.6 × 108)
• 2.15 ⋅ 107 − (4.6 ⋅ 102) • (13.52 × 103+5) + (7.6 × 108)
4 • (13.52 × 108) + (7.6 × 108)
• (13.52 + 7.6) × 108
• 0.5375 × 1010–7 – (4.6 × 102) • 21.13 × 108
• (0.5375 × 103) – (4.6 × 102)
• (5.375 × 102) – (4.6 × 102) Answer: 2.113 × 109
• (5.375 – 4.6) × 102
• 0.775 × 102
Answer: 7.75 × 101

Extension Activity

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

* MP4: Apply mathematics in everyday life.

Using only the digits 1-9, create as many true equations as possible. For each equation, the
digits are only to be used once.

▭.▭ ▭.▭ ▭.▭( × 106) + ( × 106) = × 106

▭.▭ ▭.▭ ▭.▭( × 106) ─ ( × 106) = × 106

Copyright © Swun Math 268Grade 8 Unit 3 Lesson 7 P TE

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

269 Copyright © Swun Math Grade 8 Unit 3 Lesson 7 P TE

Homework Name: ___________________________
Date: ___________________________
Unit 3 · Lesson 7: Scientific Notation:
Mixed Practice

Objective: I will multiply, divide, subtract, and add numbers in scientific notation.

Vocabulary Steps

Adding & Subtracting in Scientific Notation 1. Check the operation you are using first.
2. If adding or subtracting, convert to the same
(4.342 × 10²) + (3.871 × 10³) =
exponent.
Convert to same power: 3. Work with coefficients.
(4.342 × 10²) + (38.71 × 10²)
(Use commutative/associative properties)
Add decimals: 4. Work with exponents. (Use exponent rules)
4.342 + 38.71 = 43.052 5. Convert answer to proper scientific form.

Bring down exponent:
43.052 × 10² =

Proper Scientific Form
4.3052 × 10³

Multiplying in Scientific Notation
1. Multiply coefficients.
2. Add exponents.

(3 × 102) ⋅ (5 × 104) =

3 × 5 = 15

102+4 = 106

15 × 106

1.5 × 107

Proper Scientific Form

Dividing in Scientific Notation
1. Divide coefficients.
2. Subtract exponents.

(15 × 106) ÷ (3 × 102) =

15
3 =5
106−2 = 104

5 × 104

Copyright © Swun Math 270Grade 8 Unit 3 Lesson 7 P TE

Homework

Unit 3 · Lesson 7: Scientific Notation:
Mixed Practice

Example # 1 Example # 2

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

(3.6 × 109) + (0.7 × 1010) (1.3 × 101) × (1.2 × 1010)

Solution: Solution:
• We need to change (0.7 × 1010) into the correct form of • (1.3 × 1.2) × (101 × 1010)

scientific notation (7 × 109) • 1.56 × 101 + 10
• (3.6 × 109) + (7 × 109)
• (3.6 + 7) × 109 • 1.56 × 1011
• 10.6 × 109 Rewrite in the correct form of scientific Answer: 1.56 × 1011

notation.
• 1.06 × 1010
Answer: 1.06 × 1010

271 Copyright © Swun Math Grade 8 Unit 3 Lesson 7 P TE

Homework

Unit 3 · Lesson 7: Scientific Notation:
Mixed Practice

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

1. (5.4 × 102) × (0.51 × 103) 2. (23.85 × 102) ÷ (5.3 × 101)

3. (0.42 × 104) + (4.5 × 103) 4. (2.6 × 106)2

Copyright © Swun Math 272Grade 8 Unit 3 Lesson 7 P TE

Homework 6. (1.65 × 103) + (3.1 × 102)

Unit 3 · Lesson 7: Scientific Notation:
Mixed Practice

5. (6 × 104) – (15 × 103)

Explain the steps you used to solve problem number _______.

