PRE-ALGEBRA BY MYRL SHIREMAN
|
|
- Lynette Sparks
- 5 years ago
- Views:
Transcription
1 PRE-ALGEBRA BY MYRL SHIREMAN COPYRIGHT 1994 Mark Twain Media, Inc. ISBN 10-digit: digit: Printing No. CD-1876 Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa Publishing Company, Inc. The purchase of this book entitles the buyer to reproduce the student pages for classroom use only. Other permissions may be obtained by writing Mark Twain Media, Inc., Publishers. All rights reserved. Printed in the United States of America.
2 TABLE OF CONTENTS Introduction... ii... 1 Number Systems... 1 The Integer Number System... 2 Number Properties... 4 Whole Numbers... 5 Commutative Property for Multiplication... 6 Associative Property for Addition... 7 Associative Property for Multiplication... 8 Distributive Property of Multiplication Over Addition... 9 Properties of Subtraction and Division Properties of Zero/Identity Elements Order of Operations Integers Addition of Integers Addition of Integers: Exercises Subtraction of Integers Subtraction of Integers: Rule/Exercises Subtraction of Integers: Exercises/Rule Review Addition and Subtraction of Integers: Exercises Having Fun With Integers Multiplication of Integers Multiplication Chart Division of Integers Division of Integers: Rule Review Variables and Exponents Variables Variables and Multiplication Variables and Division/Variable Exercises Exponents Exponents: Maximum Power, Minimum Space Exponents: Rules to Remember Adding Exponents Reviewing Exponents Multiplying Exponents Zero and Negative Integer Exponents Scientific Notation Simplifying Large Numbers With Scientific Notation iii
3 TABLE OF CONTENTS (continued) Even and Odd Numbers Reviewing Even and Odd Numbers Factoring Learning About Factoring Learning About Prime Factors Finding Prime Factors Learning About the Greatest Common Factor Finding the Greatest Common Factor Learning About the Least Common Multiple Radicals; Square and Cube Roots Radicals and Roots Finding Square Roots Adding Radicals Subtracting Radicals Multiplying and Dividing Radicals Simplifying Radicals Multiplying and Simplifying Radicals Dividing and Simplifying Radicals Simple Equations Learning About Simple Equations Finding the Value of the Unknown I Finding the Value of the Unknown II Reviewing Simple Equations Solving Equations With Multiplication Solving Equations With Division Rectangular Coordinate Systems; Graphing Learning About the Rectangular Coordinate System Reviewing the Parts of the Rectangular Coordinate System Learning About Coordinates Plotting the Point The Rectangular Coordinate System and Equations Linear Equations With Two Variables Linear Equations With Two Variables Plotting Points for Linear Equations Finding the Slope and y Intercept of a Straight Line Answer Key iv
4 Number Systems You have been working with number systems for a long time. The number systems you are most familiar with are the counting numbers and the whole numbers. The counting numbers begin with the number 1, while the whole numbers being with 0. So the whole numbers, which you have used often, include the counting numbers plus 0. In your study of algebra you will need to get to know another number system to solve problems. These new numbers are called the integer numbers. The integer numbers include the whole numbers and a new set of numbers known as negative numbers. The integers are called signed numbers since they include both positive and negative numbers. Let s review the number systems we have talked about. 1, 2, 3, 4, 5, 6, 7, 8, 9... Counting Numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9... Whole Numbers... -7, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, +7, +8, Integer Numbers You can see from the above that the integers include numbers to the right and left of 0. The numbers on the right are positive and are noted with the small plus (+) sign. The numbers on the left side of 0 are the negative numbers, and they are noted with the small minus (-) sign. Remember, the integers are known as signed numbers > You can see on the above number line that the integers to the right and left of 0 are exactly the same except for the sign. Any given number on the right has an opposite number on the left. The +5 integer has an opposite on the left, and it is -5. All other numbers except 0 also have an opposite. Complete the following: Counting numbers begin with the number (a). Whole numbers begin with (b). Whole numbers include the counting numbers plus (c). The integer number system includes positive and (d) the left of 0 have a (e) numbers. Those integers to sign, while those to the right have a (f) sign. Integer numbers have opposites. The opposite of +4 is (g). The opposite of -7 is (h). The opposite of +60 is (i). 1
