Pre-Algebra Chapter 3

Exponents and Roots

Name: ___________________________ Period: _______

Common Core State Standards CC.8.EE.1 - Know and apply the properties of integer exponents to generate equivalent

numerical expressions.

CC.8.EE.2 - Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x2 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is√2 irrational.

CC.8.EE.3 - Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is that the other.

CC.8.EE.4 - Perform operations with numbers expressed in scientific notation, including

problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.

CC.8.NS.1 - Understand informally that every number has a decimal expansion; the rational

numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.

CC.8.NS.2 - Use rational approximations of irrational numbers to compare the size of irrational

numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

CC.8.G.6 - Explain a proof of the Pythagorean Theorem converse. CC.8.G.7 - Apply the Pythagorean Theorem to determine unknown side lengths in rigth

triangles in real-world and mathematical problems in two and three dimensions. CC.8.G.8 - Apply the Pythagorean Theorem to find the distance between two points in a

coordinate system.

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Scope and Sequence Day 1 Lesson 3-1 Day 11 Lesson 3-6

Day 2 Lesson 3-2 Day 12 Lesson 3-6

Day 3 Lesson 3-2 Day 13 Lesson 3-7

Day 4 Lesson 3-3 Day 14 Lesson 3-7

Day 5 Lesson 3-4 Day 15 Extension

Day 6 Lesson 3-4 Day 16 Lesson 3-8

Day 7 Tech Lab Day 17 Lesson 3-9

Day 8 Quiz Day 18 Review Day 1

Day 9 Lesson 3-5 Day 19 Review Day 2

Day 10 Lesson 3-5 Day 20 Test

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IXL Modules SMART Score of 80 is required

Due the day of the exam

Lesson 1 8.F.6 Understanding negative exponents

8.F.7 Evaluate negative exponents

Lesson 2 8.F.8 Multiplication with exponents

8.F.9 Division with exponents

8.F.10 Multiplication and division with exponents

8.F.11 Power rule

Lesson 3 8.G.1 Convert between standard and scientific notation

Lesson 4 8.G.3 Multiply numbers written in scientific notation

8.G.4 Divide numbers written in scientific notation

Lesson 5 8.F.13 Square roots of perfect squares

8.F.14 Positive and negative square roots

8.F.16 Relationship between squares and square roots

Lesson 6 8.F.15 Estimate positive and negative square roots

8.F.18 Cube roots of perfect cubes

8.F.20 Estimate cube roots

Lesson 7 8.A.8 Classify Numbers

Lesson 8 8.O.1 Pythagorean theorem: find the length of the hypotenuse

8.O.2 Pythagorean theorem: find the missing leg length

8.O.3 Pythagorean theorem: find the perimeter

8.O.4 Pythagorean theorem: word problems

Lesson 9 8.O.5 Converse of the Pythagorean theorem: is it a right triangle?

8.P.4 Distance between two points

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Lesson 3-1

Integer Exponents

Warm-Up

Examples: Using a Pattern to Simplify Negative Exponents

Simplify. Write in decimal form.

10-2

10-1

10-8

10-9

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Examples: Evaluating Negative Exponents

Simplify. 5-3

(-10)-3

4-2

(-7)-4

Examples: Using the Order of Operations

Evaluate 5 - (6 - 4)-3 + (-2)0

Evaluate 3 + (7 - 4)-2 + (-8)0

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Lesson 3-2

Properties of Exponents

Warm-Up

Examples: Multiplying Powers with the Same Base

Multiply. Write the product as one power.

66 63•

n5 n7•

25 2•

244 244•

42 44•

x2 x3•

x5 y2•

412 417•

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Examples: Dividing Powers with the Same Base

Divide. Write the quotient as one power.

75

73

x10

x9

99

92

e10

e5

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Examples: Raising a Power to a Power

Simplify.

(54)2 (67)9

(172)-20

(33)4 (48)2

(134

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Lesson 3-3

Scientific Notation

Warm-Up

Numbers written in scientific notation are written as ____________ factors. One factor is a

number ____________ than or equal to 1 and ____________ than 10. The other factor is a

____________ of 10.

Examples: Translating Scientific Notation to Standard Notation

Write the number in standard notation.

1.35 x 105

2.7 x 10-3

2.01 x 104

2.87 x 109

1.9 x 10-5

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Examples: Translating Standard Notation to Scientific Notation

Write 0.00709 in scientific notation.

Write 0.000811 in scientific notation.

Examples: Application

A pencil is 18.7 cm long. If you were to lay 10,000 pencils end-to-end, how many millimeters long would they be? Write the answer in scientific notation.

An oil rig can hoist 2,400,000 pounds with its main derrick. It distributes the weight evenly between 8 cables. What’s the weight that each cable can hold? Answer in scientific notation.

A certain cell has a diameter of approximately 4.11 x 10-5 meters. A second cell has as a diameter of 1.5 x 10-5 meters. Which cell has a greater diameter?

A certain cell has a diameter of approximately 5 x 10-3 meters. A second cell has as a diameter of 5.11 x 10-3 meters. Which cell has a greater diameter?