______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

273 Copyright © Swun Math Grade 8 Unit 3 Lesson 7 P TE

Answer Key

Extension Activity 2. (23.85 × 102) ÷ (5.3 × 101) not in scientific notation

Answers will vary. Sample responses: (2.385 × 103) ÷ (5.3 × 101)
Addition .
1.4 × 106 + 8.3 × 106 = 9.7 × 106 . ⋅
2.3 × 106 + 4.5 × 106 = 6.8 × 106
Subtraction 0.45 × 103-1
8.7 × 106 ─ 2.3 × 106 = 6.4 × 106
9.8 × 106 ─ 6.7 × 106 = 3.1 × 106 0.45 × 102 not in scientific notation

Homework

1. (5.4 × 102) × (0.51 × 103) not in scientific notation
(5.4 × 102) × (5.1 × 102)
(5.4 × 5.1) × (102 × 102)
27.54 × 104 not in scientific notation
2.754 × 105

4.5 × 101

3. (0.42 × 104) + (4.5 × 103) not in scientific notation 4. (2.6)2 × (106)2
(4.2 × 103) + (4.5 × 103) 6.76 × 106 × 2
(4.2 + 4.5) × 103 6.76 × 1012
8.7 × 103
6. (1.65 × 103) + (3.1 × 102) do not have the same
5. (6 × 104) – (15 × 103) not in scientific notation exponent
(6 × 104) – (1.5 × 104) (1.65 × 101 × 102) + (3.1 × 102)
(6 – 1.5) × 104
4.5 × 104 (16.5 × 102) + (3.1 × 102)
(16.5 + 3.1) × 102
19.6 × 102 not in scientific notation
1.96 × 103

Copyright © Swun Math 274Grade 8 Unit 3 Lesson 7 P TE

Scientific Notation MPs Applied MP

Math Task * Embedded MP

Grade 8 · Unit 3 · Lesson 8 12345678

MC: 8.EE.4 * ** * *

Student Journal Pages

150-151

Objective: I will demonstrate how to multiply or divide numbers in scientific notation.

Student Practice

• Explain the problem and ask students to independently solve the problem on
their recording sheet.

• While students are working, look for 3 - 4 student examples to review during
presentations.

Reaching Consensus

• Students listen to other members explain how they solved the task.
• Students reach consensus on the answer, not on the solution process.

Student Presentations

• When selecting students to give presentations, choose those who will provide the
greatest teaching opportunity.

• Students who completed the Student Practice incorrectly and received help during
Reaching Consensus should present their mistake and how they corrected it.

275 Copyright © Swun Math Grade 8 Unit 3 Lesson 8 T TE

Final Check for Understanding

• Are students able to articulate metacognition?
• Are students able to articulate what they would do differently to solve the problem?
• How did you solve the problem?
• Are the students’ answers reasonable?
• How would you describe the problem in your own words?
• In what way does this problem connect to other mathematical concepts?
• What approach are you considering trying first?

Reflective Closure

• Were students able to demonstrate how to multiply or divide numbers in scientific
notation?

• Were students able to verbalize and use mathematical language?

Answer Key 2. 7.685 × 10-1
4. 5.2206 × 1010
Homework

1. 2.5 × 10-4
3. 1.37124 × 1013

Copyright © Swun Math Grade 8 Unit 3 Lesson 8 T TE

276

Math Task Name: ____________________________
Date: ____________________________
Unit 3 · Lesson 8: Scientific Notation

Directions: Use different methods to simplify the following expressions. Then rewrite answers
in a notation other than scientific notation.

1. (5.6 × 105) ÷ (2 × 106) ─ (1.4 × 10–1)

2. (45 × 102) × (4.7 × 109) + (5.2 × 10²)

3. (356 × 102) × (9.8 × 102) ÷ (2.8 × 105)

1. Solution: 2. Solution: 3. Solution:
• Simplify multiplication portion
• (5.6 × 105) ÷ (2 × 106) • Simplify multiplication portion
first.
• 5.6⋅105 = • (45 × 102) × (4.7 × 109) first.
2⋅106 • (45 × 4.7) × (102 × 109)
105 • 211.5 × 102+9 • [(356 × 102) × (9.8 × 102)] ÷ (2.8 ×
• 5.6 ⋅ 106 • 211.5 × 1011 (not scientific
2 105)
105 notation)
• 2.8 ⋅ 106 • 2.115 × 1013 • [(356 × 9.8) × (102 × 102)] ÷ (2.8 ×

• (2.8 × 105–6 ) ─ (1.4 × 10–1) Answer: 2.115 × 1013 105)

Answer: 1.4 × 10–1 • (3488.8 × 104) ÷ (2.8 × 105)

• Needs to be rewritten in

scientific notation

• (3.4888 × 107) ÷ (2.8 × 105)