5 The Integer Number System A number line can be very helpful in understanding the integer number system a number system that you use quite frequently in your daily life. Let s use the number line below to keep track of the yards lost and gained in a football game. The distance between each number represents 1 yard. 1st down gain > 2nd down loss Let s say your team has a first down and gains 7 yards. This is a gain, so it is represented on the number line by +7. Now on the second down your team loses 4 yards. A four-yard loss is a -4, so this is represented by showing a -4-yard move to the left from +7. So for the two downs your team has a net gain of +3 yards M T A thermometer, which is much like a number line, can be used to understand positive and negative numbers. Refer to the thermometer at the left, and read the following paragraph. Let s say you live where the winters are very cold. Monday you leave for school and the temperature is +20. Since the 20 has a positive sign it is 20 above 0, which has been marked with the letter M for Monday. Now on Tuesday you leave for school and note the mercury in the thermometer is at point T for Tuesday. Since the T is by the 10 below 0, it has a negative sign and you say it is 10 below zero. Let s practice with the number line below so that you become comfortable with using positive and negative numbers. Point A is at +5 on the number line. If you were told to move +3 places, you would move 3 places to the right of A and be at Point B or at +8. If you were told to move -3 places from Point A, you would be at Point C, which is located at +2. C -3 A +3 B Use the number line at the top of page 3 to locate the following: (a) +3 places from +10 is at (b) -4 places from +6 is at (c) +8 places from -9 is at (e) +10 places from -4 is at (f) -4 places from -2 is at (g) -6 places from -6 is at (d) -7 places from +3 is at 2
6 The Integer Number System (continued) Use the number line below to answer the questions that follow: To get from +4 to +9 you must move spaces in the positive direction. 2. To get from -3 to -9 you must move spaces in the direction. 3. To get from +3 to -4 you must move spaces in the direction. 4. To get from -2 to +6 you must move spaces in the direction. Review: Integers on a number line Those integers on a number line to the left of zero are called (a) numbers. The integers to the right of zero are called (b) numbers. Integers have opposites. The opposite of -7 is +7. What is the opposite of each of the following: (c) +2 is opposite (d) -40 is opposite (e) +800 is opposite (f) +6 is opposite (g) -249 is opposite (h) is opposite
7 Number Properties In algebra you will study number properties. These properties are known as commutative, associative, and distributive. The commutative property of addition says that the order in which you add whole numbers will not change the sum. For example, = 8 and = 8, so = In your study with algebra you will often see letters used to stand for numbers. These letters are called unknowns. You will see the commutative property for addition stated as a + b = b + a where a and b are unknown and can be any whole numbers. Complete the following: = so + 7 = 10 Solve so that a + b = b + a = 35 so 10 + = = so = = 104 so + 84 = = 90 so 65 + = 90 Complete the following using a + b = b + a when you fill in the blank for each problem. a + b = b + a = a=5 b= = + a=35 b= = + a=111 b= = + a=37 b= = + a=2101 b= = + a=10 b= = + a=12 b=23 4
Helping Students Understand Pre-Algebra
Helping Students Understand Pre-Algebra By Barbara Sandall, Ed.D., & Mary Swarthout, Ph.D. COPYRIGHT 2005 Mark Twain Media, Inc. ISBN 10-digit: 1-58037-294-5 13-digit: 978-1-58037-294-7 Printing No. CD-404021
More informationPre-Algebra Practice
By Dr. Barbara Sandall, Ed.D., Dr. Melfried Olson, Ed.D., and Travis Olson, M.S. COPYRIGHT 2006 Mark Twain Media, Inc. ISBN 978-1-58037-755-3 Printing No. 404041-EB Mark Twain Media, Inc., Publishers Distributed
More informationMath 171 Proficiency Packet on Integers
Math 171 Proficiency Packet on Integers Section 1: Integers For many of man's purposes the set of whole numbers W = { 0, 1, 2, } is inadequate. It became necessary to invent negative numbers and extend
More informationAlgebra 2 Common Core Summer Skills Packet
Algebra 2 Common Core Summer Skills Packet Our Purpose: Completion of this packet over the summer before beginning Algebra 2 will be of great value to helping students successfully meet the academic challenges
