Corinne: I m thinking of a number between 220 and 20. What s my number? Benjamin: Is it 25?


 Daniella McDaniel
 2 years ago
 Views:
Transcription
1 Walk the Line Adding Integers, Part I Learning Goals In this lesson, you will: Model the addition of integers on a number line. Develop a rule for adding integers. Corinne: I m thinking of a number between 220 and 20. What s my number? Benjamin: Is it 25? Corinne: Lower. Benjamin: 22? Corinne: That s not lower than 25. Benjamin: Oh, right. How about 211? Corinne: Higher. Benjamin: 28? Corinne: Lower. Benjamin: 29? Corinne: You got it! Try this game with a partner. See who can get the number with the fewest guesses. 4.2 Adding Integers, Part I 205
2 Problem 1 Adding on Number Lines 1. Use the number line and determine the number described by each. Explain your reasoning. a. the number that is 7 more than 29 b. the number that is 2 more than 26 c. the number that is 10 more than 28 d. the number that is 10 less than 6 e. the number that is 5 less than 24 f. the number that is 2 less than Chapter 4 Addition and Subtraction with Rational Numbers
3 A number line can be used to model integer addition. When adding a positive integer, move to the right on a number line. When adding a negative integer, move to the left on a number line. Example 1: The number line shows how to determine Step 1 5 Step 2 8 Example 2: The number line shows how to determine 5 1 (28). 8 5 Step 1 Step 2 2. Compare the first steps in each example. a. What distance is shown by the first term in each example? b. Describe the graphical representation of the first term. Where does it start and in which direction does it move? Why? c. What is the absolute value of the first term in each example? Remember that the absolute value of a number is its distance from Adding Integers, Part I 207
4 3. Compare the second steps in each example. a. What distance is shown by the second term in each example? b. Why did the graphical representation for the second terms both start at the endpoints of the first terms but then continue in opposite directions? Explain your reasoning. c. What are the absolute values of the second terms? 4. Use the number line to determine each sum. Show your work. a b. 3 1 (27) Chapter 4 Addition and Subtraction with Rational Numbers
5 c (27) 5 d Notice that the first term in each expression in parts (a) through (d) was either 3 or (23). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? 6. Notice that the second term in each expression was either 7 or (27). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? 4.2 Adding Integers, Part I 209
6 7. Use the number line to determine each sum. Show your work. a b. 9 1 (25) 5 c (25) 5 d Chapter 4 Addition and Subtraction with Rational Numbers
7 8. Notice that the first term in each expression in parts (a) through (d) was either 9 or (29). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? 9. Notice that the second term in each expression was either 5 or (25). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? How is knowing the absolute value of each term important? 4.2 Adding Integers, Part I 211
8 10. Use the number line to determine each sum. Show your work. a b. 8 1 (22) 5 c (22) 5 d Use the number line to determine each sum. Show your work. a Chapter 4 Addition and Subtraction with Rational Numbers
9 b. 4 1 (211) 5 c (211) 5 d In Questions 4 through 11, what patterns do you notice when: a. you are adding two positive numbers? b. you are adding two negative numbers? c. you are adding a negative and a positive number? Can you see how knowing the absolute value is important when adding and subtracting signed numbers? 4.2 Adding Integers, Part I 213
10 13. Complete each number line model and number sentence. a b c d Be prepared to share your solutions and methods. 214 Chapter 4 Addition and Subtraction with Rational Numbers
Opposites are all around us. If you move forward two spaces in a board game
TwoColor Counters Adding Integers, Part II Learning Goals In this lesson, you will: Key Term additive inverses Model the addition of integers using twocolor counters. Develop a rule for adding integers.