• 3.4888 ⋅107
2.8⋅105
107
• 3.4888 ⋅ 105
2.8

• 1.246 × 107-5

Answer: 1. 246 × 102

277 Copyright © Swun Math Grade 8 Unit 3 Lesson 8 T TE

Homework Name: ____________________________
Date: ____________________________
Unit 3 · Lesson 8: Scientific Notation
2. (4.3036 × 104) ÷ (5.6 × 104)
Directions: Solve.
1. (1.15 × 105) ÷ (4.6 × 108)

3. (5.86 × 108) × (2.34 × 104) 4. (6.78 × 107) × (7.7 × 102)

Copyright © Swun Math Grade 8 Unit 3 Lesson 8 T TE

278

Unit 3 ∙ Constructed Response Name: ____________________________
Scientific Notation
Date: ______________________________
Task 1: Scientific Notation
Student Journal Pages
Directions: Read and solve each problem.
152-155

1. The table below shows measurements written in different forms. Complete the table
for a-f, and give real-life examples that could have these measurements.

Decimal or Scientific Notation Example
Whole Number
a

b

c

d

e

f

279 Copyright © Swun Math Grade 8 Unit 3 Constructed Response TE

Unit 3 ∙ Constructed Response
Scientific Notation

2. Craig and Suzanne are monitoring a large colony of honey bees. During the spring
months, they estimate the colony has a population of 6.53 x 10 4 . In the winter
months, the population drops by 7.89 x 103 . What is the total population of the
honey bee colony in the winter months?

a. Write an equation to find the population in the winter months.

Equation: __________________________________

b. Solve the equation written in 2a.

Answer: __________________________________

Copyright © Swun Math 280Grade 8 Unit 3 Constructed Response TE

Unit 3 ∙ Constructed Response
Scientific Notation

3. This table shows the area of each of the five oceans on Earth. Use this information
to answer the following questions.

Ocean Name Size
Arctic Ocean ?
Atlantic Ocean
Indian Ocean
Pacific Ocean
Southern Ocean

a. How many times greater is the area of the Indian Ocean than the Southern Ocean?
Show work, and give the answer in scientific notation.

Answer: __________________________________

b. Explain the process to prove that your answer in 3a is correct.

Process Explanation of Steps

281 Copyright © Swun Math Grade 8 Unit 3 Constructed Response TE

Unit 3 ∙ Constructed Response
Scientific Notation

c. The area of the Pacific Ocean is 1.18 x 10 1 times larger than the area of the Arctic
Ocean. What is the area of the Pacific Ocean?
Show work, and give the answer in scientific notation.

Answer: __________________________________

d. What math concepts helped you find the solution in 3a and 3c? Explain which
mathematical notations were important to finding each solution.

Copyright © Swun Math 282Grade 8 Unit 3 Constructed Response TE

Unit 3 ∙ Constructed Response Unit 1 ∙ Constructed
Scientific Notation ResponseSCORING RUBRIC

TASK 1: Scientific Notation

# Answer/Exemplar Standard Points

1a. 8.EE.3 6

Decimal or Whole Scientific Notation Example
Number Height of a tree

a 40 m Length of a cockroach
Distance between
b 0.035 m planets
Thickness of a coin
c 60,000,000 m
Length of a truck
d 0.0009 m m Height of a mountain

3m
e

f 9,000 m

2a. 6.53 x 10 4 ─ 7.89 x 10 3 8.EE.4 1
1
2b. 5.741 x 104 8.EE.4 1
3a. 3.626 x 10 0 8.EE.4 1

3b. Process: Student should multiply by 8.EE.4 1
1
Explanation of Steps: To prove that my answer is correct I must

multiply the size of the Southern Ocean, , by my answer

from 3a. The product is the size of the Indian Ocean that I was

given in the table, which means that my answer is correct.

3c. 2.52 x 10 8 8.EE.4

3d. In 3a, I had to divide the area of the Indian Ocean by the area of the
Southern Ocean. So, I subtracted the exponents to find the final
power of ten in my answer. For 3c, I was given how many times
larger the area of the Pacific Ocean was than the area of the
Atlantic Ocean, and given the size of the Atlantic Ocean. Therefore,
I only had to multiply these two numbers. I added the exponents
to find the final power of ten in my answer.

