Pre-Algebra Chapter 3 Exponents and Roots
|
|
- Valerie Ferguson
- 6 years ago
- Views:
Transcription
1 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 x 2 = p and x 2 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is 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 - CC.8.G.7 - CC.8.G.8 - Explain a proof of the Pythagorean Theorem converse. Apply the Pythagorean Theorem to determine unknown side lengths in rigth triangles in real-world and mathematical problems in two and three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 1
2 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 2
3 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 8.F.10 8.F.11 Division with exponents Multiplication and division with exponents 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 8.F.16 Positive and negative square roots Relationship between squares and square roots Lesson 6 8.F.15 Estimate positive and negative square roots 8.F.18 8.F.20 Cube roots of perfect cubes 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 8.O.3 8.O.4 Pythagorean theorem: find the missing leg length Pythagorean theorem: find the perimeter 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 3
4 Lesson 3-1 Integer Exponents Warm-Up Examples: Using a Pattern to Simplify Negative Exponents Simplify. Write in decimal form
5 Examples: Evaluating Negative Exponents Simplify. 5-3 (-10) (-7) -4 Examples: Using the Order of Operations Evaluate 5 - (6-4) -3 + (-2) 0 Evaluate 3 + (7-4) -2 + (-8) 0 5
6 Lesson 3-2 Properties of Exponents Warm-Up Examples: Multiplying Powers with the Same Base Multiply. Write the product as one power n 5 n x 2 x 3 x 5 y
7 Examples: Dividing Powers with the Same Base Divide. Write the quotient as one power. 7 5 x x e 10 e 5 7
8 Examples: Raising a Power to a Power Simplify. (5 4 ) 2 (6 7 ) 9 (17 2 ) -20 (3 3 ) 4 (4 8 ) 2 (13 4 8
9 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 x x x x x
10 Examples: Translating Standard Notation to Scientific Notation Write in scientific notation. Write 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? 10
11 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 kg. About how many times smaller is Pluto s mass than Earth s mass? (Earth s mass is 5.97 x 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 ) 11
12 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 ) The average mass of a grain of sand on a beach is about 1.5 x There are about 6.1 x 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 10 7 to 2.1 x 10 7 from 1941 to After becoming protected, the lake increased in volume by 5.0 x 10 6 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 10 24, Neptune mass is 1.02 x ) 12
13 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
14 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? Simplify the expression. Examples: Evaluating Expressions Involving Square Roots
15 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 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. 15
16 A tent was advertised in the newspaper as having an enclosed square area of 168 ft 2. 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 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
17 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. Write all names that apply to each number Examples: Classifying Real Numbers
18 Examples: Determining the Classification of All Numbers State if each number is rational, irrational or not a real number 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. 18
19 Examples: Applying the Density Property of Real Numbers 2 3 Find a real number between 3 5 and Find a real number between 4 7 and
20 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. 20
21 Examples: Finding the Length of a Leg in a Right Triangle Solve for the unknown side in the right triangle to the nearest tenth. 21
22 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? 22
23 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? 23
24 Examples: Finding the Distance on the Coordinate Plane Find the distances between the points to the nearest tenth. J and K L and M 24
25 J and L K and M 25
26 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 26
Exponents 4-1. Lesson Objectives. Vocabulary. Additional Examples. Evaluate expressions with exponents. exponential form (p. 162) exponent (p.