More informationModule 7 Highlights. Mastered Reviewed. Sections ,
Sections 5.3 5.6, 6.1 6.6 Module 7 Highlights Andrea Hendricks Math 0098 Pre-college Algebra Topics Degree & leading coeff. of a univariate polynomial (5.3, Obj. 1) Simplifying a sum/diff. of two univariate
More informationTable of Contents. Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1
Table of Contents Table of Contents Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1 Chapter 1: Real Numbers...5 Real Numbers...5 Checking Progress: Real Numbers...8
More informationChapter 1 Operations With Numbers
Chapter 1 Operations With Numbers Part I Negative Numbers You may already know what negative numbers are, but even if you don t, then you have probably seen them several times over the past few days. If
More informationMiddle School Math 3 and 8th GLEs
Middle School Math 3 and 8th GLEs Chapter. Lesson GLE's Description 1.1 1.2 1.3 1.4 1.5 3.1.1 Use Graphs to analyze data 1.1.6 Order of Operations 1.5.4, 1.5.5(7th) Write and Evalutate Variable Expressions
More informationIs the statement sufficient? If both x and y are odd, is xy odd? 1) xy 2 < 0. Odds & Evens. Positives & Negatives. Answer: Yes, xy is odd
Is the statement sufficient? If both x and y are odd, is xy odd? Is x < 0? 1) xy 2 < 0 Positives & Negatives Answer: Yes, xy is odd Odd numbers can be represented as 2m + 1 or 2n + 1, where m and n are
More informationAlgebraically Speaking Chalkdust Algebra 1 Fall Semester
Algebraically Speaking Chalkdust Algebra 1 Fall Semester Homework Assignments: Chapter 1 The Real Number System: Lesson 1.1 - Real Numbers: Order and Absolute Value Do the following problems: # 1 9 Odd,
More informationOdd-Numbered Answers to Exercise Set 1.1: Numbers
Odd-Numbered Answers to Exercise Set.: Numbers. (a) Composite;,,, Prime Neither (d) Neither (e) Composite;,,,,,. (a) 0. 0. 0. (d) 0. (e) 0. (f) 0. (g) 0. (h) 0. (i) 0.9 = (j). (since = ) 9 9 (k). (since
More informationSummer Math Packet for Students Going Into Pre-algebra 8
Summer Math Packet for Students Going Into Pre-algebra 8 Purpose: The purpose of this packet is to review skills that are necessary for the student to have attained in order to be successful in the math
More informationMath 6 Unit 2: Understanding Number Review Notes
Math 6 Unit 2: Understanding Number Review Notes Key unit concepts: Use place value to represent whole numbers greater than one million Solve problems involving large numbers, using technology Determine
More informationCollege Prep Algebra II Summer Packet
Name: College Prep Algebra II Summer Packet This packet is an optional review which is highly recommended before entering CP Algebra II. It provides practice for necessary Algebra I topics. Remember: When
More informationALGEBRA 1 NOTES. Quarter 3. Name: Block
2016-2017 ALGEBRA 1 NOTES Quarter 3 Name: Block Table of Contents Unit 8 Exponent Rules Exponent Rules for Multiplication page 4 Negative and Zero Exponents page 8 Exponent Rules Involving Quotients page
More informationMatrices. A Matrix (This one has 2 Rows and 3 Columns) To add two matrices: add the numbers in the matching positions:
Matrices A Matrix is an array of numbers: We talk about one matrix, or several matrices. There are many things we can do with them... Adding A Matrix (This one has 2 Rows and 3 Columns) To add two matrices:
More informationThese are square roots, cube roots, etc. Intermediate algebra Class notes Radicals and Radical Functions (section 10.1)
Intermediate algebra Class notes Radicals and Radical Functions (section 10.1) These are square roots, cube roots, etc. Worksheet: Graphing Calculator Basics: This will go over basic home screen and graphing
More informationGateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 5-8
NUMBER SENSE & OPERATIONS 5.N.7 Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents. Fractions 1/2, 1/3, 1/4, 1/5, 1/10 and equivalent decimals
More informationSection A Arithmetic ( 5) Exercise A
Section A Arithmetic In the non-calculator section of the examination there might be times when you need to work with quite awkward numbers quickly and accurately. In particular you must be very familiar
More informationReteaching Transforming Linear Functions
Name Date Class Transforming Linear Functions INV 6 You have graphed linear functions on the coordinate plane. Now you will investigate transformations of the parent function for a linear function, f(x)
More informationGAP CLOSING. Integers. Intermediate / Senior Facilitator s Guide
GAP CLOSING Integers Intermediate / Senior Facilitator s Guide Topic 3 Integers Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions solutions...5 Using Intervention
