Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers.
|
|
- Anabel Perkins
- 6 years ago
- Views:
Transcription
1 Real Numbers and The Number Line Properties of Real Numbers Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers. Square root, radicand, radical, perfect square, set, element of a set, subset, rational numbers, natural numbers, whole numbers, integers, irrational numbers, real numbers, inequality
2 Square Root A square root is one of two equal factors of a number. For example one square root of 64 is 8 since 88 or 8 is 64 2 A number like 64, whose square root is a rational number is called a perfect square 5 5or 5 66 or is 25 is 36
3 Square Root The symbol called a radical sign, is used to indicate the principal square root of the expression under the radical sign For example: indicates 64 8 the principalsquare root of 64 8 indicates the negative square root of indicates both square roots of 64 Note that is not the same as is not a real number since no real number multiplied by itself is negative 64
4 Find Square Roots a note: a b a b b c d is undefined for real numbers
5 REAL NUMBERS NATURAL NUMBERS {1, 2, 3, } WHOLE NUMBERS {0, 1, 2, 3, } INTEGERS { -2, -1, 0, 1, 2, } RATIONAL NUMBERS: Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals Irrational numbers Numbers that can not be expressed as rational numbers The set of Real Numbers consists of the set of rational numbers and the set of irrational numbers.
6 Real Numbers Natural Numbers 2 3 Rational Numbers Integers Whole Numbers Irrational Numbers
7 Completeness Property Each point on the number line corresponds to exactly one real number Example: Graph each set of numbers: 5 ( -4, -2, 0,,4, 48, )
8 RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE NATURAL NUMBERS (or counting numbers)
9 RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE WHOLE NUMBERS
10 RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE INTEGERS
11 RATIONAL NUMBERS EXAMPLES OF RATIONAL NUMBERS already fraction a
12 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE
13 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE / 3
14 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE / 5
15 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE {-3, -2, 0, 5}
16 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE {0, 2, 4, 6, }
17 REVIEW TRUE OR FALSE 0 is the smallest natural number. NO, 1 is the smallest
18 REVIEW TRUE OR FALSE -1 is the largest negative integer. YES
19 REVIEW TRUE OR FALSE Name a rational number that is not an integer. Any pure fraction ½, 0.6, 2.3, etc
20 REVIEW Name a whole number that is not a natural number. 0
21 REVIEW Name a whole number that is not an integer. NOT POSSIBLE
22 a. b. c. d. Your turn Example: classify real numbers = ( Repeating decimal)-rational number =11 (natural, whole integer number) Rational number = (which is not repeating or terminating decimal) Irrational number = - 9 (integer) Rational number
23 An inequality is a mathematical sentence that compares the values of two expressions using an inequality symbol. less than less than or equal to greater than greater than or equal to
24 Compare Real numbers Replace the with <, >, or = to make the sentence true. Answer:
25 Order Real numbers from least to greatest 2 Write 4, 0.4,, 2,and -1.5in order from least togreatest 3 Write each number as a decimal From the least to the greatest
26 Properties of Real Numbers Essential Understanding. Relationships that are always true for real numbers are called properties, which are rules used to rewrite and compare expressions. Two algebraic expressions are equivalent expressions if they have the same value for all values of the variable (s).
27 Properties of Real Numbers. Commutative Properties of Addition and Multiplication Let be a and b any real numbers a b b a Associative Properties of Addition and Multiplication Let a,b and c any real numbers a b c a b c and a bc ab c Identity Properties of Addition and Multiplication Zero property of multiplication. Multiplication property of -1. and a b a 0 a and a 1 a a0 0 1a a ba
NAME 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 informationMA 180 Lecture. Chapter 0. College Algebra and Calculus by Larson/Hodgkins. Fundamental Concepts of Algebra
0.) Real Numbers: Order and Absolute Value Definitions: Set: is a collection of objections in mathematics Real Numbers: set of numbers used in arithmetic MA 80 Lecture Chapter 0 College Algebra and Calculus
More informationbc7f2306 Page 1 Name:
Name: Questions 1 through 4 refer to the following: Solve the given inequality and represent the solution set using set notation: 1) 3x 1 < 2(x + 4) or 7x 3 2(x + 1) Questions 5 and 6 refer to the following:
More informationChapter 3: Factors, Roots, and Powers
Chapter 3: Factors, Roots, and Powers Section 3.1 Chapter 3: Factors, Roots, and Powers Section 3.1: Factors and Multiples of Whole Numbers Terminology: Prime Numbers: Any natural number that has exactly
More informationSECTION Types of Real Numbers The natural numbers, positive integers, or counting numbers, are
SECTION.-.3. Types of Real Numbers The natural numbers, positive integers, or counting numbers, are The negative integers are N = {, 2, 3,...}. {..., 4, 3, 2, } The integers are the positive integers,
More informationSkills Practice Skills Practice for Lesson 4.1
Skills Practice Skills Practice for Lesson.1 Name Date Thinking About Numbers Counting Numbers, Whole Numbers, Integers, Rational and Irrational Numbers Vocabulary Define each term in your own words. 1.