LESSON 4-1 Exponents Lesson Objectives Evaluate expressions with exponents Vocabulary exponential form (p. 16) exponent (p. 16) base (p. 16) power (p. 16) Additional Examples Example 1 Write in exponential
More informationHow can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots
. Approximating Square Roots How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots Work with a partner. Archimedes was a Greek mathematician,
More informationNOTES: Chapter 11. Radicals & Radical Equations. Algebra 1B COLYER Fall Student Name:
NOTES: Chapter 11 Radicals & Radical Equations Algebra 1B COLYER Fall 2016 Student Name: Page 2 Section 3.8 ~ Finding and Estimating Square Roots Radical: A symbol use to represent a. Radicand: The number
More informationIntroductory Algebra Chapter 9 Review
Introductory Algebra Chapter 9 Review Objective [9.1a] Find the principal square roots and their opposites of the whole numbers from 0 2 to 2 2. The principal square root of a number n, denoted n,is the
More informationNAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
More information5-7 The Pythagorean Theorem
5-7 The Pythagorean Theorem Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Classify each triangle by its angle measures. 1. 2. acute right 3. Simplify 12 4. If a = 6, b = 7, and c = 12, find
More information2nd 9 Weeks Test 2. Rankin County Assessment CCSS Math 8th Grade ID: Sample Item Not Available
Rankin County Assessment CCSS Math 8th Grade ID: 201585 2nd 9 Weeks Test 2 Directions: Read the question. Fill in the bubble next to the corresponding question number on your answer sheet. Sample Question
More informationMath 8 Curriculum Map and I Can Statements Diane Hamilton
Math 8 Curriculum Map and I Can Statements 203 204 Diane Hamilton Unit : Numbers Review A Whole Numbers Place Value 2 Identify the place value of a whole number 2 Decimals Place Value 2 Identify the place
More informationSection 9.2 Objective: Students will be able to define and work with irrational numbers.
Lincoln Public Schools Math 8 McDougall Littell Middle School Math Course 3 Chapter 9 Items marked A, B, C are increasing in difficulty. Group A questions are the most basic while Group C are the most
More information8 th Grade Intensive Math
8 th Grade Intensive Math Ready Florida MAFS Student Edition August-September 2014 Lesson 1 Part 1: Introduction Properties of Integer Exponents Develop Skills and Strategies MAFS 8.EE.1.1 In the past,
More informationCopy Material. Grade 8 Unit 7. Introduction to Irrational Numbers Using Geometry. Eureka Math. Eureka Math
Copy Material Grade 8 Unit 7 Introduction to Irrational Numbers Using Geometry Eureka Math Eureka Math Lesson 1 Name Date Lesson 1: The Pythagorean Theorem Exit Ticket 1. Determine the length of the unknown
More informationIrrational Numbers Study Guide
Square Roots and Cube Roots Positive Square Roots A positive number whose square is equal to a positive number b is denoted by the symbol b. The symbol b is automatically denotes a positive number. The
More informationPre-Algebra Curriculum Map Unit 1: The Number System M08.A-N Essential Questions Standards Content Skills Vocabulary
Unit 1: The Number System M08.A-N Essential Questions Standards Content Skills Vocabulary Why is it helpful to write numbers in different ways? M08.A-N.1.1.1 Determine whether a number is rational or irrational.
More informationLESSON 9.1 ROOTS AND RADICALS
LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical
More informationSquares and Square Roots. The Pythagorean Theorem. Similar Figures and Indirect Measurement
Lesson 9-1 Lesson 9-2 Lesson 9-3 Lesson 9-4 Lesson 9-5 Lesson 9-6 Squares and Square Roots The Real Number System Triangles The Pythagorean Theorem The Distance Formula Similar Figures and Indirect Measurement
More informationBig Ideas: determine an approximate value of a radical expression using a variety of methods. REVIEW Radicals
Big Ideas: determine an approximate value of a radical expression using a variety of methods. REVIEW N.RN. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
More informationSimplifying Radicals. multiplication and division properties of square roots. Property Multiplication Property of Square Roots
10-2 Simplifying Radicals Content Standard Prepares for A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Objective To simplify
More informationUsing the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles
Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean
More informationChapter 8 RADICAL EXPRESSIONS AND EQUATIONS
Name: Instructor: Date: Section: Chapter 8 RADICAL EXPRESSIONS AND EQUATIONS 8.1 Introduction to Radical Expressions Learning Objectives a Find the principal square roots and their opposites of the whole
More informationRadicals and Radical Functions
0 Radicals and Radical Functions So far we have discussed polynomial and rational expressions and functions. In this chapter, we study algebraic expressions that contain radicals. For example, + 2,, or.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Rationalize the denominator and simplify. 1 1) B) C) 1 D) 1 ) Identify the pair of like
More informationControlling the Population
Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1
More informationSkill: determine an approximate value of a radical expression using a variety of methods.
