Chapter 1: Foundations for Algebra
|
|
- William Rose
- 6 years ago
- Views:
Transcription
1 Chapter 1: Foundations for Algebra 1
2 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 9) Commutative Property 10) Associative Property 11) Identity 12) Inverse Property 13) Distributive Property 2
3 Day 1: Classification of Real Numbers N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number irrational. Warm-Up Rewrite each fraction as a decimal How are the decimals of the first two fractions different from the decimals of the second two fractions? All the numbers that we know positives, negatives, radicals, decimals, and fractions are called real numbers and they can be placed in different groups. Natural numbers (N), or counting numbers, are the numbers we count with: 1, 2, 3, Whole numbers (W) are the natural numbers plus zero: 0, 1, 2, 3, Integers (Z) are whole numbers and their opposites: -2, -1, 0, 1, 2. Rational numbers can be expressed in the form of a fraction (or ratio). Rational numbers include terminating and repeating decimals. Terminating decimals end, such as: 0.57, 2.3, or 0.05 Repeating decimals repeat the same digit or set of digits, like or Note: Since all integers can be written as fractions, integers are also rational. Also, since the square roots of perfect squares are integers, they are also rational. Irrational numbers cannot be expressed in the form of a fraction. In decimal form, these decimals are nonterminating and nonrepeating. 3
4 The following Venn diagram can help you classify any real number: Exercise 1) Classify the following numbers. Remember that a number may belong to more than one category. a) 4 b) 0 c) 5 d) - 5 e) 4 f)
5 g) 3 4 h) 0.23 i) 3 j) π k) l) 5 2 Quick Check for Understanding Classify the following numbers. Remember that a number may belong to more than one category. a) 2 5 b) 121 c)
6 Putting it All Together Let s recall some of the number sets we did today. Closing Activity 1) Explain the difference between a rational number and an irrational number. 2) Give an example of a number that is an integer but not a whole number. Explain your choice. 3) Tell all of the sets to which the number ½ belongs. Homework Chapter 1, Day 1 Vocabulary Using the definitions in your packet, write and define these terms on page 2. 1) Natural numbers 5) Irrational Numbers 2) Whole numbers 6) Real Numbers 3) Integers 7) Terminating decimal 4) Rational Numbers 8) Repeating decimal 6
7 Homework continued 7
8 Homework Continued 17) 18) 8
9 Day 2: Properties of Rationals and Irrationals N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational. Warm-Up Give an example of each type of number. a) A rational number that is a fraction b) An irrational number that is a fraction c) A rational number that contains a radical sign d) An irrational number that contains a radical sign e) A rational number that is written in decimal form f) An irrational number that is written in decimal form Exploration 1: Rationals + Rationals Expression Sum Rational or Irrational? Conclusion 1: The sum of two rational numbers must be. Exploration 2: Rationals Rationals Expression Product Rational or Irrational? Conclusion 2: The product of two rational numbers must be 9
10 Quick Check for Understanding The sum of and must be (A) rational (B) irrational (C) an integer (D) a whole number Exploration 3: Rationals + Irrationals Expression Sum Rational or Irrational? π Conclusion 3: The sum of a rational and an irrational number must be. Why do you think that is? Exploration 4: Rationals Irrationals Expression Product Rational or Irrational? Conclusion 4: The product of a rational and an irrational number must be Why do you think that is? 10
11 Quick Check for Understanding 1) 2) Summary Summary The sum of two rational numbers is a rational number. The product of two rational numbers is a rational number. The sum of a rational and an irrational number is irrational. The product of a rational number and an irrational number is irrational. Homework Chapter 1, Day 2 p. 35 #7-10 p. 36 #