More informationAddition and Subtraction with Rational Numbers
Addition and Subtraction with Rational Numbers Although baseball is considered America's national pastime, football attracts more television viewers in the U.S. The Super Bowlthe championship football
More information(2 4 + 9)+( 7 4) + 4 + 2
5.2 Polynomial Operations At times we ll need to perform operations with polynomials. At this level we ll just be adding, subtracting, or multiplying polynomials. Dividing polynomials will happen in future
More informationLesson 4: Efficiently Adding Integers and Other Rational Numbers
Classwork Example 1: Rule for Adding Integers with Same Signs a. Represent the sum of 3 + 5 using arrows on the number line. i. How long is the arrow that represents 3? ii. iii. How long is the arrow that
More informationequals equals equals equals
Addition of Integers Rules Same Sign  Add  Keep the Sign Different Signs  Subtract  Take the sign of the integer with the larger absolute value plus plus plus
More informationSolving Rational Equations
Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,
More informationPURPOSE: To practice adding and subtracting integers with number lines and algebra tiles (charge method). SOL: 7.3 NUMBER LINES
Name: Date: Block: PURPOSE: To practice adding and subtracting integers with number lines and algebra tiles (charge method). SOL: 7.3 Examples: NUMBER LINES Use the below number lines to model the given
More informationAdding and Subtracting Positive and Negative Numbers
Adding and Subtracting Positive and Negative Numbers Absolute Value For any real number, the distance from zero on the number line is the absolute value of the number. The absolute value of any real number
More informationAccentuate the Negative: Homework Examples from ACE
Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 1215, 47, 4952 Investigation 2: Adding and Subtracting Rational Numbers, ACE 1822, 38(a),
More informationSupplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Section 5 Subtracting Integers
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Please watch Section 5 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm
More informationRules of Signs for Decimals
CHAPTER 6 C Rules of Signs for Decimals c GOAL Apply the rules of signs for calculating with decimals. You will need number lines a calculator with a sign change key Learn about the Math Positive and negative
More informationInquiry Based Lesson Adding Integers using Integer Chips Jackie Wolf Pat Canterbury. Part I
Inquiry Based Lesson Adding Integers using Integer Chips Jackie Wolf Pat Canterbury Part I 1. Lesson Title: Adding integers using integer chips 2. Lesson Summary: In this lesson, students will use integer
More informationPick any positive integer. If the integer is even, divide it by 2. If it is odd,
Multiplying and Dividing Integers Learning Goals In this lesson, you will: Multiply integers. Divide integers. Pick any positive integer. If the integer is even, divide it by 2. If it is odd, multiply
More informationSection 1.9 Algebraic Expressions: The Distributive Property
Section 1.9 Algebraic Expressions: The Distributive Property Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Apply the Distributive Property.
More information2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.
Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard
More informationAlgebra Tiles Activity 1: Adding Integers
Algebra Tiles Activity 1: Adding Integers NY Standards: 7/8.PS.6,7; 7/8.CN.1; 7/8.R.1; 7.N.13 We are going to use positive (yellow) and negative (red) tiles to discover the rules for adding and subtracting
More informationLesson 4: Efficiently Adding Integers and Other Rational Numbers
Lesson 4: Efficiently Adding Integers and Other Rational Numbers Student Outcomes Students understand the rules for adding integers: Add integers with the same sign by adding the absolute values and using
More informationIntegers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
More informationFor any two different places on the number line, the integer on the right is greater than the integer on the left.
Positive and Negative Integers Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5,.... Negative integers are all the opposites of these whole numbers: 1, 2, 3, 4, 5,. We
More informationObjective. Materials. TI73 Calculator
0. Objective To explore subtraction of integers using a number line. Activity 2 To develop strategies for subtracting integers. Materials TI73 Calculator Integer Subtraction What s the Difference? Teacher
More information2.6 Exponents and Order of Operations
2.6 Exponents and Order of Operations We begin this section with exponents applied to negative numbers. The idea of applying an exponent to a negative number is identical to that of a positive number (repeated
More informationMath 8 PRACTICE TEST  Integers
Name: Date: Math 8 PRACTICE TEST Integers Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which expression has the same product as 2(3)? a. 2( 3) c. 2(
More informationListen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7
Number Sense and Numeration Integers Adding and Subtracting Listen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A
More informationUSING THE PROPERTIES TO SIMPLIFY EXPRESSIONS
5 (1 5) Chapter 1 Real Numbers and Their Properties 1.8 USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS In this section The properties of the real numbers can be helpful when we are doing computations. In
More informationToday. Binary addition Representing negative numbers. Andrew H. Fagg: Embedded Real Time Systems: Binary Arithmetic
Today Binary addition Representing negative numbers 2 Binary Addition Consider the following binary numbers: 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 How do we add these numbers? 3 Binary Addition 0 0 1 0 0 1 1
More informationFractions and Linear Equations
Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps
More informationObservation 1. Observation 2. What is the sign of the answer to the problem L3 Q L11?