Skill: determine an approximate value of a radical expression using a variety of methods. N.RN.A. Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational
More informationAssignment. Get Radical or (Be) 2! Radicals and the Pythagorean Theorem. Simplify the radical expression. 45x 3 y 7
Assignment Assignment for Lesson.1 Name Date Get Radical or (Be) 2! Radicals and the Pythagorean Theorem Simplify the radical expression. 1. 60 2. 108. 28x 5 4. 45x y 7 5. 1 49 6. 7. 6 8. 2 12 9. A plane
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name Date Get Radical or (Be)! Radicals and the Pythagorean Theorem Vocabulary Write the term that best completes each statement. 1. An expression that includes
More informationCommon Core Coach. Mathematics. First Edition
Common Core Coach Mathematics 8 First Edition Contents Domain 1 The Number System...4 Lesson 1 Understanding Rational and Irrational Numbers...6 Lesson 2 Estimating the Value of Irrational Expressions...
More informationMath 8A. Content Description Content Location U01-L01-A05. Learn: Text. Video U04-L18-A05. Learn: Text and. Video. Learn: Text and U04-L19-A03.
Know that there are numbers that are not rational, and approximate them by rational numbers. NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number
More informationMy Math Plan Assessment #1 Study Guide
My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.
More informationRemember, you may not use a calculator when you take the assessment test.
Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.
More informationFind the side length of each square tile. Use a complete sentence to explain how you found your answer cm 2
Assignment Assignment for Lesson.1 Name Date Tiling a Bathroom Wall Simplifying Square Root Expressions Find the side length of each square tile. Use a complete sentence to explain how you found your answer.
More informationChapter 7 Review Sections labeled at the start of the related problems
Chapter 7 Review Sections labeled at the start of the related problems.6 State whether the equation is an example of the product rule, the quotient rule, the power rule, raising a product to a power, or
More informationMathematics: Pre-Algebra Eight
Mathematics: Pre-Algebra Eight Students in 8 th Grade Pre-Algebra will study expressions and equations using one or two unknown values. Students will be introduced to the concept of a mathematical function
More informationNew Rochelle High School Geometry Summer Assignment
NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and
More informationSkills available for New York eighth grade math standards
Skills available for New York eighth grade math standards Standards are in bold, followed by a list of the IXL math skills that are aligned to that standard. Students can practice these skills online at
More informationRational Numbers and Equations
http://uva.onlinejudge.org/external/113/p11327.png Rational Numbers and Equations http://math.phillipmartin.info/math_rational_numbers.gif http://www.karlscalculus.org/counting.gif 1 Rational Numbers Understand
More informationBlock 2 ~ The Pythagorean Theorem Self-Assessment. Progress (shade this in) Name Per. Track your understanding. Lesson #
Block 2 ~ The Pythagorean Theorem Self-Assessment Track your understanding. Lesson # 2.1 2.2 2.3 2. 2. 2.7 Target I can recognize and find the values of perfect squares. I can estimate the value of square
More informationContents. 2 Lesson. Common Core State Standards. Lesson 1 Irrational Numbers Lesson 2 Square Roots and Cube Roots... 14
Contents Common Core State Standards Lesson 1 Irrational Numbers.... 4 Lesson 2 Square Roots and Cube Roots... 14 Lesson 3 Scientific Notation... 24 Lesson 4 Comparing Proportional Relationships... 34
More informationNote-Taking Guides. How to use these documents for success
1 Note-Taking Guides How to use these documents for success Print all the pages for the module. Open the first lesson on the computer. Fill in the guide as you read. Do the practice problems on notebook
More informationMy Math Chapter 1, Lesson 7