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Lesson 3-4

Operating With Scientific Notation

Warm-Up

Examples: Division With Scientific Notation

Pluto was demoted from planet to dwarf planet in 2006, in part because of its small size. The mass of Pluto is about 1.3 x 1022 kg. About how many times smaller is Pluto’s mass than Earth’s mass? (Earth’s mass is 5.97 x 1024 kg)

About how many times greater is the mass of Saturn than the mass of Earth? Write your answer in scientific notation. (Saturn’s mass is 5.69 x 1026)

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Examples: Multiplication with Scientific Notation

The mass of Venus is about 66 times the mass of the moon. What is the mass of the moon? Write your answer in scientific notation. (Mass of Venus is 4.87 x 1024)

The average mass of a grain of sand on a beach is about 1.5 x 10-5. There are about 6.1 x 1012 grains of sand in a beach volleyball court. What is the mass of the grains of sand in the beach volleyball court?

Examples: Addition and Subtraction with Scientific Notation

The water in Mono Lake, CA, was used for residents of LA. As a result, the lake’s volume, in acre-feet, dropped from 4.3 x 107 to 2.1 x 107 from 1941 to 1982. After becoming protected, the lake increased in volume by 5.0 x 106 acre-feet in the next 20 years. What was its volume in 2002?

How much greater is the mass of Neptune than the mass of Earth? Write your answer in scientific notation. (Earth mass is 5.97 x 1024, Neptune mass is 1.02 x 1026)

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Lesson 3-5

Equations, Tables and Graphs

Warm-Up

A number that when multiplied by ____________ to form a product is the square root of that

product. Taking the square root of a number is the ____________ of squaring the number.

Every positive number has two square roots, one ____________ and one ____________. The

radical symbol indicates the nonnegative or principal square root. They symbol - is used to√  √ 

indicate a negative square root.

The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number

that has ____________ as its square roots. Other perfect squares include 1, 4, 9, 25 and 64.

Examples: Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number.

A. 49

B. 100 C. 225

A. 25

B. 144 C. 289

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Examples: Application

A square window has an area of 169 square inches. How wide is the window?

A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?

Examples: Evaluating Expressions Involving Square Roots Simplify the expression.

3 + 7 √36

     √1625 + 4

3

2 + 4 √25

     √ 218 + 4

1

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Lesson 3-6

Estimating Square Roots

Warm-Up

Examples: Estimating Square Roots of Numbers The square root is between two integers. Name the integers. Explain your answer.

 √55

-  √90

 √80

-  √45

Examples: Application

You want to sew a fringe on a square tablecloth with an area of 500 square inches. Calculate the length of each side of the tablecloth and the length of fringe you will need to the nearest tenth of an inch.

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A tent was advertised in the newspaper as having an enclosed square area of 168 ft2. What is the approximate length of the sides of the square area? Round your answer to the nearest foot.

Examples: Approximating Square Roots to the Nearest Hundredth Approximate to the nearest hundredth.

 √141

 √240

Examples: Using a Calculator to Estimate the Value of a Square Root

Use a calculator to find the square root. Round to the nearest tenth.

 √600

 √800

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Lesson 3-7

The Real Numbers

Warm-Up

Irrational numbers can only be written as decimals that do ____________ terminate or

repeat. If a whole number is not a ____________ square, then its square root is an irrational

number.

The set of real numbers consists of the set of ____________ numbers and the set of

____________ numbers.

Examples: Classifying Real Numbers Write all names that apply to each number.

 √5

-12.75

 √9

-35.9

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Examples: Determining the Classification of All Numbers

State if each number is rational, irrational or not a real number.

     √21

30

     √− 4

√94

 √23

09

     √− 7

 √8164

The Density Property of real numbers states that ____________ any two real numbers is

another real number. This property is also true for rational numbers, but ____________ for

whole numbers or integers.

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Examples: Applying the Density Property of Real Numbers

Find a real number between 3 and 3 .52

53

Find a real number between 4 and 4 .73

74

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Lesson 3-8

The Pythagorean Theorem

Warm-Up

Examples: Finding the Length of a Hypotenuse Find the length of the hypotenuse to the nearest hundredth.

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Examples: Finding the Length of a Leg in a Right Triangle

Solve for the unknown side in the right triangle to the nearest tenth.

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Examples: Using the Pythagorean Theorem for Measurement

Two airplanes leave the same airport at the same time. The first plane flies to a landing strip 350 miles south, while the other plane flies to an airport 725 miles west. How far apart are the two planes after they land?

Two birds leave the same spot at the same time. The first bird flies to his nest 11 miles sout, while the other bird flies to his nest 7 miles west. How far apart are the two birds after they reach their nests?

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Lesson 3-9

Applying the Pythagorean Theorem and Its Converse

Warm-Up

Examples: Marketing Application

What is the diagonal length of the projector screen?

What is the diagonal length of the projector screen?

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Examples: Finding the Distance on the Coordinate Plane

Find the distances between the points to the nearest tenth.

J and K

L and M

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J and L

K and M

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Examples: Identifying a Right Triangle

Tell whether the given side lengths form a right triangle.

9, 12, 15

8, 10, 13

5, 6, 9

8, 15, 17

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