More informationExample: Which of the following expressions must be an even integer if x is an integer? a. x + 5
8th Grade Honors Basic Operations Part 1 1 NUMBER DEFINITIONS UNDEFINED On the ACT, when something is divided by zero, it is considered undefined. For example, the expression a bc is undefined if either
More informationIntegers. Integer Definition. Slide 1 / 237. Slide 2 / 237. Slide 3 / 237. Integer Unit Topics
Slide 1 / 237 Integers Integer Unit Topics Integer Definition Click on the topic to go to that section Absolute Value Comparing and Ordering Integers Integer Addition Turning Subtraction Into Addition
More informationSchool Year:
School Year: 2010 2011 1 McDougal Littell CA Math Algebra 1 Pacing Guide Begin First Semester During the first two weeks of school, teachers will work with students on study skills and diagnostic assessments
More informationNumber System. Introduction. Natural Numbers (N) Whole Numbers (W) Integers (Z) Prime Numbers (P) Face Value. Place Value
1 Number System Introduction In this chapter, we will study about the number system and number line. We will also learn about the four fundamental operations on whole numbers and their properties. Natural
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. Decide if the given number is a solution to the given equation. ) p + 3p - 2 = 62; 8 ) A)
More informationExam 2 Review. 2. What the difference is between an equation and an expression?
Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? 2. What the difference is between an equation and an expression? 3. How to tell if an equation is linear? 4. How
More informationChapter 5. Radicals. Lesson 1: More Exponent Practice. Lesson 2: Square Root Functions. Lesson 3: Solving Radical Equations
Chapter 5 Radicals Lesson 1: More Exponent Practice Lesson 2: Square Root Functions Lesson 3: Solving Radical Equations Lesson 4: Simplifying Radicals Lesson 5: Simplifying Cube Roots This assignment is
More informationChapter 1: Foundations for Algebra
Chapter 1: Foundations for Algebra Dear Family, The student will follow the order of operations, a set of rules that standardize how to simplify expressions. Order of Operations 1. Perform operations within
More informationIllinois Math Assessment Framework, Grade 7. correlated to
Illinois Math Assessment Framework, Grade 7 correlated to Grade 7 correlated to Chapter 1 Variables, Expressions, and Integers (pp. 1 61) Lesson 1.1 (pp. 5 9) Expressions and Variables Evaluate and write
More informationPrentice Hall Mathematics: Course Correlated to: Massachusetts State Learning Standards Curriculum Frameworks (Grades 7-8)
Massachusetts State Learning Standards Curriculum Frameworks (Grades 7-8) NUMBER SENSE AND OPERATIONS 8.N.1 8.N.2 8.N.3 8.N.4 8.N.5 8.N.6 8.N.7 8.N.8 Compare, order, estimate, and translate among integers,
More informationAlgebra II Radical Equations
1 Algebra II Radical Equations 2016-04-21 www.njctl.org 2 Table of Contents: Graphing Square Root Functions Working with Square Roots Irrational Roots Adding and Subtracting Radicals Multiplying Radicals
More information( 3) ( 4 ) 1. Exponents and Radicals ( ) ( xy) 1. MATH 102 College Algebra. still holds when m = n, we are led to the result
Exponents and Radicals ZERO & NEGATIVE EXPONENTS If we assume that the relation still holds when m = n, we are led to the result m m a m n 0 a = a = a. Consequently, = 1, a 0 n n a a a 0 = 1, a 0. Then
More informationProperties and Definitions
Section 0.1 Contents: Operations Defined Multiplication as an Abbreviation Visualizing Multiplication Commutative Properties Parentheses Associative Properties Identities Zero Product Answers to Exercises
More informationGAP CLOSING. Grade 9. Facilitator s Guide
GAP CLOSING Grade 9 Facilitator s Guide Topic 3 Integers Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions solutions... 5 Using Intervention Materials...8
More informationMAT 003 Brian Killough s Instructor Notes Saint Leo University
MAT 003 Brian Killough s Instructor Notes Saint Leo University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
More informationMath Glossary Numbers and Arithmetic
Math Glossary Numbers and Arithmetic Version 0.1.1 September 1, 200 Next release: On or before September 0, 200. E-mail edu@ezlink.com for the latest version. Copyright 200 by Brad Jolly All Rights Reserved
More informationIntegers and Rational Numbers
A A Family Letter: Integers Dear Family, The student will be learning about integers and how these numbers relate to the coordinate plane. The set of integers includes the set of whole numbers (0, 1,,,...)