24 Compute with numbers written in scientific notation; Apply word problem strategies to identify the appropriate operation; Evaluate a newspaper headline using exponents and scientific notation. Common
More informationSpring Lake Middle School- Accelerated Math 7 Curriculum Map Updated: January 2018
Domain Standard Learning Targets Resources Ratios and Proportional Relationships 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured
More informationMathematics Pacing. Instruction: 9/7/17 10/31/17 Assessment: 11/1/17 11/8/17. # STUDENT LEARNING OBJECTIVES NJSLS Resources
# STUDENT LEARNING OBJECTIVES NJSLS Resources 1 Describe real-world situations in which (positive and negative) rational numbers are combined, emphasizing rational numbers that combine to make 0. Represent
More informationSummary for a n = b b number of real roots when n is even number of real roots when n is odd
Day 15 7.1 Roots and Radical Expressions Warm Up Write each number as a square of a number. For example: 25 = 5 2. 1. 64 2. 0.09 3. Write each expression as a square of an expression. For example: 4. x
More informationPre-Algebra Unit 2. Rational & Irrational Numbers. Name
Pre-Algebra Unit 2 Rational & Irrational Numbers Name Core Table 2 Pre-Algebra Name: Unit 2 Rational & Irrational Numbers Core: Table: 2.1.1 Define Rational Numbers Vocabulary: Real Numbers the set of
More informationUnit 8 Practice Problems Lesson 1
Unit 8 Practice Problems Lesson 1 Problem 1 Find the area of each square. Each grid square represents 1 square unit. 17 square units. 0 square units 3. 13 square units 4. 37 square units Problem Find the
More informationDISCOVERY TEST A: AUGUST CCSS
8 th Grade Mathematics Quarter Curriculum Map 20-204 Unit : Real Numbers and the Coordinate Plane st Nine Weeks Suggested Instructional Days: 20-24 Unit Summary (Learning Target/Goal): Develop an understanding
More informationEquations and Inequalities. College Algebra
Equations and Inequalities College Algebra Radical Equations Radical Equations: are equations that contain variables in the radicand How to Solve a Radical Equation: 1. Isolate the radical expression on
More informationKey Learning: Students will demonstrate an understanding of expression and equations with respect to linear equations. Unit Essential Question
Student Learning Map for Unit Topic: PA Common Core: M08.B-E.1 Demonstrate an understanding of expressions and equations with radicals and integer exponents. M08.B-E.2 Understand the connections between
More informationRadicals and connections to geometry
Algebra Assignment Sheet Name: Date: Period: # Radicals and connections to geometry (1) Worksheet (need) (2) Page 514 #10 46 Left () Page 514 #1 49 right (4) Page 719 #18 0 Even (5) Page 719 #1 9 all (6)
More informationCommon Core State Standards for Mathematics Grade 8 Houghton Mifflin Harcourt Go Math, Grade 8 Common Core Edition 2014
Correlation to the Common Core State Standards for Mathematics Grade 8 Houghton Mifflin Harcourt Go Math, Grade 8 Common Core Edition 2014 Houghton Mifflin Harcourt Go Math, Grade 8 Common Core Edition
More informationGrade 8. Concepts and Procedures. The Number System. Expressions and Equations
Grade 8 Concepts and Procedures The Number System Target A: Know that there are numbers that are not rational and approximate them by rational numbers. identify pi as not rational, classify numbers as
More informationChapter Review. Write each expression using exponents SOLUTION: The base 6 is a factor 5 times. So, the exponent is 5.
Write each expression using exponents. 1. 6 6 6 6 6 2. 4 The base 6 is a factor 5 times. So, the exponent is 5. 6 6 6 6 6 = 6 5 6 5 The base 4 is a factor 1 time. So, the exponent is 1. 4 = 4 1 4 1 3.
More informationLESSON 11 PRACTICE PROBLEMS
LESSON 11 PRACTICE PROBLEMS 1. a. Determine the volume of each of the figures shown below. Round your answers to the nearest integer and include appropriate units of b. Determine the volume of each of
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationMath-2A Lesson 2-1. Number Systems
Math-A Lesson -1 Number Systems Natural Numbers Whole Numbers Lesson 1-1 Vocabulary Integers Rational Numbers Irrational Numbers Real Numbers Imaginary Numbers Complex Numbers Closure Why do we need numbers?
