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)
Copyright © Swun Math Grade 8 Unit 3 Lesson 3 C TE 228
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