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 informationOrder of Operations. Real numbers
Order of Operations When simplifying algebraic expressions we use the following order: 1. Perform operations within a parenthesis. 2. Evaluate exponents. 3. Multiply and divide from left to right. 4. Add
More informationAssociative property
Addition Associative property Closure property Commutative property Composite number Natural numbers (counting numbers) Distributive property for multiplication over addition Divisibility Divisor Factor
More information10.1 Radical Expressions and Functions Math 51 Professor Busken
0. Radical Expressions and Functions Math 5 Professor Busken Objectives Find square roots without a calculator Simplify expressions of the form n a n Evaluate radical functions and find the domain of radical
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 informationReal Numbers. Real numbers are divided into two types, rational numbers and irrational numbers
Real Numbers Real numbers are divided into two types, rational numbers and irrational numbers I. Rational Numbers: Any number that can be expressed as the quotient of two integers. (fraction). Any number
More information5) ) y 20 y 10 =
Name Class Date 7.N.4 Develop the laws of exponents for multiplication and division Directions: Rewrite as a base with an exponent. 1) 3 6 3-4 = 2) x 7 x 17 = 3) 10-8 10 3 = 5) 12-3 = -3 12 6) y 20 y 10
More informationUNIT 4 NOTES: PROPERTIES & EXPRESSIONS
UNIT 4 NOTES: PROPERTIES & EXPRESSIONS Vocabulary Mathematics: (from Greek mathema, knowledge, study, learning ) Is the study of quantity, structure, space, and change. Algebra: Is the branch of mathematics
More informationReference Material /Formulas for Pre-Calculus CP/ H Summer Packet
Reference Material /Formulas for Pre-Calculus CP/ H Summer Packet Week # 1 Order of Operations Step 1 Evaluate expressions inside grouping symbols. Order of Step 2 Evaluate all powers. Operations Step
More information8-5. A rational inequality is an inequality that contains one or more rational expressions. x x 6. 3 by using a graph and a table.
A rational inequality is an inequality that contains one or more rational expressions. x x 3 by using a graph and a table. Use a graph. On a graphing calculator, Y1 = x and Y = 3. x The graph of Y1 is
More informationcorrelated to the Utah 2007 Secondary Math Core Curriculum Algebra 1
correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 McDougal Littell Algebra 1 2007 correlated to the Utah 2007 Secondary Math Core Curriculum Algebra 1 The main goal of Algebra is to
More informationChapter Review. Connecting BIG ideas and Answering the Essential Questions. n+3 I n I 3 I r. 68 Chapter 1 Chapter Review
Chapter Review Connecting BIG ideas and Answering the Essential Questions 1 Variable You can use variables to represent quantities and to write algebraic expressions and equations. / Variables and Expressions
More informationSEVENTH EDITION and EXPANDED SEVENTH EDITION
SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 5-1 Chapter 5 Number Theory and the Real Number System 5.1 Number Theory Number Theory The study of numbers and their properties. The numbers we use to
More informationEvaluate algebraic expressions for given values of the variables.