More informationFree Pre-Algebra Lesson 59! page 1
Free Pre-Algebra Lesson 59! page 1 Lesson 59: Review for Final Exam Section VII. Proportions and Percents Comprehensive Practice Lessons 37-42 Lesson 37: Scale and Proportion Skill: Write ratios of sides
More informationAcademic Outcomes Mathematics
Academic Outcomes Mathematics Mathematic Content Standards Overview: TK/ Kindergarten Counting and Cardinality: Know number names and the count sequence. Count to tell the number of objects. Compare numbers.
More informationWarm Up Lesson Presentation Lesson Quiz. Holt Algebra 2 2
8-8 Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Simplify each expression. Assume all variables are positive. 1. 2. 3. 4. Write each expression in radical form. 5. 6. Objective Solve radical equations
More informationQ4 Week 2 HW Exponents and Equations
Name: lass: ate: I: Q4 Week 2 HW Exponents and Equations Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Write (b)(b)(b)(b)(b) in exponential form. a. 5
More informationPRE-ALGEBRA SUMMARY WHOLE NUMBERS
PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in
More informationLevel 1: Simplifying (Reducing) Radicals: 1 1 = 1 = 2 2 = 4 = 3 3 = 9 = 4 4 = 16 = 5 5 = 25 = 6 6 = 36 = 7 7 = 49 =
Name Period Date Unit 5:Special Right Triangles and TrigonometryNotes Packet #1 Section 7.2/7.3: Radicals, Pythagorean Theorem, Special Right Triangles (PA) CRS NCP 24-27 Work with squares and square roots
More informationName: Period: Unit 3 Modeling with Radical and Rational Functions
Name: Period: Unit Modeling with Radical and Rational Functions 1 Equivalent Forms of Exponential Expressions Before we begin today s lesson, how much do you remember about exponents? Use expanded form
More informationHigh School Preparation for Algebra 1
High School Preparation for Algebra 1 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence
More informationCommon Core Coach. Mathematics. First Edition
Common Core Coach Mathematics 8 First Edition Contents Domain 1 The Number System...4 Lesson 1 Understanding Rational and Irrational Numbers...6 Lesson 2 Estimating the Value of Irrational Expressions...
More informationEureka Math. Grade 8, Module 7. Student File_B. Contains Exit Ticket and Assessment Materials
A Story of Ratios Eureka Math Grade 8, Module 7 Student File_B Contains and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced,
More informationCK-12 Middle School Math Grade 8
CK-12 Middle School Math aligned with COMMON CORE MATH STATE STANDARDS INITIATIVE Middle School Standards for Math Content Common Core Math Standards for CK-12 Middle School Math The Number System (8.NS)
More informationMATH Spring 2010 Topics per Section
MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line
More informationMATHEMATICS Grade 7 Standard: Number, Number Sense and Operations. Organizing Topic Benchmark Indicator Number and Number Systems
Standard: Number, Number Sense and Operations Number and Number Systems A. Represent and compare numbers less than 0 through familiar applications and extending the number line. 1. Demonstrate an understanding
More informationSummer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages
8 Common Core Mathematics 6 6 Vocabulary absolute value additive inverse property adjacent angles the distance between a number and zero on a number line. Example: the absolute value of negative seven
More information7th and 8th Grade Pre-Algebra - General and Resource Room
Davison Community Schools ADVISORY CURRICULUM COUNCIL Phase II, April 18, 2016 Lorie Smith, Amy Gottlieb, Amber Rogers, Janet Davidson, Matt Lobban, Sarah-Smith Clark Course Essential Questions: 7th and
More informationA is any of ordered pairs. The set of all. components of the pairs is called the of the
Section 8.1: INTRODUCTION TO FUNCTIONS When you are done with your homework you should be able to Find the domain and range of a relation Determine whether a relation is a function Evaluate a function
More informationChapter 1: Fundamentals of Algebra Lecture notes Math 1010
Section 1.1: The Real Number System Definition of set and subset A set is a collection of objects and its objects are called members. If all the members of a set A are also members of a set B, then A is
More informationCROSSWalk. for the Co on Core State Standards
Mathematics Grade 8 CROSSWalk for the Co on Core State Standards Table of Contents Common Core State Standards Correlation Chart... 6 Domain 1 The Number System.... Domain 1: Diagnostic Assessment for
More informationMath Review Packet. for Pre-Algebra to Algebra 1
Math Review Packet for Pre-Algebra to Algebra 1 Epressions, Equations, Eponents, Scientific Notation, Linear Functions, Proportions, Pythagorean Theorem 2016 Math in the Middle Evaluating Algebraic Epressions
More information7 = 8 (Type a simplified fraction.)