12 Day 3: Evaluation of Expressions 6. EE. 2. Write, read, and evaluate expressions in which letters stand for numbers. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. Warm-Up To evaluate an expression means to substitute (plug in) numbers for its variables and determine a numerical answer. Rule #1: The number you substitute must always go in parentheses. Evaluate each expression when x = 5, y = - 4, z = -2. 1) x + y 2) z y 3) z yx 4) y 2 5) x 2 6) z 2 5z 7) x 3 8) 4 + y 3 9) z 3 2y 12
13 Quick Check for Understanding Evaluate 3a 2 a 3 when a = 2. Rule #2: Remember to close the parentheses at the appropriate time. Evaluate each expression when a = 3, b = 4, c = 2. Round all values to the nearest hundredth, if needed. 1) a + 3 2) a + 3 3) b 4) c 5) c a 6) c 1 7) 3 c+5 8) b 1 2 9) a b c Quick Check for Understanding Evaluate c b when c = 4 and b =
14 Evaluation Skills and Problem Solving Evaluate each expression for the value of the variable. Expression Value(s) Calculations/Answer 1) 15(x 40) ) 5x 2 12x ) x ) (x 5 2 )2 2 5) 25 t+1 4 6) x x 75 7) 3V 2π 10 8) 2 x ) 1 3 x ) 7 3 (x )
15 11) Is 3x + 7 5x < 15 true when x = -2? Explain. 12) Evaluate each expression for the value of the variable. Tell which expression has the greater value. Write (1) or (2). (1) (2) x = 3 x 2x + 5 Which is greater? HW Chapter 1 Day 3 Page 43 # #76, 77 15
16 Day 4: Identify and use Properties of Real Numbers 6.EE. 3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Warm up 1) 2) Directions: Classify each number as: real, rational, irrational, whole, natural, and integer. 3) 3 4 4) 56 5) 5 6)
17 Simplifying Expressions Using Properties 1) Examples of Properties of Real Numbers Commutative Property Commutative means that the order does not make any difference. Associative Property Associative means that the grouping does not make any difference. Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. Additive Identity Multiplicative Identity Inverse Properties Additive Inverse (Opposite) Multiplicative Inverse (Reciprocal) 2) How might the commutative property help you with the following problem? = 3) How might the associative property help you with the following problem? (6 + 3) + 7 = 4) Why do you think 0 is called the identity element for addition? 5) Why do you think 1 is called the identity element for multiplication? 17
18 6) Model Problems Identify the property illustrated by each statement. a) (x + y) + z = x + (y + z) b) (x + y) + z = z + (x + y) c) 2(x + y) = 2x + 2y d) x + 0 = x e) x 1 x 1 f) x + (-x) = 0 g) x 1 x Quick Check for Understanding 7) Identify the property illustrated by each statement. a) (48)3 = 3(48) b) (5 + 9) + 13 = 5 + (9 + 13) c) 5(x + 9) = 5x d) e) f) = 3 18
19 8) Rewrite each expression using the property given = (commutative) 4 + (x + y) = (associative) a(x + 2) = (distributive) Summary Exit Ticket 19
20 Homework Chapter 1 Day 4 Word Bank: Commutative, Distributive, Associative, Additive /Multiplicative Inverse, Additive/Multiplicative Identity 1) Rewrite using the commutative property: = a + (b + c) = 2) Rewrite using the associative property: 7*(4*6) = (5 + 1) + 4 = 3) Rewrite using the distributive property: 2(3 + 5) = x(d + m) = 4) A method for solving 5(x 2) - 2(x- 5) = 9 is shown below. Identify the property used to obtain each of the two indicated steps. Identify which property is illustrated for each example. 5) x (yz) = x (zy) 6) x(yz) = (xy)z 7) 2(x + y) = 2x + 2y 8) x + ( x) = ( x) + x 9) 1(x) = x 10) (x + y) + z = x + (y + z) 11) x + 0 = x 12) 1(x) = (x)1 13) (x + y) + z = (y + x) + z 14) x(y z) = xy xz 20
21 Homework Continued 15) 16) 17) 18) [Use your calculator to answer this question] 19) [Use your calculator to answer this question] 21
22 Day 5 Unit 1: Review Classifying Numbers 1) Place a check mark for each set that the number is part of. - 7 ¾ Whole Number Integer Rational Number Irrational Number Real Number ) True or False? If false, explain why. a) All integers are rational. b) If a number is rational, then it must be a whole number. c) Some irrational numbers are integers. d) All irrational numbers are real numbers. 22
23 3) Is the set of rational numbers closed under addition? Write an example to support your answer. 4) Is the set of rational numbers closed under multiplication? Write an example to support your answer. 5) Is the set of irrational numbers closed under addition? Write an example to support your answer. 6) Is the set of irrational numbers closed under multiplication? Write an example to support your answer. Expressions with Exponents and Absolute Value Simplify each expression. 7) ) (-7) 2 9) (-11) 2 10) (6) 2 11) -5(-4) 2 12) 2(-3) 3 13) (-4) 3 14) 8 ( 3) 2 15) ) ) )