Algebra I Unit Lesson Title Lesson Objectives 1 FOUNDATIONS OF ALGEBRA Variables and Expressions Exponents and Order of Operations Identify a variable expression and its components: variable, coefficient,
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 information8th Grade Math Definitions
8th Grade Math Definitions Absolute Value: 1. A number s distance from zero. 2. For any x, is defined as follows: x = x, if x < 0; x, if x 0. Acute Angle: An angle whose measure is greater than 0 and less
More informationCHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic
CHAPTER EIGHT: SOLVING QUADRATIC EQUATIONS Review April 9 Test April 17 The most important equations at this level of mathematics are quadratic equations. They can be solved using a graph, a perfect square,
More informationChapter 2. Real Numbers and Monomials. 8/2016 LSowatsky 1
Chapter 2 Real Numbers and Monomials 8/2016 LSowatsky 1 2.1.A Powers and Exponents Main Idea: Use powers and exponents to write large and small numbers. LSowatsky 2 LSowatsky 3 Example: Write each expression
More informationAlgebra SUMMER PACKET Ms. Bank
2016-17 SUMMER PACKET Ms. Bank Just so you know what to expect next year We will use the same text that was used this past year: published by McDougall Littell ISBN-13:978-0-6185-9402-3. Summer Packet
More informationWorking with Square Roots. Return to Table of Contents
Working with Square Roots Return to Table of Contents 36 Square Roots Recall... * Teacher Notes 37 Square Roots All of these numbers can be written with a square. Since the square is the inverse of the
More informationMath 110 (S & E) Textbook: Calculus Early Transcendentals by James Stewart, 7 th Edition
Math 110 (S & E) Textbook: Calculus Early Transcendentals by James Stewart, 7 th Edition 1 Appendix A : Numbers, Inequalities, and Absolute Values Sets A set is a collection of objects with an important
More informationPart 2 - Beginning Algebra Summary
Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian
More informationMA094 Part 2 - Beginning Algebra Summary
MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page
More informationP.1 Prerequisite skills Basic Algebra Skills
P.1 Prerequisite skills Basic Algebra Skills Topics: Evaluate an algebraic expression for given values of variables Combine like terms/simplify algebraic expressions Solve equations for a specified variable
More informationUnit 4, Ongoing Activity, Little Black Book of Algebra II Properties
Unit 4, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 4 - Radicals & the Complex Number System 4.1 Radical Terminology define radical sign,
More informationBecause it is a square root, look to see if you have any pairs of identical numbers. If you do, then group them, if not then you cannot simplify.
Outcome 2A Review Worksheet Outcome #2A Students will demonstrate understanding of irrational numbers by determining if a number is an irrational number, ordering rational numbers, and knowing where they
More informationRational Exponents Connection: Relating Radicals and Rational Exponents. Understanding Real Numbers and Their Properties
Name Class 6- Date Rational Exponents Connection: Relating Radicals and Rational Exponents Essential question: What are rational and irrational numbers and how are radicals related to rational exponents?
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 informationAbsolute Value of a Number
Algebra 1 Notes Section 2.1: Use Integers and Rational Numbers Name: Hour: Objective: Vocabulary: I. Whole Numbers: The numbers II. Integers: The numbers consisting of the (see the glossary) integers,,
More informationNatural Numbers: Also called the counting numbers The set of natural numbers is represented by the symbol,.
Name Period Date: Topic: Real Numbers and Their Graphs Standard: 9-12.A.1.3 Objective: Essential Question: What is the significance of a point on a number line? Determine the relative position on the number
More information( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2
470 Algebra I / Technical Algebra Absolute Value: A number s distance from zero on a number line. A number s absolute value is nonnegative. 4 = 4 = 4 Algebraic Expressions: A mathematical phrase that can
More informationa + b = b + a and a b = b a. (a + b) + c = a + (b + c) and (a b) c = a (b c). a (b + c) = a b + a c and (a + b) c = a c + b c.
Properties of the Integers The set of all integers is the set and the subset of Z given by Z = {, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, }, N = {0, 1, 2, 3, 4, }, is the set of nonnegative integers (also called
More informationProperties of the Integers
Properties of the Integers The set of all integers is the set and the subset of Z given by Z = {, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, }, N = {0, 1, 2, 3, 4, }, is the set of nonnegative integers (also called
More informationMIDTERM REVIEW. Write an algebraic expression to represent the following verbal expressions. 1) Double the difference of a number and 7.