283 Copyright © Swun Math Grade 8 Unit 3 Constructed Response Rubric TE

NUnotites1 ∙ Constructed Response
The Number System — Part 1

Copyright © Swun Math 284Grade 8 Unit 3 Constructed Response Rubric TE

Grade 8

Unit 4: Linear Equations

Table of Contents

Lesson # Lesson Type Lesson Title MC MP Applied Page

1C Model Equations 8.EE.7 4, 5 287

2P One-Step Equations 8.EE.7 1, 7 295

3C Collect Like Terms 8.EE.7b 1, 6 307

4P Two-Step Equations 8.EE.7b 6, 7 315
5C
6P Simplify Expressions: Distributive 8.EE.7b 7, 8 327
7C Property
8P
Solve Equations: Distributive Property 8.EE.7b 2, 7 335

Equations with Variables on Both 8.EE.7b 7, 8 345
Sides

Equations with Rational Numbers 8.EE.7b 7, 8 353

9C Equations: No Solution or Many 8.EE.7a 2, 8 363

10 P Equations: No Solution or Many 8.EE.7a 1, 7 371

11 P Write Linear Equations 8.EE.7b 4, 6 381

12 MT Linear Equations 8.EE.7 393

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

285 Copyright © Swun Math Grade 8 Unit 4 Table of Contents TE

Grade 8 • Unit 4
Table of Contents, continued

Constructed Response

Task Lesson Title MC Page

1 Solve Equations with the Distributive Property 8.EE.7b 398
8.EE.7ab 401
2 Solve Equations with One or More Solutions 8.EE.7b 404
406
3 Real-World Application: Write & Solve Equations

Constructed Response Scoring Guide

Materials Needed

Lesson Materials

2, 3, 7, 9 Algebra tiles (some optional)

12 Graph paper

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

Copyright © Swun Math 286Grade 8 Unit 4 Table of Contents TE

Model Equations MPs Applied MP
* Embedded MP
Conceptual Lesson
Grade 8 · Unit 4 · Lesson 1 123 4 5 678

MC: 8.EE.7 *  *

Problem of the Day Student Journal Pages

Objective: I will solve one-step equations using visual models. 158-161

Vocabulary Teacher Resources

Inverse Operations: operations that undo each Considerations:
other; the opposite operation
Review the commutative property of addition
Addition Subtraction and multiplication. Explicitly instruct students
Multiplication Division about using the inverse as this becomes
important in later lessons. Area models and tape
Area Model: using area to multiply two quantities diagrams (bar models) were first introduced in
the upper elementary grades. Review these
23 × 37 = 7 visual models as needed. The intention of this
30 lesson is to create and use visual models, as a
strategy to solve, before moving to the abstract
skills of using properties.

20 x 30 = 600 20 x 7= 140

20 Steps:
1. Identify the variable and draw a model.
3 30 x 3 = 90 3 x 7 = 21 2. Solve for the variable using reasoning and
logic.

600 + 140 + 90 + 21 = 851

Application of MPs:

Tape Diagram: a visual model representing parts MP4: How does making a model help you .
of a whole; also called a bar model understand the variable?
The model helps me to understand the
x + 13 = 20 variable by
13
MP5: How do you decide which model to use?
20 To figure out which model I should create, I
.

287 Copyright © Swun Math Grade 8 Unit 4 Lesson 1 C TE

Input/Model

(Teacher Presents)

Directions: Draw a model for the given equation. Solve.

1. 11.3 × 7.2 = x 2. 5 = 7.5

Solution: 0.3 Solution:
• Step 1 - Draw a model: • Step 1 - Draw a model:

11 7.5

7 × 11 = 77 7 × 0.3= 2.1

7

0.2 0.2 × 11 = 2.2 0.2 × 0.3 = 0.06 • Step 2 - Solve using reason or logic: I think, what
number times 5 equals 7.5? I divide 7.5 by 5, and
get 1.5.

• Step 2 – Solve by multiplying each box. Answer: = 1.5
• Step 3 – Add the products of each box together.

77 + 2.2 + 2.1 + .06 = x

Answer: = 81.36

Copyright © Swun Math 288Grade 8 Unit 4 Lesson 1 C TE

Structured Guided Practice

(A/B Partners Practice)

Directions: Draw a model for the given equation. Solve.

1. 4 = 2.8 2. 4.5 × 10.3 = p

Solution: 2.8 Solution: 4 0.5

10 40 5
Answer: = 0.7 0.3
1.2 .15

Answer: p = 46.35

289 Copyright © Swun Math Grade 8 Unit 4 Lesson 1 C TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Draw a model for the given equation. Solve.