24 Evaluating Polynomial Expressions 19) Evaluate x 2 6x + 3 when x = ) Find the value of x 2 3x when x = 2. 21) Evaluate w 3x 2 when w = -6 and x = 3. 22) What is the value of the expression 3a 2 + 4b 2 when a = -3 and b = 4? 23) Name the property illustrated by each statement. a. 5 1 = 5 b. (3 + 5) + 4 = 3 + (5 + 4) c. abc = 1abc g. 7 + (-7) = 0 h = 9 i. x + 9 = 9 + x 24
25 24) The statement = 2 is an example of the use of which property of real numbers? (1) associative (3) additive inverse (2) additive identity (4) distributive 25) Which property is illustrated by the equation ax + ay = a(x + y)? (1) associative (3) distributive (2) commutative (4) identity 26) Which property is illustrated by the equation 6 + (4 + x) = 6 + (x + 4) (1) associative property of addition (2) associative property of multiplication (3) distributive property (4) commutative property of addition 27) Which property of real numbers is illustrated by the equation 52 + ( ) = ( ) + 36? (1) commutative property (2) distributive property (3) associative property (4) identity property of addition 28) What is the additive inverse of the expression a - b? (1) a + b (3) -a + b (2) a - b (4) -a - b 29) Which equation illustrates the associative property? (1) a( 1) a (3) a( b c) ( ab) ( ac) (2) a b b a (4) ( a b) c a ( b c) 25
26 26
Chapter 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 informationPowers, Roots and Radicals. (11) Page #23 47 Column, #51, 54, #57 73 Column, #77, 80
Algebra 2/Trig Unit Notes Packet Name: Period: # Powers, Roots and Radicals () Homework Packet (2) Homework Packet () Homework Packet () Page 277 # 0 () Page 277 278 #7 6 Odd (6) Page 277 278 #8 60 Even
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 informationREVIEW Chapter 1 The Real Number System
REVIEW Chapter The Real Number System In class work: Complete all statements. Solve all exercises. (Section.4) A set is a collection of objects (elements). The Set of Natural Numbers N N = {,,, 4, 5, }
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 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 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 informationClassify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers.
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,
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 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 informationSYMBOL NAME DESCRIPTION EXAMPLES. called positive integers) negatives, and 0. represented as a b, where
EXERCISE A-1 Things to remember: 1. THE SET OF REAL NUMBERS SYMBOL NAME DESCRIPTION EXAMPLES N Natural numbers Counting numbers (also 1, 2, 3,... called positive integers) Z Integers Natural numbers, their
More informationPerform the following operations. 1) (2x + 3) + (4x 5) 2) 2(x + 3) 3) 2x (x 4) 4) (2x + 3)(3x 5) 5) (x 4)(x 2 3x + 5)
2/24 week Add subtract polynomials 13.1 Multiplying Polynomials 13.2 Radicals 13.6 Completing the square 13.7 Real numbers 15.1 and 15.2 Complex numbers 15.3 and 15.4 Perform the following operations 1)
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 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 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 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 informationVariables and Expressions
Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic
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 informationMay 2 nd May 6 th. Unit 10: Rational & Irrational Numbers
Math 8: Week 33 Math Packet May 2 nd May 6 th Unit 10: Rational & Irrational Numbers Jump Start Directions: Fill out all the BINGO boards on pages 1-2 with the following perfect square numbers: 2, 4, 9,
More informationFOR STUDENTS WHO HAVE COMPLETED ALGEBRA 1 (Students entering Geometry)
FOR STUDENTS WHO HAVE COMPLETED ALGEBRA (Students entering Geometry) Dear Parent/Guardian and Student, Name: Date: Period: Attached you will find a review packet of skills which each student is expected
More informationUnit Essential Questions. What are the different representations of exponents? Where do exponents fit into the real number system?