More informationMath, Lower Adolescent. Unit 1 Money. Basics
Math, Lower Adolescent Unit 1 Money Basics Equations and Algebraic Equations Adding, subtracting, multiplying, and dividing integers (7.3) Concrete Ratios (7.4) Writing Algebraic Equations (7.13) Using
More informationMiddle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8
Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8 State Goal 6: Number Sense 6.8.01: 6.8.02: 6.8.03: 6.8.04: 6.8.05: = ALEKS
More informationCommon Core State Standards. August 2010
August 2010 Grade Six 6.RP: Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 1. Understand the concept of a ratio and use ratio language to describe
More informationCollege Readiness (597 topics) Course Name: College Prep Math Spring 2014 Course Code: ARTD4-3N6XJ
Course Name: College Prep Math Spring 2014 Course Code: ARTD4-3N6XJ ALEKS Course: Math for College Readiness Instructor: Ms. Dalton Course Dates: Begin: 01/19/2015 End: 06/18/2015 Course Content: 606 Topics
More informationProblem. Prove that the square of any whole number n is a multiple of 4 or one more than a multiple of 4.
CHAPTER 8 Integers Problem. Prove that the square of any whole number n is a multiple of 4 or one more than a multiple of 4. Strategy 13 Use cases. This strategy may be appropriate when A problem can be
More informationDEPARTMENT OF ACADEMIC UPGRADING
DEPARTMENT OF ACADEMIC UPGRADING COURSE OUTLINE WINTER 2014 INTRODUCTION TO MATH 0081 INSTRUCTOR: Joelle Reynolds PHONE: (780) 539-2810 or 2204 OFFICE: Math Lab A210 E-MAIL: jreynolds@gprc.ab.ca OFFICE
More informationRtI 7. Curriculum (219 topics additional topics)
RtI 7 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 needs. Curriculum
More informationMaintaining Mathematical Proficiency
NBHCA SUMMER WORK FOR ALGEBRA 1 HONORS AND GEOMETRY HONORS Name 1 Add or subtract. 1. 1 3. 0 1 3. 5 4. 4 7 5. Find two pairs of integers whose sum is 6. 6. In a city, the record monthly high temperature
More informationMath Content
2013-2014 Math Content PATHWAY TO ALGEBRA I Hundreds and Tens Tens and Ones Comparing Whole Numbers Adding and Subtracting 10 and 100 Ten More, Ten Less Adding with Tens and Ones Subtracting with Tens
More informationAppendix 14C: TIMSS 2015 Eighth Grade Mathematics Item Descriptions Developed During the TIMSS 2015 Benchmarking
Appendix 14C: TIMSS 2015 Eighth Grade Mathematics Item Descriptions Developed During the TIMSS 2015 Benchmarking Items at Low International Benchmark (400) Number M04_01 M07_01 Recognizes a 7-digit number
More information1 of 39 8/14/2018, 9:48 AM
1 of 39 8/14/018, 9:48 AM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework150bbbbtsiallnew 1. Graph each integer in the list on the same number line.
