Lesson 1: Exponential Notation 8•1 Lesson 1

Lesson 1
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 1: Exponential Notation
Exit Ticket
1.
a.
Express the following in exponential notation:
(−13) × ⋯ × (−13)
�������������
35 𝑡𝑖𝑚𝑒𝑠
b.
2.
Will the product be positive or negative?
Fill in the blank:
2
2 4
2
× ⋯× = � �
��
3
3
3 �����
_______𝑡𝑖𝑚𝑒𝑠
3.
Arnie wrote:
(−3.1)
(−3.1)
⋯ ×��
��
�������
���� = −3.14
4 𝑡𝑖𝑚𝑒𝑠
Is Arnie correct in his notation? Why or why not?
Lesson 1:
Date:
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Exponential Notation
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Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 2: Multiplication of Numbers in Exponential Form
Exit Ticket
Simplify each of the following numerical expressions as much as possible:
1.
Let 𝑎 and 𝑏 be positive integers. 23𝑎 × 23𝑏 =
2.
53 × 25 =
3.
Let 𝑥 and 𝑦 be positive integers and𝑥 > 𝑦.
4.
213
8
11𝑥
11𝑦
=
=
Lesson 2:
Date:
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Multiplication of Numbers in Exponential Form
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Lesson 3
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 3: Numbers in Exponential Form Raised to a Power
Exit Ticket
Write each answer as a simplified expression that is equivalent to the given one.
1.
(93 )6 =
2.
(1132 × 37 × 514 )3 =
3.
Let 𝑥, 𝑦, 𝑧 be numbers. (𝑥 2 𝑦𝑧 4 )3 =
4.
Let 𝑥, 𝑦, 𝑧 be numbers and let 𝑚, 𝑛, 𝑝, 𝑞 be positive integers. (𝑥 𝑚 𝑦 𝑛 𝑧 𝑝 )𝑞 =
5.
48
58
=
Lesson 3:
Date:
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Numbers in Exponential Form Raised to a Power
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Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 4: Numbers Raised to the Zeroth Power
Exit Ticket
1.
Simplify the following expression as much as possible.
410 0
∙7 =
410
2.
Let 𝑎 and 𝑏 be two numbers. Use the distributive law and the definition of zeroth power to show that the numbers
(𝑎0 + 𝑏 0 )𝑎0 and (𝑎0 + 𝑏 0 )𝑏 0 are equal.
Lesson 4:
Date:
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Numbers Raised to the Zeroth Power
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Lesson 4 Sprint
NYS COMMON CORE MATHEMATICS CURRICULUM
8•1
Sprint 1: Rewrite each item as an equivalent expression in exponential notation. All letters denote numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
22 ∙ 23 =
23.
22 ∙ 25 =
25.
38 ∙ 31 =
27.
76 ∙ 72 =
29.
76 ∙ 74 =
31.
1116 ∙ 11 =
33.
212 ∙ 24 =
35.
995 ∙ 992 =
37.
997 ∙ 994 =
39.
68 ∙ 62 =
41.
𝑟8 ∙ 𝑟2 =
43.
22 ∙ 24 =
24.
37 ∙ 31 =
26.
39 ∙ 31 =
28.
76 ∙ 73 =
30.
1115 ∙ 11 =
32.
212 ∙ 22 =
34.
212 ∙ 26 =
36.
996 ∙ 993 =
38.
58 ∙ 52 =
40.
78 ∙ 72 =
42.
𝑠8 ∙ 𝑠2 =
44.
Lesson 4:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
63 ∙ 62 =
62 ∙ 63 =
(−8)3 ∙ (−8)7 =
(−8)7 ∙ (−8)3 =
(0.2)3 ∙ (0.2)7 =
(0.2)7 ∙ (0.2)3 =
(−2)12 ∙ (−2)1 =
(−2.7)12 ∙ (−2.7)1 =
1.16 ∙ 1.19 =
576 ∙ 579 =
𝑥6 ∙ 𝑥9 =
28 ∙ 4 =
28 ∙ 42 =
28 ∙ 16 =
16 ∙ 43 =
32 ∙ 9 =
32 ∙ 27 =
32 ∙ 81 =
54 ∙ 25 =
54 ∙ 125 =
8 ∙ 210 =
16 ∙ 210 =
Numbers Raised to the Zeroth Power
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Lesson 4 Sprint
NYS COMMON CORE MATHEMATICS CURRICULUM
8•1
Sprint 2: Rewrite each item as an equivalent expression in exponential notation. All letters denote numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
52 ∙ 53 =
23.
52 ∙ 55 =
25.
28 ∙ 21 =
27.
46 ∙ 42 =
29.
46 ∙ 44 =
31.
816 ∙ 8 =
33.
912 ∙ 94 =
35.
235 ∙ 232 =
37.
237 ∙ 234 =
39.
157 ∙ 153 =
41.
𝑥7 ∙ 𝑥3 =
43.
52 ∙ 54 =
24.
27 ∙ 21 =
26.
29 ∙ 21 =
28.
46 ∙ 43 =
30.
815 ∙ 8 =
32.