Student: Date: Assignment: Exponential and Radical Equations 1. Perform the indicated computation. Write the answer in scientific notation. 3. 10 6 10. 3. 4. 3. 10 6 10 = (Use the multiplication symbol
More informationMath 46 Final Exam Review Packet
Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.
More information6-5 Study Guide and Intervention
6-5 Study Guide and Intervention Simplify Radicals Product Property of Radicals For any real numbers a and b, and any integer n > 1: 1. if n is even and a and b are both nonnegative, then n ab n a n b.
More informationDetermine whether the given lengths can be side lengths of a right triangle. 1. 6, 7, , 15, , 4, 5
Algebra Test Review Name Instructor Hr/Blk Determine whether the given lengths can be side lengths of a right triangle. 1., 7, 8. 17, 1, 8.,, For the values given, a and b are legs of a right triangle.
More informationAlignments to SuccessMaker. Providing rigorous intervention for K-8 learners with unparalleled precision
Alignments to SuccessMaker Providing rigorous intervention for K-8 learners with unparalleled precision Lesson 1-6 Lesson 1-7 Lesson 1-4 Lesson 1-5 Lesson 1-8 Lesson 1-9 Lesson 1-10 Lesson 2-5 Lesson 2-6
More information10.1. Square Roots and Square- Root Functions 2/20/2018. Exponents and Radicals. Radical Expressions and Functions
10 Exponents and Radicals 10.1 Radical Expressions and Functions 10.2 Rational Numbers as Exponents 10.3 Multiplying Radical Expressions 10.4 Dividing Radical Expressions 10.5 Expressions Containing Several
More informationDays 1-2: Perfect Squares/ Perfect Cubes Days 3-4: Square Roots of Perfect Squares /Cube Roots of
Common Core 8 Math Regular Pacing Guide Unit & Days Objectives Topic Performance Tasks QUARTER 1 PACING GUIDE Unit 1: Number Sense-Squares, Square Roots, Cubes & Cube Roots 8.EE.2 Use square root and cube
More informationMath-2 Section 1-1. Number Systems
Math- Section 1-1 Number Systems Natural Numbers Whole Numbers Lesson 1-1 Vocabulary Integers Rational Numbers Irrational Numbers Real Numbers Imaginary Numbers Complex Numbers Closure Why do we need numbers?