Unit Essential Questions What are the different representations of exponents? Where do exponents fit into the real number system? How can exponents be used to depict real-world situations? REAL NUMBERS
More informationAlgebra II First Semester Assignment #5 (Review of Sections 1.1 through 1.8)
Algebra II First Semester Assignment #5 (Review of Sections 1.1 through 1.8) Do not rely solely on this review to prepare for the test. These problems are meant only as a means to remind you of the types
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 informationRadical Expressions, Equations, and Functions
Radical Expressions, Equations, and Functions 0 Real-World Application An observation deck near the top of the Sears Tower in Chicago is 353 ft high. How far can a tourist see to the horizon from this
More informationUnit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions
CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.
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 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 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 informationLAKOTA WEST HIGH SCHOOL HONORS ALGEBRA II EXPECTATIONS ( )
LAKOTA WEST HIGH SCHOOL HONORS ALGEBRA II EXPECTATIONS (07-08) Upon entering Honors Algebra II class at Lakota West HS it will be expected that you to have an excellent understanding of certain topics
More informationSection 1.1 Real Numbers and Number Operations
Section. Real Numbers and Number Operations Objective(s): Differentiate among subsets of the real number system. Essential Question: What is the difference between a rational and irrational number? Homework:
More informationUNIT 5 QUADRATIC FUNCTIONS Lesson 2: Creating and Solving Quadratic Equations in One Variable Instruction
Prerequisite Skills This lesson requires the use of the following skills: simplifying radicals working with complex numbers Introduction You can determine how far a ladder will extend from the base of
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 informationGraphing Radicals Business 7
Graphing Radicals Business 7 Radical functions have the form: The most frequently used radical is the square root; since it is the most frequently used we assume the number 2 is used and the square root
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 informationRadical Expressions and Functions What is a square root of 25? How many square roots does 25 have? Do the following square roots exist?
Topic 4 1 Radical Epressions and Functions What is a square root of 25? How many square roots does 25 have? Do the following square roots eist? 4 4 Definition: X is a square root of a if X² = a. 0 Symbolically,
More informationLesson 7: Algebraic Expressions The Commutative and Associative Properties
: Algebraic Expressions The Commutative and Associative Properties Four Properties of Arithmetic: The Commutative Property of Addition: If a and b are real numbers, then a + b = b + a. The Associative
More informationAlgebra 2 and Trigonometry
Algebra 2 and Trigonometry Chapter 7: Exponential Functions Name: Teacher: Pd: 1 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs.
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 informationNever leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!
1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a
More informationARITHMETIC AND BASIC ALGEBRA
C O M P E T E N C Y ARITHMETIC AND BASIC ALGEBRA. Add, subtract, multiply and divide rational numbers expressed in various forms Addition can be indicated by the expressions sum, greater than, and, more
More informationIntro to Algebra Today. We will learn names for the properties of real numbers. Homework Next Week. Due Tuesday 45-47/ 15-20, 32-35, 40-41, *28,29,38
Intro to Algebra Today We will learn names for the properties of real numbers. Homework Next Week Due Tuesday 45-47/ 15-20, 32-35, 40-41, *28,29,38 Due Thursday Pages 51-53/ 19-24, 29-36, *48-50, 60-65
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 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 information27 Wyner Math 2 Spring 2019
27 Wyner Math 2 Spring 2019 CHAPTER SIX: POLYNOMIALS Review January 25 Test February 8 Thorough understanding and fluency of the concepts and methods in this chapter is a cornerstone to success in the
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 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 informationOrder of Operations Practice: 1) =
Order of Operations Practice: 1) 24-12 3 + 6 = a) 6 b) 42 c) -6 d) 192 2) 36 + 3 3 (1/9) - 8 (12) = a) 130 b) 171 c) 183 d) 4,764 1 3) Evaluate: 12 2-4 2 ( - ½ ) + 2 (-3) 2 = 4) Evaluate 3y 2 + 8x =, when
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 informationCommon Core Standards Addressed in this Resource
Common Core Standards Addressed in this Resource.EE.3 - Apply the properties of operations to generate equivalent expressions. Activity page: 4 7.RP.3 - Use proportional relationships to solve multistep
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 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 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 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 informationArithmetic Operations. The real numbers have the following properties: In particular, putting a 1 in the Distributive Law, we get
MCA AP Calculus AB Summer Assignment The following packet is a review of many of the skills needed as we begin the study of Calculus. There two major sections to this review. Pages 2-9 are review examples
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 informationx 9 or x > 10 Name: Class: Date: 1 How many natural numbers are between 1.5 and 4.5 on the number line?