912 ∙ 92 =
34.
912 ∙ 96 =
36.
236 ∙ 233 =
38.
147 ∙ 143 =
40.
167 ∙ 163 =
42.
𝑦7 ∙ 𝑦3 =
44.
Lesson 4:
Date:
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73 ∙ 72 =
72 ∙ 73 =
(−4)3 ∙ (−4)11 =
(−4)11 ∙ (−4)3 =
(0.2)3 ∙ (0.2)11 =
(0.2)11 ∙ (0.2)3 =
(−2)9 ∙ (−2)5 =
(−2.7)5 ∙ (−2.7)9 =
3.16 ∙ 3.16 =
576 ∙ 576 =
𝑧6 ∙ 𝑧6 =
4 ∙ 28 =
42 ∙ 28 =
16 ∙ 28 =
16 ∙ 42 =
9 ∙ 32 =
33 ∙ 9 =
33 ∙ 27 =
56 ∙ 25 =
56 ∙ 125 =
210 ∙ 4 =
210 ∙ 16 =
Numbers Raised to the Zeroth Power
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Lesson 5
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 5: Negative Exponents and the Laws of Exponents
Exit Ticket
Write each answer as a simplified expression that is equivalent to the given one.
1.
76543−4 =
2.
Let 𝑓 be a nonzero number. 𝑓 −4 =
3.
671 × 28796−1 =
4.
Let 𝑎, 𝑏 be numbers (𝑏 ≠ 0). 𝑎𝑏 −1 =
5.
Let 𝑔 be a nonzero number.
1
𝑔−1
Lesson 5:
Date:
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=
Negative Exponents and the Laws of Exponents
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Lesson 6
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 6: Proofs of Laws of Exponents
Exit Ticket
1.
Show directly that for any positive integer 𝑥, 𝑥 −5 ∙ 𝑥 −7 = 𝑥 −12 .
2.
Show directly that for any positive integer 𝑥, (𝑥 −2 )−3 = 𝑥 6 .
Lesson 6:
Date:
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Proofs of Laws of Exponents
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Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 7: Magnitude
Exit Ticket
1.
Let 𝑀𝑀 = 118,526.65902. Find the smallest power of 10 that will exceed 𝑀𝑀.
2.
Scott said that 0.09 was a bigger number than 0.1. Use powers of 10 to show that he is wrong.
Lesson 7:
Date:
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Magnitude
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Lesson 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 8: Estimating Quantities
Exit Ticket
Most English-speaking countries use the short-scale naming system, in which a trillion is expressed as
1,000,000,000,000. Some other countries use the long-scale naming system, in which a trillion is expressed as
1,000,000,000,000,000,000,000. Express each number as a single-digit integer times a power of ten. How many times
greater is the long-scale naming system than the short-scale?
Lesson 8:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Estimating Quantities
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Lesson 8 Sprint
NYS COMMON CORE MATHEMATICS CURRICULUM
8•1
Sprint 1: Simplify each item as much as possible. Answers should have only positive exponents. All letters denote
numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
45 ∙ 4−4 =
15.
45 ∙ 4−2 =
17.
7−4 ∙ 710 =
19.
9−4 ∙ 9−3 =
21.
9−4 ∙ 9−1 =
23.
50 ∙ 51 =
25.
50 ∙ 53 =
27.
45 ∙ 4−3 =
16.
7−4 ∙ 711 =
18.
7−4 ∙ 79 =
20.
9−4 ∙ 9−2 =
22.
9−4 ∙ 90 =
24.
50 ∙ 52 =
26.
(123 )9 =
28.
Lesson 8:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
(123 )10 =
(123 )11 =
(7−3 )−8 =
(7−3 )−9 =
(7−3 )−10 =
1 9
� � =
2
1 8
� � =
2
1 7
� � =
2
1 6
� � =
2
(3𝑥)5 =
(3𝑥)7 =
(3𝑥)9 =
(8−2 )3 =
(8−3 )3 =
Estimating Quantities
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Lesson 8 Sprint
NYS COMMON CORE MATHEMATICS CURRICULUM
29.
30.
31.
32.
33.
34.
35.
36.
(8−4 )3 =
37.
(220 )55 =
39.
(220 )50 =
38.
(220 )60 =
40.
1 −5
� � =
11
41.
1 −6
� � =
11
42.
1 −7
� � =
11
43.
56−23
=
56−34
44.
Lesson 8:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
8•1
87−12
=
87−34
23−15
=
23−17
(−2)−12 ∙ (−2)1 =
2𝑦
=
𝑦3
5𝑥𝑦 7
=
15𝑥 7 𝑦
16𝑥 6 𝑦 9
=
8𝑥 −5 𝑦 −11
(23 ∙ 4)−5 =
(9−8 )(27−2 ) =
Estimating Quantities
7/24/13
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Lesson 8 Sprint
NYS COMMON CORE MATHEMATICS CURRICULUM
8•1
Sprint 2: Simplify each item as much as possible. Answers should have only positive exponents. All letters denote
numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
115 ∙ 11−4 =
15.