NAME MIDTERM REVIEW DATE Write an algebraic epression to represent the following verbal epressions. 1) Double the difference of a number and 7. ) Find the value of the epression 0. Solve each equation.
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 informationCollege Algebra. Chapter 1 Review Created by: Lauren Atkinson. Math Coordinator, Mary Stangler Center for Academic Success
College Algebra Chapter 1 Review Created by: Lauren Atkinson Math Coordinator, Mary Stangler Center for Academic Success Note: This review is composed of questions from the chapter review at the end of
More informationNatural Numbers Positive Integers. Rational Numbers
Chapter A - - Real Numbers Types of Real Numbers, 2,, 4, Name(s) for the set Natural Numbers Positive Integers Symbol(s) for the set, -, - 2, - Negative integers 0,, 2,, 4, Non- negative integers, -, -
More informationAlgebra 1 First Semester Exam Answer Section
Algebra 1 First Semester Exam Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: Level B REF: MALG0086 TOP: Lesson 1.2 Apply Order of Operations KEY: whole variable evaluate substitute rational expression
More informationVirginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning
BUI L T F O VIR R G INIA 2014 2015 Virginia -Specific Learning Pathways Grades 6-Algebra I: Standards of Learning Table of Contents Grade 6...3 Grade 7...6 Grade 8...9 Algebra I... 11 Grade 6 Virginia
More informationAlgebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , )
Algebra I+ Pacing Guide Days Units Notes Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
More informationSolving Quadratic Equations by Formula
Algebra Unit: 05 Lesson: 0 Complex Numbers All the quadratic equations solved to this point have had two real solutions or roots. In some cases, solutions involved a double root, but there were always
More informationIntermediate Algebra with Applications
Lakeshore Technical College 10-804-118 Intermediate Algebra with Applications Course Outcome Summary Course Information Alternate Title Description Total Credits 4 Total Hours 72 Pre/Corequisites Prerequisite
More information(1) Assignment # 1 Absolute Value. (2) Assignment # 2 Compound Absolute Values. (3) Assignment # 3 Exponents. (4) Assignment # 4 Simplifying Radicals
Alg_0 Packet # The beginning of our Quest () Assignment # Absolute Value () Assignment # Compound Absolute Values () Assignment # Eponents () Assignment # Simplifying Radicals (5) Assignment # 5 Fractional
More informationHONORS GEOMETRY Summer Skills Set
HONORS GEOMETRY Summer Skills Set Algebra Concepts Adding and Subtracting Rational Numbers To add or subtract fractions with the same denominator, add or subtract the numerators and write the sum or difference
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 information1-2 Study Guide and Intervention
1- Study Guide and Intervention Real Numbers All real numbers can be classified as either rational or irrational. The set of rational numbers includes several subsets: natural numbers, whole numbers, and
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 informationAlgebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More informationChapter 1A -- Real Numbers. iff. Math Symbols: Sets of Numbers
Fry Texas A&M University! Fall 2016! Math 150 Notes! Section 1A! Page 1 Chapter 1A -- Real Numbers Math Symbols: iff or Example: Let A = {2, 4, 6, 8, 10, 12, 14, 16,...} and let B = {3, 6, 9, 12, 15, 18,
More informationMath 90 Lecture Notes Chapter 1
Math 90 Lecture Notes Chapter 1 Section 1.1: Introduction to Algebra This textbook stresses Problem Solving! Solving problems is one of the main goals of mathematics. Think of mathematics as a language,
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Order of Operations Expression Variable Coefficient
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 informationChapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra 1 Unit 1: Vocabulary 1) Natural Numbers 2) Whole Numbers 3) Integers 4) Rational Numbers 5) Irrational Numbers 6) Real Numbers 7) Terminating Decimal 8) Repeating Decimal
More informationUnits: 10 high school credits UC requirement category: c General Course Description:
Summer 2015 Units: 10 high school credits UC requirement category: c General Course Description: ALGEBRA I Grades 7-12 This first year course is designed in a comprehensive and cohesive manner ensuring
More informationKnow why the real and complex numbers are each a field, and that particular rings are not fields (e.g., integers, polynomial rings, matrix rings)
COMPETENCY 1.0 ALGEBRA SKILL 1.1 1.1a. ALGEBRAIC STRUCTURES Know why the real and complex numbers are each a field, and that particular rings are not fields (e.g., integers, polynomial rings, matrix rings)
More informationMini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models
Mini Lecture. Introduction to Algebra: Variables and Mathematical Models. Evaluate algebraic expressions.. Translate English phrases into algebraic expressions.. Determine whether a number is a solution
More informationSection 1.1: Variables and Expression
Section 1.1: Variables and Expression Mathematical Quantities: anything that can be measured or counted. some quantities stay constant some quantities change Variables: Symbols used to represent values
More informationAlgebra 1. Standard 1: Operations With Real Numbers Students simplify and compare expressions. They use rational exponents and simplify square roots.