More informationPre-Algebra Notes Unit One: Variables, Expressions, and Integers
Pre-Algebra Notes Unit One: Variables, Expressions, and Integers Evaluating Algebraic Expressions Syllabus Objective: (.) The student will evaluate variable and numerical expressions using the order of
More information6th Grade Arithmetic (with QuickTables)
6th Grade Arithmetic (with QuickTables) 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 informationKate Collins Middle School Pre-Algebra Grade 6
Kate Collins Middle School Pre-Algebra Grade 6 1 1 - Real Number System How are the real numbers related? *some numbers can appear in more than one subset *the attributes of one subset can be contained
More informationDEPARTMENT OF ACADEMIC UPGRADING
DEPARTMENT OF ACADEMIC UPGRADING COURSE OUTLINE WINTER 2013 INTRODUCTION TO MATH 0081 INSTRUCTOR: Sukhvir Sandhu PHONE: (780) 539-2810 or 2234 OFFICE: Math Lab A210 or C310 E-MAIL: ssandhu@gprc.ab.ca OFFICE
More informationAlgebra II Chapter 6: Rational Exponents and Radical Functions
Algebra II Chapter 6: Rational Exponents and Radical Functions Chapter 6 Lesson 1 Evaluate nth Roots and Use Rational Exponents Vocabulary 1 Example 1: Find nth Roots Note: and Example 2: Evaluate Expressions
More informationName Date. FINAL EXAM STUDY GUIDE Pre-Algebra Course 3
Name Date FINAL EXAM STUDY GUIDE Pre-Algebra Course 3 The following is an outline of key elements that should have been mastered during the course of the year (Grade 8 Green Book Course 3). Use it wisely
More informationPrepared by Sa diyya Hendrickson. Package Summary
Introduction Prepared by Sa diyya Hendrickson Name: Date: Package Summary Exponent Form and Basic Properties Order of Operations Using Divisibility Rules Finding Factors and Common Factors Primes, Prime
More informationMontana City School GRADE 5
Montana City School GRADE 5 Montana Standard 1: Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications, and using appropriate
More informationMath 1 Variable Manipulation Part 2 Exponents & Roots
Math 1 Variable Manipulation Part 2 Exponents & Roots 1 PRE-ALGEBRA REVIEW: WORKING WITH EXPONENTS Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand
More informationWorking with Algebraic Expressions
2 Working with Algebraic Expressions This chapter contains 25 algebraic expressions; each can contain up to five variables. Remember that a variable is just a letter that represents a number in a mathematical
More informationProperties. Comparing and Ordering Rational Numbers Using a Number Line
Chapter 5 Summary Key Terms natural numbers (counting numbers) (5.1) whole numbers (5.1) integers (5.1) closed (5.1) rational numbers (5.1) irrational number (5.2) terminating decimal (5.2) repeating decimal
More informationUsing the Best of Both!
Using the Best of Both! A Guide to Using Connected Mathematics 2 with Prentice Hall Mathematics Courses 1, 2, 3 2012, and Algebra Readiness MatBro111707BestOfBothPH10&CMP2.indd 1 6/7/11 11:59 AM Using
More informationSquare roots: We say that the square root of 16 is 4. We write this as 16 4.
Intermediate algebra Class notes Radicals and Radical Functions (section 10.1) These are square roots, cube roots, etc. Square roots: We say that the square root of 16 is 4. We write this as 16 4. Root
More informationAlgebra II Chapter 4: Quadratic Functions and Factoring Part 1
Algebra II Chapter 4: Quadratic Functions and Factoring Part 1 Chapter 4 Lesson 1 Graph Quadratic Functions in Standard Form Vocabulary 1 Example 1: Graph a Function of the Form y = ax 2 Steps: 1. Make
More informationSummer Math Assignments for Students Entering Algebra II
Summer Math Assignments for Students Entering Algebra II Purpose: The purpose of this packet is to review pre-requisite skills necessary for the student to be successful in Algebra II. You are expected
More informationFunctions 3.6. Fall Math (Math 1010) M / 13
Functions 3.6 Fall 2013 - Math 1010 (Math 1010) M 1010 3.6 1 / 13 Roadmap 3.6 - Functions: Relations, Functions 3.6 - Evaluating Functions, Finding Domains and Ranges (Math 1010) M 1010 3.6 2 / 13 3.6
More informationPrep 8 Year: Pre-Algebra Textbook: Larson, Boswell, Kanold & Stiff. Pre-Algebra. Common Core Edition Holt McDougal, 2012.