Name Date Number Sense: Integers Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review, if necessary). Read
More informationLesson Plan  Rational Number Operations
Lesson Plan  Rational Number Operations Chapter Resources  Lesson 312 Rational Number Operations  Lesson 312 Rational Number Operations Answers  Lesson 313 Take Rational Numbers to WholeNumber
More informationGrade 7 Red Math Weekly Schedule December 6 th December 10 th Mr. Murad
Lesson 1&2 6/12/2015 Lesson 3 7/12/2015 Lesson 4 8/12/2015 Lesson 5&6 9/12/2015 Grade 7 Red Math Weekly Schedule December 6 th December 10 th Mr. Murad Date Class Work Home Work 21 find the absolute
More informationScholastic Fraction Nation
Scholastic correlated to the ematics: Grades 48 2010 TM & Scholastic Inc. All rights reserved. SCHOLASTIC,, and associated logos are trademarks and/or registered trademarks of Scholastic Inc. Scholastic
More informationSolution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2
5.7 Introduction to Square Roots The Square of a Number The number x is called the square of the number x. EX) 9 9 9 81, the number 81 is the square of the number 9. 4 4 4 16, the number 16 is the square
More informationDedekind Cuts. Rich Schwartz. September 17, 2014
Dedekind Cuts Rich Schwartz September 17, 2014 1 Decimal Expansions How would you define a real number? It would seem that the easiest way is to say that a real number is a decimal expansion of the form
More informationGrade 7 Math The Number System Grade 7 Math Grade 7 Math Start Date: August 30, 2012 End Date : September 28, 2012
Unit Overview Students will be able to: describe real life situations for quantities that combine to make zero understand the distance between two on a number line show how opposites have a sum of zero
More informationChapter 1 Section 5: Equations and Inequalities involving Absolute Value
Introduction The concept of absolute value is very strongly connected to the concept of distance. The absolute value of a number is that number s distance from 0 on the number line. Since distance is always
More informationRational Numbers CHAPTER Introduction
RATIONAL NUMBERS Rational Numbers CHAPTER. Introduction In Mathematics, we frequently come across simple equations to be solved. For example, the equation x + = () is solved when x =, because this value
More informationREVIEW: Write each statement as an inequality and then graph the inequality.
LESSON 15 NOTES (Part A): SOLVING INEQUALITIES Words like "at most" and "at least" suggest a relationship in which two quantities may not be equal. These relationships can be represented by a mathematical
More informationHFCC Math Lab Intermediate Algebra  7 FINDING THE LOWEST COMMON DENOMINATOR (LCD)
HFCC Math Lab Intermediate Algebra  7 FINDING THE LOWEST COMMON DENOMINATOR (LCD) Adding or subtracting two rational expressions require the rational expressions to have the same denominator. Example
More informationSolving Equations with Integers
Solving Equations with Integers Properties for solving equations: Addition property  the same number can be added to each side of an equation without changing the equation Subtraction property  the same
More information1.3 Order of Operations
1.3 Order of Operations As it turns out, there are more than just 4 basic operations. There are five. The fifth basic operation is that of repeated multiplication. We call these exponents. There is a bit
More informationChapter 13: Polynomials
Chapter 13: Polynomials We will not cover all there is to know about polynomials for the math competency exam. We will go over the addition, subtraction, and multiplication of polynomials. We will not
More informationMANCHESTER COLLEGE Department of Education. Length: 25 minutes Grade Intended: PreAlgebra (7 th )
LESSON PLAN by: Kyler Kearby Lesson: Multiplying and dividing integers MANCHESTER COLLEGE Department of Education Length: 25 minutes Grade Intended: PreAlgebra (7 th ) Academic Standard: 7.2.1: Solve
More information1.3. Properties of Real Numbers Properties by the Pound. My Notes ACTIVITY
Properties of Real Numbers SUGGESTED LEARNING STRATEGIES: Create Representations, Activating Prior Knowledge, Think/Pair/Share, Interactive Word Wall The local girls track team is strength training by
More informationDigital Arithmetic. Digital Arithmetic: Operations and Circuits Dr. Farahmand
Digital Arithmetic Digital Arithmetic: Operations and Circuits Dr. Farahmand Binary Arithmetic Digital circuits are frequently used for arithmetic operations Fundamental arithmetic operations on binary
More informationTHE NUMBERS GAME Unit 2 of 4
1 College Guild PO Box 6448, Brunswick ME 04011 THE NUMBERS GAME Unit 2 of 4 To be proficient in math, one must know and be able to use the basic number facts; that is, the simple addition and multiplication
More information25 Integers: Addition and Subtraction
25 Integers: Addition and Subtraction Whole numbers and their operations were developed as a direct result of people s need to count. But nowadays many quantitative needs aside from counting require numbers
More informationLesson 16: Applying the Properties of Operations to Multiply and Divide Rational Numbers
Applying the Properties of Operations to Multiply and Divide Rational Numbers Student Outcomes Students use properties of operations to multiply and divide rational numbers without the use of a calculator.
More informationSupplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Section 9 Order of Operations
Supplemental Worksheet Problems To Accompany: The PreAlgebra Tutor: Volume 1 Please watch Section 9 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm
More informationAdding and Subtracting Integers. Objective: 1a. The student will add and subtract integers with the aid of colored disks.