Standard 1: Operations With Real Numbers Students simplify and compare expressions. They use rational exponents and simplify square roots. A1.1.1 Compare real number expressions. A1.1.2 Simplify square
More informationTHE REAL NUMBERS Chapter #4
FOUNDATIONS OF ANALYSIS FALL 2008 TRUE/FALSE QUESTIONS THE REAL NUMBERS Chapter #4 (1) Every element in a field has a multiplicative inverse. (2) In a field the additive inverse of 1 is 0. (3) In a field
More informationChapter R - Review of Basic Algebraic Concepts (26 topics, no due date)
Course Name: Math 00023 Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 08/15/2014 End: 08/15/2015 Course Content: 245 topics Textbook: Miller/O'Neill/Hyde:
More informationMONDAY, AUG 8 (10 MIN) Grab handouts on the way in and sit in your assigned seat If you are buying a binder from Ms. Ewalefo, give her your $1 now
MONDAY, AUG 8 (10 MIN) Grab handouts on the way in and sit in your assigned seat If you are buying a binder from Ms. Ewalefo, give her your $1 now and collect your binder Take out binder and label your
More informationdownload from
Table of Contents Chapter 1 Basic Concepts Pretests... 1 Mini-Lectures... Additional Exercises... 1 Chapter Tests... 19 Chapter Equations and Inequalities Pretests... 7 Mini-Lectures... 1 Additional Exercises...
More informationSection 1.1 Notes. Real Numbers
Section 1.1 Notes Real Numbers 1 Types of Real Numbers The Natural Numbers 1,,, 4, 5, 6,... These are also sometimes called counting numbers. Denoted by the symbol N Integers..., 6, 5, 4,,, 1, 0, 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 informationBeginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:
More informationALGEBRA I CURRICULUM OUTLINE
ALGEBRA I CURRICULUM OUTLINE 2013-2014 OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines
More informationFoundations of Discrete Mathematics
Foundations of Discrete Mathematics Chapter 0 By Dr. Dalia M. Gil, Ph.D. Statement Statement is an ordinary English statement of fact. It has a subject, a verb, and a predicate. It can be assigned a true
More informationA decimal number that has digits that repeat forever.
1.1 Expressing Rational Numbers as Decimals EQ: How do you rewrite rational numbers and decimals, take square roots and cube roots and approximate irrational numbers? What is a terminating decimal? A decimal
More informationx y x y ax bx c x Algebra I Course Standards Gap 1 Gap 2 Comments a. Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational
More informationChapter 4: Exponents and Radicals
Math 0C Name: Chapter 4: Exponents and Radicals 4. Square Roots and Cube Roots Review. Evaluate the following. a. 8 b. 36 Outcome: Demonstrate an understanding of factors of whole numbers by determining
More informationFlorida Math Curriculum (433 topics)
Florida Math 0028 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 to meet curricular
More informationAlgebra 1 Seamless Curriculum Guide
QUALITY STANDARD #1: REAL NUMBERS AND THEIR PROPERTIES 1.1 The student will understand the properties of real numbers. o Identify the subsets of real numbers o Addition- commutative, associative, identity,
More informationArithmetic, Algebra, Number Theory
Arithmetic, Algebra, Number Theory Peter Simon 21 April 2004 Types of Numbers Natural Numbers The counting numbers: 1, 2, 3,... Prime Number A natural number with exactly two factors: itself and 1. Examples:
More informationCHAPTER 1 REAL NUMBERS KEY POINTS
CHAPTER 1 REAL NUMBERS 1. Euclid s division lemma : KEY POINTS For given positive integers a and b there exist unique whole numbers q and r satisfying the relation a = bq + r, 0 r < b. 2. Euclid s division
More information1-1. Expressions and Formulas. Lesson 1-1. What You ll Learn. Active Vocabulary
1-1 Expressions and Formulas What You ll Learn Skim the lesson. Write two things you already know about expressions and formulas. 1. Active Vocabulary 2. Review Vocabulary Identify the four grouping symbols
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationStandards of Learning Content Review Notes. Grade 8 Mathematics 1 st Nine Weeks,
Standards of Learning Content Review Notes Grade 8 Mathematics 1 st Nine Weeks, 2016-2017 Revised September 2015 2 Mathematics Content Review Notes Grade 8 Mathematics: First Nine Weeks 2015-2016 -This
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 informationBIG Ideas. Assessment Teacher Resources Standards
Course Name: Unit: Introductory Time Line: 2 weeks Students will be able to simplify expressions. 1. Real Life Problems Solve problems using the four-step plan. Identify and use problemsolving strategies.