115 ∙ 11−2 =
17.
7−8 ∙ 79 =
19.
(−6)−4 ∙ (−6)−3 =
21.
(−6)−4 ∙ (−6)−1 =
23.
𝑥 0 ∙ 𝑥1 =
25.
𝑥0 ∙ 𝑥3 =
27.
115 ∙ 11−3 =
16.
7−7 ∙ 79 =
18.
7−9 ∙ 79 =
20.
(−6)−4 ∙ (−6)−2 =
22.
(−6)−4 ∙ (−6)0 =
24.
𝑥0 ∙ 𝑥2 =
26.
(125 )9 =
28.
Lesson 8:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
(126 )9 =
(127 )9 =
(7−3 )−4 =
(7−4 )−4 =
(7−5 )−4 =
3 8
� � =
7
3 7
� � =
7
3 6
� � =
7
3 5
� � =
7
(18𝑥𝑦)5 =
(18𝑥𝑦)7 =
(18𝑥𝑦)9 =
(5.2−2 )3 =
(5.2−3 )3 =
Estimating Quantities
7/24/13
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Lesson 8 Sprint
NYS COMMON CORE MATHEMATICS CURRICULUM
29.
30.
31.
32.
33.
34.
35.
36.
(5.2−4 )3
(226 )0
37.
=
38.
=
(2212 )0
39.
=
(2218 )0 =
40.
4 −5
� � =
5
41.
4 −6
� � =
5
4 −7
� � =
5
−11
6−2
� 5�
7
42.
43.
44.
=
Lesson 8:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
−12
6−2
� 5�
7
−13
6−2
� 5�
7
−15
6−2
� 5�
7
42𝑎𝑏10
=
14𝑎−9 𝑏
8•1
=
=
=
5𝑥𝑦 7
=
25𝑥 7 𝑦
22𝑎15 𝑏 32
=
121𝑎𝑏 −5
(7−8 ∙ 49)−5 =
(369 )(216−2 ) =
Estimating Quantities
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Lesson 9
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 9: Scientific Notation
Exit Ticket
1.
The approximate total surface area of Earth is 5.1 × 108 𝑘𝑚2 . Salt water has an approximate surface area of
352,000,000 𝑘𝑚2 and freshwater has an approximate surface area of 9 × 106 𝑘𝑚2 . How much of Earth’s surface is
covered by water, including both salt and fresh water? Write your answer in scientific notation.
2.
How much of Earth’s surface is covered by land? Write your answer in scientific notation.
3.
Approximately how many times greater is the amount of Earth’s surface that is covered by water, compared to the
amount of Earth’s surface that is covered by land?
Lesson 9:
Date:
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Scientific Notation
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Lesson 10
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 10: Operations with Numbers in Scientific Notation
Exit Ticket
1.
The speed of light is 3 × 108 meters per second. The sun is approximately 230,000,000,000 meters from Mars.
How many seconds does it take for sunlight to reach Mars?
2.
If the sun is approximately 1.5 × 1011 meters from Earth, what is the approximate distance from Earth to Mars?
Lesson 10:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Operations with Numbers in Scientific Notation
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Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 11: Efficacy of the Scientific Notation
Exit Ticket
1.
The two largest mammals on earth are the blue whale and the elephant. An adult male blue whale weighs about
170 tonnes or long tons. (1 tonne = 1000 kg)
Show that the weight of an adult blue whale is 1.7 × 105 kg.
2.
An adult male elephant weighs about 9.07 × 103 kg.
Compute how many times heavier an adult male blue whale is than an adult male elephant (that is, find the value of
the ratio). Round your final answer to the nearest one.
Lesson 11:
Date:
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Efficacy of the Scientific Notation
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NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
Lesson 12
8•1
Date____________________
Lesson 12: Choice of Unit
Exit Ticket
1.
The table below shows an approximation of the national debt at the beginning of each decade over the last century.
Choose a unit that would make a discussion of the increase in the national debt easier. Name your unit and explain
your choice.
Year
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2.
Debt in Dollars
2.1 × 109
2.7 × 109
2.6 × 1010
1.6 × 1010
4.3 × 1010
2.6 × 1011
2.9 × 1011
3.7 × 1011
9.1 × 1011
3.2 × 1012
5.7 × 1012
Using the new unit you have defined, rewrite the debt for years 1900, 1930, 1960, and 2000.
Lesson 12:
Date:
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Choice of Unit
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Lesson 13
NYS COMMON CORE MATHEMATICS CURRICULUM
Name ___________________________________________________
8•1
Date____________________
Lesson 13: Comparison of Numbers Written in Scientific Notation
and Interpreting Scientific Notation Using Technology
Exit Ticket
1.
Compare 2.01 × 1015 and 2.8 × 1013 . Which number is larger?
2.
The wavelength of the color red is about 6.5 × 10−9 m. The wavelength of the color blue is about 4.75 × 10−9 m.
Show that the wavelength of red is longer than the wavelength of blue.
Lesson 13:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Comparison of Numbers Written in Scientific Notation and
Interpreting Scientific Notation Using Technology
7/24/13
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