More informationMay 16, Aim: To review for Quadratic Function Exam #2 Homework: Study Review Materials. Warm Up - Solve using factoring: 5x 2 + 7x + 2 = 0
Aim: To review for Quadratic Function Exam #2 Homework: Study Review Materials Warm Up - Solve using factoring: 5x 2 + 7x + 2 = 0 Review Topic Index 1. Consecutive Integer Word Problems 2. Pythagorean
More informationRadical and. Exponential Functions
Preview of Algebra II Radical and Exponential Functions 11A Radical Functions and Equations 11-1 Square-Root Functions 11-2 Radical Expressions 11-3 Adding and Subtracting Radical Expressions 11-4 Multiplying
More informationTopic 16 - Radicals. 1. Definition of a Radicals
Topic 16 - Radicals 1. Definition of a Radicals Definition: In Mathematics an efficient way of representing repeated multiplication is by using the notation a n, such terms are called exponentials where
More informationReview Topics. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Topics MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. On the real number line, label the points with the given coordinates. 1) 11,- 11 1)
More informationUnit 3 Day 13 Review 1
Unit 3 Day 13 Review 1 Warm-up! Graph the following functions, with at least 4 points. Find the domain and range. Then, tell how they are changed from their parent graph. (Hint: Remember that the order
More informationMiddle School Math Course 3. Correlation of the ALEKS course Middle School Math Course 3 to the Common Core State Standards for Grade 8 (2010)
Middle School Math Course 3 Correlation of the ALEKS course Middle School Math Course 3 to the Common Core State Standards for Grade 8 (2010) 8.NS: The Number System 8.NS.A.1: 8.NS.A.2: = ALEKS course
More informationPRACTICE PROBLEMS CH 8 and Proofs
GEOM PRACTICE PROBLEMS CH 8 and Proofs Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 2 Stud Guide-Chapters 8 and 9 Name Date: Time: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all square roots of the number. ) 600 9,
More informationWhat You ll Learn. or irrational. New Vocabulary perfect square, square root, irrational numbers, real numbers. Why Learn This?
-. Plan - Exploring Square Roots and Irrational Numbers Objective To find and estimate square roots and to classify numbers as rational or irrational Examples Finding Square Roots of Perfect Squares Estimating
More informationUnit 1 Foundations of Algebra
1 Unit 1 Foundations of Algebra Real Number System 2 A. Real Number System 1. Counting Numbers (Natural Numbers) {1,2,3,4, } 2. Whole Numbers { 0,1,2,3,4, } 3. Integers - Negative and Positive Whole Numbers
More information8-6. Square Roots and Cube Roots. Vocabulary. Areas of Squares and Powers as Squares. Activity 1. Lesson
Lesson 8-6 Square Roots and Cube Roots BIG IDEA If a fi rst number is the square (or the cube) of a second number, then the second number is a square root (or cube root) of the fi rst. Areas of Squares
More informationVisit us at: for a wealth of information about college mathematics placement testing!
North Carolina Early Mathematics Placement Testing Program, 9--4. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution and Answer to Question # will be provided net Monday, 9-8-4 North Carolina Early Mathematics
More informationFlorida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper
Florida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper Whole Numbers MDECL1: Perform operations on whole numbers (with applications,
More informationMath K-1 CCRS Level A Alignment College & Career Readiness Standards Version: April 2017
Math K-1 CCRS Level A Alignment Standard Math K Lessons Math 1 Lessons Number and Operations: Base Ten Understand place value 6 Compare 1, 26 Compare 50, 33 Skip Count 5s and 10s, 35 Group 10s, 36 Compare
More informationScott%County%Public%Schools%
!! & & Scott%County%Public%Schools%! Eighth&Grade&Mathematics& Revised&2013& & & Pacing&Guide&and&Curriculum&Map& Scott County Pacing Guide 8 th Grade Math Intro Unit - 4 days School Procedures Classroom
More informationPrerequisites. Introduction CHAPTER OUTLINE
Prerequisites 1 Figure 1 Credit: Andreas Kambanls CHAPTER OUTLINE 1.1 Real Numbers: Algebra Essentials 1.2 Exponents and Scientific Notation 1. Radicals and Rational Expressions 1. Polynomials 1. Factoring
More informationYou will graph and compare positive and negative numbers. 0, 1, 2, 3,... numbers. repeats. 0 number line. opposite. absolute value of a
Algebra 1 Notes Section 2.1: Use Integers and Rational Numbers Name: Hour: Objective: You will graph and compare positive and negative numbers. Vocabulary: I. Whole Numbers: The numbers 0, 1, 2, 3,...
More informationReady To Go On? Skills Intervention 7-1 Integer Exponents
7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:
More information