More informationChetek-Weyerhaeuser High School
Chetek-Weyerhaeuser High School Unit 1 Variables and Expressions Math RtI Units and s Math RtI A s 1. I can use mathematical properties to evaluate expressions. I can use mathematical properties to evaluate
More informationNFC ACADEMY COURSE OVERVIEW
NFC ACADEMY COURSE OVERVIEW Algebra I Fundamentals is a full year, high school credit course that is intended for the student who has successfully mastered the core algebraic concepts covered in the prerequisite
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 informationMATH 190 KHAN ACADEMY VIDEOS
MATH 10 KHAN ACADEMY VIDEOS MATTHEW AUTH 11 Order of operations 1 The Real Numbers (11) Example 11 Worked example: Order of operations (PEMDAS) 7 2 + (7 + 3 (5 2)) 4 2 12 Rational + Irrational Example
More informationFoundations for Algebra. Introduction to Algebra I
Foundations for Algebra Introduction to Algebra I Variables and Expressions Objective: To write algebraic expressions. Objectives 1. I can write an algebraic expression for addition, subtraction, multiplication,
More information1-1. Variables and Expressions. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
- Variables and Expressions Vocabulary Review What mathematical operation is shown in each equation? Write addition, subtraction, multiplication, or division.. 6? 2 5 2 2. 4 2 4 5 0. 27 4 5 9 4. 7 5 20
More informationAlgebra 1 Mod 1 Review Worksheet I. Graphs Consider the graph below. Please do this worksheet in your notebook, not on this paper.
Algebra 1 Mod 1 Review Worksheet I. Graphs Consider the graph below Please do this worksheet in your notebook, not on this paper. A) For the solid line; calculate the average speed from: 1) 1:00 pm to
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 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 informationAlgebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher
Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work
More informationALGEBRA CLAST MATHEMATICS COMPETENCIES
2 ALGEBRA CLAST MATHEMATICS COMPETENCIES IC1a: IClb: IC2: IC3: IC4a: IC4b: IC: IC6: IC7: IC8: IC9: IIC1: IIC2: IIC3: IIC4: IIIC2: IVC1: IVC2: Add and subtract real numbers Multiply and divide real numbers
More informationMath-2 Lesson 2-4. Radicals
Math- Lesson - Radicals = What number is equivalent to the square root of? Square both sides of the equation ( ) ( ) = = = is an equivalent statement to = 1.7 1.71 1.70 1.701 1.7008... There is no equivalent
More informationP.1. Real Numbers. Copyright 2011 Pearson, Inc.
P.1 Real Numbers Copyright 2011 Pearson, Inc. What you ll learn about Representing Real Numbers Order and Interval Notation Basic Properties of Algebra Integer Exponents Scientific Notation and why These
More informationNotice that we are switching from the subtraction to adding the negative of the following term
MTH95 Day 6 Sections 5.3 & 7.1 Section 5.3 Polynomials and Polynomial Functions Definitions: Term Constant Factor Coefficient Polynomial Monomial Binomial Trinomial Degree of a term Degree of a Polynomial
More informationAlgebra II Vocabulary Word Wall Cards
Algebra II Vocabulary Word Wall Cards Mathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development. The cards should
More information