1 How many natural numbers are between 1.5 and 4.5 on the number line? 2 How many composite numbers are between 7 and 13 on the number line? 3 How many prime numbers are between 7 and 20 on the number
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 informationAppendix Prerequisites and Review
BMapp0AppendixPrerequisitesFundamentalsofAlgebra.qxd 6//3 4:35 PM Page 5 Appendix Prerequisites and Review BMapp0AppendixPrerequisitesFundamentalsofAlgebra.qxd 6//3 4:35 PM Page 53 IN THIS APPENDIX real
More information4.1 Estimating Roots Name: Date: Goal: to explore decimal representations of different roots of numbers. Main Ideas:
4.1 Estimating Roots Name: Goal: to explore decimal representations of different roots of numbers Finding a square root Finding a cube root Multiplication Estimating Main Ideas: Definitions: Radical: an
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 informationAlgebra 1 Unit 6 Notes
Algebra 1 Unit 6 Notes Name: Day Date Assignment (Due the next class meeting) Monday Tuesday Wednesday Thursday Friday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday
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 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 informationUnit: Solving Quadratic Equations
Unit: Solving Quadratic Equations Name Dates Taught Outcome 11P.R.1. Factor polynomial expressions of the of the form o ax 2 - bx +c = 0, a 0 o a 2 x 2 b 2 y 2 - c = 0, a 0 b 0 o a(f(x)) 2 b(f(x))x +c
More informationDATE: Algebra 2. Unit 1, Lesson 2: n th roots and when are n th roots real or not real?
Algebra 2 DATE: Unit 1, Lesson 2: n th roots and when are n th roots real or not real? Objectives - Students are able to evaluate perfect n th roots. - Students are able to estimate non-perfect n th roots
More informationLESSON 6.2 POLYNOMIAL OPERATIONS I
LESSON 6. POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIALS OPERATIONS I 63 OVERVIEW Here's what you'll learn in this lesson: Adding and Subtracting a. Definition of polynomial, term, and coefficient b. Evaluating
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 informationMATCHING. Match the correct vocabulary word with its definition
Name Algebra I Block UNIT 2 STUDY GUIDE Ms. Metzger MATCHING. Match the correct vocabulary word with its definition 1. Whole Numbers 2. Integers A. A value for a variable that makes an equation true B.
More informationP.1: Algebraic Expressions, Mathematical Models, and Real Numbers
Chapter P Prerequisites: Fundamental Concepts of Algebra Pre-calculus notes Date: P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Algebraic expression: a combination of variables and
More informationCP Algebra 2 Unit 2-1: Factoring and Solving Quadratics WORKSHEET PACKET
CP Algebra Unit -1: Factoring and Solving Quadratics WORKSHEET PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor
More informationMath 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS:
Math 2 Variable Manipulation Part 2 Powers & Roots PROPERTIES OF EXPONENTS: 1 EXPONENT REVIEW PROBLEMS: 2 1. 2x + x x + x + 5 =? 2. (x 2 + x) (x + 2) =?. The expression 8x (7x 6 x 5 ) is equivalent to?.
More informationAlgebra I. Book 2. Powered by...
Algebra I Book 2 Powered by... ALGEBRA I Units 4-7 by The Algebra I Development Team ALGEBRA I UNIT 4 POWERS AND POLYNOMIALS......... 1 4.0 Review................ 2 4.1 Properties of Exponents..........