Prep 8 Year: Pre-Algebra Textbook: Larson, Boswell, Kanold & Stiff. Pre-Algebra. Common Core Edition Holt McDougal, 2012. Course Description: The students entering prep year have differing ranges of exposure
More informationMath Lesson Plan 6th Grade Curriculum Total Activities: 302
TimeLearning Online Learning for Homeschool and Enrichment www.timelearning.com Languages Arts, Math and more Multimedia s, Interactive Exercises, Printable Worksheets and Assessments Student Paced Learning
More informationChapter 1: Number and Operations
Chapter 1: Number and Operations 1.1 Order of operations When simplifying algebraic expressions we use the following order: 1. Perform operations within a parenthesis. 2. Evaluate exponents. 3. Multiply
More informationAlignment to the Texas Essential Knowledge and Skills Standards
Alignment to the Texas Essential Knowledge and Skills Standards Contents Kindergarten... 2 Level 1... 4 Level 2... 6 Level 3... 8 Level 4... 10 Level 5... 13 Level 6... 16 Level 7... 19 Level 8... 22 High
More informationGrade 7 Math (Master) Essential Questions Content Skills
Wilmette Public Schools, District 39 Created 2006-2007 Fall Grade 7 Math (Master) Why is it important to differentiate between various multiplication methods? How can a procedure lead you to an accurate
More informationSUMMER REVIEW PACKET 2 FOR STUDENTS ENTERING ALGEBRA 1
SUMMER REVIEW PACKET FOR STUDENTS ENTERING ALGEBRA Dear Students, Welcome to Ma ayanot. We are very happy that you will be with us in the Fall. The Math department is looking forward to working with you
More informationAlgebra 1 Notes Quarter
Algebra 1 Notes Quarter 3 2014 2015 Name: ~ 1 ~ Table of Contents Unit 9 Exponent Rules Exponent Rules for Multiplication page 6 Negative and Zero Exponents page 10 Exponent Rules Involving Quotients page
More informationPCTI Geometry. Summer Packet
PCTI Geometry Summer Packet 2017 1 This packet has been designed to help you review various mathematical topics that will be necessary for your success in Geometry. INSTRUCTIONS: Do all problems without
More informationFamily Literacy. readers. Easy Algebra Reading Practice
Family Literacy readers Easy Algebra Reading Practice UNIT 2 Integers and Expressions 2.0 A Review of Unit 1 preface About Family Literacy Algebra Prep Readers These readers are not intended to be a complete
More informationThis assignment is due the first day of school. Name:
This assignment will help you to prepare for Geometry A by reviewing some of the topics you learned in Algebra 1. This assignment is due the first day of school. You will receive homework grades for completion
More informationMathematics LV 5 (with QuickTables)
Mathematics LV 5 (with QuickTables) 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 informationAlgebra 2 Semester 1 (#2221)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the 2016-2017 Course Guides for the following course: Algebra 2 Semester
More informationStudents will understand 1. that numerical expressions can be written and evaluated using whole number exponents
Grade 6 Expressions and Equations Essential Questions: How do you use patterns to understand mathematics and model situations? What is algebra? How are the horizontal and vertical axes related? How do
More information1 5 Integer Operations
1 5 Integer Operations Positive and Negative Integers A glance through any newspaper shows that many quantities are expressed using negative numbers. For example, negative numbers show below-zero temperatures.
More informationMathematics 700 Unit Lesson Title Lesson Objectives 1 - INTEGERS Represent positive and negative values. Locate integers on the number line.
Mathematics 700 Unit Lesson Title Lesson Objectives 1 - INTEGERS Integers on the Number Line Comparing and Ordering Integers Absolute Value Adding Integers with the Same Sign Adding Integers with Different
More informationr the COR d e s 3 A lg e b r a Alabama Pathways
BUI LT fo COM r the MON COR E Gra 2013 2014 d e s 3 A lg e b r a Alabama Pathways I Grade 3 Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Number
More informationSummer Assignment Glossary
Algebra 1.1 Summer Assignment Name: Date: Hour: Directions: Show all work for full credit using a pencil. Circle your final answer. This assignment is due the first day of school. Use the summer assignment
More informationr the COR d e s 3 A lg e b r a New York Common Core Pathways
BUI LT fo COM r the MON COR E Gra 2013 2014 d e s 3 A lg e b r a New York Common Core Pathways I Grade 3 Number and Operations - Fractions Measurement and Data Geometry Place Value with Whole Numbers Place
More informationName Period Date. REAL NUMBER SYSTEM Student Pages for Packet 3: Operations with Real Numbers
Name Period Date REAL NUMBER SYSTEM Student Pages for Packet : Operations with Real Numbers RNS. Rational Numbers Review concepts of experimental and theoretical probability. a Understand why all quotients
More information8.NS.1 8.NS.2. 8.EE.7.a 8.EE.4 8.EE.5 8.EE.6
Standard 8.NS.1 8.NS.2 8.EE.1 8.EE.2 8.EE.3 8.EE.4 8.EE.5 8.EE.6 8.EE.7 8.EE.7.a Jackson County Core Curriculum Collaborative (JC4) 8th Grade Math Learning Targets in Student Friendly Language I can identify
More informationA. Incorrect! To simplify this expression you need to find the product of 7 and 4, not the sum.