1. 12.6 + 8.2 + v = 25.0 2. 2.5k = 325

Solution: 25 Solution: 325 0.5
12.6 8.2

v

Answer: = 4.2 Answer: = 130

Closure

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

MP4: How does making a model help you understand the variable?
MP5: How do you decide which model to use?

Copyright © Swun Math 290Grade 8 Unit 4 Lesson 1 C TE

Homework Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 1: Model Equations

Objective: I will solve one-step equations using visual models.

Vocabulary Steps

Area Model: using area to multiply two 1. Identify the variable and draw a model.
quantities. 2. Solve for the variable using reasoning and

23 × 37 = logic.

30 7

20 20 × 30 = 600 20 × 7= 140

3 30 × 3 = 90 3 × 7 = 21

600 + 140 + 90 + 21 = 851

Tape Diagram: A visual model representing parts
of a whole; also referred to as a bar model

x + 12 = 20

13

20

1: Equations with One Variable

Example # 1 Example # 2

Directions: Draw a model for the given equation. Solve.

x + 7 = 15 5 = 7.5

Solution: Solution: 7.5

• Step 1 - Draw a model: • Step 1 - Draw a model:

15

7

• Step 2 - Solve using reason or logic: I think, what number • Step 2 - Solve using reason or logic: I think, what number times 5
plus 7 gives me 15? I can mentally subtract 15 – 7 to find equals 7.5? I divide 7.5 by 5, and get 1.5.
the missing number, 8.
Answer: = 1.5
Answer: x = 8

291 Copyright © Swun Math Grade 8 Unit 4 Lesson 1 C TE

Homework Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 1: Model Equations

Directions: Solve for the variable. Draw a model if necessary.

1. 52.4 + u + 38 = 144.9 2. 16.9 + w = 54.71

3. 14.6 × 9.1 = q 4. 3r = 22.83

5. 13x = 19.5 6. 1 × 3.8k = 292.6

Copyright © Swun Math 292Grade 8 Unit 4 Lesson 1 C TE

Answer Key

Homework

1. u = 54.5 2. w = 37.81

144.9 54.71

52.4 38 16.9

3. q = 132.86 feet2 0.6 4. r = 7.61 22.83

14 9 × 0.6=
06 5.4

9 × 14 =

9 126

0.1 0.1 × 14 = 1.4 0.1 × 0.6 =
0.06

5. x = 1.5 meters 6. k = 77

292.6 0.8


293 Copyright © Swun Math Grade 8 Unit 4 Lesson 1 C TE

Notes

Copyright © Swun Math 294Grade 8 Unit 4 Lesson 1 C TE

One-Step Equations MPs Applied MP

Procedural Lesson * Embedded MP

Grade 8 · Unit 4 · Lesson 2 12345678

MC: 8.EE.7 * * * **

Problem of the Day Student Journal Pages

Objective: I will solve one-step equations by applying inverse operations. 162-167

Vocabulary Teacher Resources

Inverse Operations: operations that undo each Considerations:
other; the opposite operation
Review inverse operations with students. Be sure to
Addition Subtraction reinforce the idea that an equation must stay equal.
Multiplication Division Whatever is done to one side, must be done to the
other. Use a visual of a balance if needed. Revisit the
Additive Inverse: a number and its opposite idea that when applying the additive inverse, a zero
whose sum is 0; also called a zero pair pair emerges, and when applying the multiplicative
inverse, a set of factors with a product of 1 emerges.
(─3) + (3) = 0

Number Additive Inverse Steps:
y + 12 = 20 1. Work on the side with the variable.
─12 ─12 2. Apply the additive inverse.
y=8 3. Apply the multiplicative inverse.
4. Check the solution by substituting.

Multiplicative Inverse: a number and its Application of MPs:
reciprocal; when these numbers are multiplied,
the product is 1. MP1: What inverse operation is needed to solve
?
−5 ⋅ 1 = 1
−5 The inverse operation needed to solve the

problem is .

Number Multiplicative Inverse .

4n = 12 MP7: What patterns do you find when solving one-
4 12
4=4 step equations?

n=3 If there is a coefficient, then I need to apply
the inverse.

If there is a constant, then I need to apply the
inverse.

295 Copyright © Swun Math Grade 8 Unit 4 Lesson 2 P TE