More informationPrerequisites for Math Standards - 1st Grade
Prerequisites for Math Standards - 1st Grade Operations and Algebraic Thinking 1.OA.1 Addition and Subtraction Word Problems with Unknowns K.OA.1, K.OA.2, K.OA.3 Operations and Algebraic Thinking 1.OA.2
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 informationChapter 9: Roots and Irrational Numbers
Chapter 9: Roots and Irrational Numbers Index: A: Square Roots B: Irrational Numbers C: Square Root Functions & Shifting D: Finding Zeros by Completing the Square E: The Quadratic Formula F: Quadratic
More informationRational Numbers. a) 5 is a rational number TRUE FALSE. is a rational number TRUE FALSE
Fry Texas A&M University!! Math 150!! Chapter 1!! Fall 2014! 1 Chapter 1A - - Real Numbers Types of Real Numbers Name(s) for the set 1, 2,, 4, Natural Numbers Positive Integers Symbol(s) for the set, -,
More informationChapter 7 - Exponents and Exponential Functions
Chapter 7 - Exponents and Exponential Functions 7-1: Multiplication Properties of Exponents 7-2: Division Properties of Exponents 7-3: Rational Exponents 7-4: Scientific Notation 7-5: Exponential Functions
More informationBasic Fraction and Integer Operations (No calculators please!)
P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry.
More informationALGEBRA 2 Summer Review Assignments Graphing
ALGEBRA 2 Summer Review Assignments Graphing To be prepared for algebra two, and all subsequent math courses, you need to be able to accurately and efficiently find the slope of any line, be able to write
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 informationHerndon High School Geometry Honors Summer Assignment
Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in
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 informationUndergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics. College Algebra for STEM
Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics College Algebra for STEM Marcel B. Finan c All Rights Reserved 2015 Edition To my children Amin & Nadia Preface From
More informationUnit 3 Day 4. Solving Equations with Rational Exponents and Radicals
Unit Day 4 Solving Equations with Rational Exponents and Radicals Day 4 Warm Up You know a lot about inverses in mathematics we use them every time we solve equations. Write down the inverse operation
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 informationFundamentals. Introduction. 1.1 Sets, inequalities, absolute value and properties of real numbers
Introduction This first chapter reviews some of the presumed knowledge for the course that is, mathematical knowledge that you must be familiar with before delving fully into the Mathematics Higher Level
More informationChapter 2. Solving Linear Equation
Chapter 2 Solving Linear Equation 2.1 Square Roots and Comparing Real Numbers I can find square roots and compare real numbers. CC.9-12.N.Q.1 Square Root of a Number: Words: If b 2 = a, then b is a square
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 informationRegina Algebra 1 and A
Regina Algebra 1 and A Summer Math Review In the following pages, you will find review materials that will prepare you for next year s math course. Please take the exercises seriously as this will allow
More informationArithmetic with Whole Numbers and Money Variables and Evaluation (page 6)
LESSON Name 1 Arithmetic with Whole Numbers and Money Variables and Evaluation (page 6) Counting numbers or natural numbers are the numbers we use to count: {1, 2, 3, 4, 5, ) Whole numbers are the counting
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 informationRadiological Control Technician Training Fundamental Academic Training Study Guide Phase I
Module 1.01 Basic Mathematics and Algebra Part 4 of 9 Radiological Control Technician Training Fundamental Academic Training Phase I Coordinated and Conducted for the Office of Health, Safety and Security
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 informationAlgebra I. abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain.
Algebra I abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain. absolute value the numerical [value] when direction or sign is not considered. (two words) additive inverse
More informationUnit 2 Day 7. Quadratic Formula & the Discriminant
Unit Day 7 Quadratic Formula & the Discriminant 1 Warm Up Day 7 1. Solve each of the quadratic functions by graphing and algebraic reasoning: a. x 3 = 0 b. x + 5x 8 = 0 c. Explain why having alternative
More informationAdding and Subtracting Polynomials
Adding and Subtracting Polynomials When you add polynomials, simply combine all like terms. When subtracting polynomials, do not forget to use parentheses when needed! Recall the distributive property:
More informationChapter 2 notes from powerpoints
Chapter 2 notes from powerpoints Synthetic division and basic definitions Sections 1 and 2 Definition of a Polynomial Function: Let n be a nonnegative integer and let a n, a n-1,, a 2, a 1, a 0 be real
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 informationALGEBRA 2 CHAPTER ONE NOTES SECTION 1-1 REAL NUMBERS Objectives: Classify and order real numbers A is a collection of items called.
ALGEBRA 2 CHAPTER ONE NOTES SECTION 1-1 REAL NUMBERS Objectives: Classify and order real numbers A is a collection of items called. A is a set whose elements belong to another set. The, denoted, is a set
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 information