Problem Solving Drill 05: Exponents and Radicals Question No. 1 of 10 Question 1. Simplify: 7u v 4u 3 v 6 Question #01 (A) 11u 5 v 7 (B) 8u 6 v 6 (C) 8u 5 v 7 (D) 8u 3 v 9 To simplify this expression you
More informationBenchmark Assessment when instruction is complete..
First Nine Weeks Powers of 10, Perfect Squares, Absolute Value 7.1 The student will a) investigate and describe the concept of negative exponents for powers of ten; b) *compare and order (no more than
More informationCentral Valley School District Math Curriculum Map Grade 8. August - September
August - September Decimals Add, subtract, multiply and/or divide decimals without a calculator (straight computation or word problems) Convert between fractions and decimals ( terminating or repeating
More informationAnadarko Public Schools MATH Power Standards
Anadarko Public Schools MATH Power Standards Kindergarten 1. Say the number name sequence forward and backward beginning from a given number within the known sequence (counting on, spiral) 2. Write numbers
More informationAlignment to Common Core State Standards Level 8 Unit Report Summary
Alignment to Common Core State Standards Level 8 Unit Report Summary No. Objective Code Common Core State Standards Objective Title Whole Number Addition and Subtraction - Level 8 - (Ascend Default Unit)
More informationWatkins Mill High School. Algebra 2. Math Challenge
Watkins Mill High School Algebra 2 Math Challenge "This packet will help you prepare for Algebra 2 next fall. It will be collected the first week of school. It will count as a grade in the first marking
More informationPITSCO Math Individualized Prescriptive Lessons (IPLs)
Orientation Integers 10-10 Orientation I 20-10 Speaking Math Define common math vocabulary. Explore the four basic operations and their solutions. Form equations and expressions. 20-20 Place Value Define
More informationSimplifying Square Root Expressions[In Class Version][Algebra 1 Honors].notebook August 26, Homework Assignment. Example 5 Example 6.
Homework Assignment The following examples have to be copied for next class Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 Example 9 Example 10 Example 11 Example 12 The
More informationSimplifying Expressions
Unit 1 Beaumont Middle School 8th Grade, 2017-2018 Math8; Intro to Algebra Name: Simplifying Expressions I can identify expressions and write variable expressions. I can solve problems using order of operations.
More informationSolving Equations with Inverse Operations
Solving Equations with Inverse Operations Math 97 Supplement LEARNING OBJECTIVES 1. Solve equations by using inverse operations, including squares, square roots, cubes, and cube roots. The Definition of
More informationObjective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions
Objective- Students will be able to use the Order of Operations to evaluate algebraic expressions. Evaluating Algebraic Expressions Variable is a letter or symbol that represents a number. Variable (algebraic)
More informationNAME UNIT 4 ALGEBRA II. NOTES PACKET ON RADICALS, RATIONALS d COMPLEX NUMBERS
NAME UNIT 4 ALGEBRA II NOTES PACKET ON RADICALS, RATIONALS d COMPLEX NUMBERS Properties for Algebra II Name: PROPERTIES OF EQUALITY EXAMPLE/MEANING Reflexive a - a Any quantity is equal to itself. Symmetric
More informationCAMI KEYS. TOPIC 1.1 Whole numbers to to to to to
TOPIC 1.1 Whole numbers GRADE 9_CAPS Curriculum 1. Numbers, operations and relationships CONTENT Properties of numbers Describing the real number system by recognizing, defining and distinguishing properties
More informationOperations and Properties
. Operations and Properties. OBJECTIVES. Represent the four arithmetic operations using variables. Evaluate expressions using the order of operations. Recognize and apply the properties of addition 4.
More informationStandardized Tests: Best Practices for the TI-Nspire CX
The role of TI technology in the classroom is intended to enhance student learning and deepen understanding. However, efficient and effective use of graphing calculator technology on high stakes tests
More information