Algebra/Geometry Institute Summer 2006 Monica Reece Grenada Middle School, Grenada, MS Grade 6 Adding and Subtracting Integers Objective: 1a. The student will add and subtract integers with the aid of
More informationSolving One Step Equations Guided Notes
CW/HW PreAlgebra Name: Date: Period: Solving One Step Equations Guided Notes I. Equations A. Vocabulary An _equation is a mathematical sentence with an equal sign. The following are all considered to
More information3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
More informationMathematics Success Level H
T393 [OBJECTIVE] The student will solve twostep inequalities and graph the solutions on number lines. [MATERIALS] Student pages S132 S140 Transparencies T372 from Lesson 15, T405, T407, T409, T411, T413,
More informationObservation 1. Observation 2. 5 and as decimals. Observation 3. 1 as percentages. Write.1875 and 4
Number Sense: Rational Numbers Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review, if necessary). Read
More informationSubtracting Negative Integers
Subtracting Negative Integers Notes: Comparison of CST questions to the skill of subtracting negative integers. 5 th Grade/65 NS2.1 Add, subtract, multiply and divide with decimals; add with negative integers;
More informationAccuplacer Arithmetic Study Guide
Testing Center Student Success Center Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole
More informationINTRODUCTION. Math Fast System, first. But if you are already proficient in basic math and pre
INTRODUCTION Welcome to the Learn Math Fast System, Volume IV. This book will cover basic Geometry. For the best results, you should read Volumes I III of the Learn Math Fast System, first. But if you
More informationELEMENTARY NUMBER THEORY AND METHODS OF PROOF
CHAPTER 4 ELEMENTARY NUMBER THEORY AND METHODS OF PROOF Copyright Cengage Learning. All rights reserved. SECTION 4.4 Direct Proof and Counterexample IV: Division into Cases and the QuotientRemainder Theorem
More information2.5 Zeros of a Polynomial Functions
.5 Zeros of a Polynomial Functions Section.5 Notes Page 1 The first rule we will talk about is Descartes Rule of Signs, which can be used to determine the possible times a graph crosses the xaxis and
More informationMultiplication and Division with Rational Numbers
Multiplication and Division with Rational Numbers Kitty Hawk, North Carolina, is famous for being the place where the first airplane flight took place. The brothers who flew these first flights grew up
More informationSection 1.1 Real Numbers
. Natural numbers (N):. Integer numbers (Z): Section. Real Numbers Types of Real Numbers,, 3, 4,,... 0, ±, ±, ±3, ±4, ±,... REMARK: Any natural number is an integer number, but not any integer number is
More informationAdding and Subtracting Integers
Adding and Subtracting Integers What s the Temperature? Lesson 81 Using Models to Add Integers ACTIVITY 8 Learning Targets: Using models, create several representations of a given integer. Using models,
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationAlgebra 1: Topic 1 Notes
Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating
More informationThe numbers that make up the set of Real Numbers can be classified as counting numbers whole numbers integers rational numbers irrational numbers
Section 1.8 The numbers that make up the set of Real Numbers can be classified as counting numbers whole numbers integers rational numbers irrational numbers Each is said to be a subset of the real numbers.
More informationPolynomials Classwork
Polynomials Classwork What Is a Polynomial Function? Numerical, Analytical and Graphical Approaches Anatomy of an n th degree polynomial function Def.: A polynomial function of degree n in the vaiable
More informationChapter 4 Fractions and Mixed Numbers
Chapter 4 Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers Parts of a Fraction Whole numbers are used to count whole things. To refer to a part of a whole, fractions are used.
More informationPreAlgebra  Integers
0.1 PreAlgebra  Integers Objective: Add, Subtract, Multiply and Divide Positive and Negative Numbers. The ability to work comfortably with negative numbers is essential to success in algebra. For this
More informationProperties of Real Numbers
16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should
More informationSimplifying Radical Expressions
In order to simplifying radical expression, it s important to understand a few essential properties. Product Property of Like Bases a a = a Multiplication of like bases is equal to the base raised to the
More information12 Mean, Median, Mode, and Range
Learn to find the mean, median, mode, and range of a data set. mean median mode range outlier Vocabulary The mean is the sum of the data values divided by the number of data items. The median is the middle
More informationLesson Plan Solving OneStep Linear Inequalities. Teacher Candidate: Grade Level/Subject Unit Title Lesson Title Duration Lesson Outcomes
Teacher Candidate: Grade Level/Subject Unit Title Lesson Title Duration Lesson Outcomes Chiara Shah 9 th /Algebra I Unit 4: Solving and Graphing Inequalities 6.1 Solving OneStep Linear Inequalities 45
More informationLesson Plan Warehouse Grade 7 Adding Integers
CCSSM: Grade 7 DOMAIN: The Number System Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Standard: 7.NS.1: Apply
More information2.4 Multiplication of Integers. Recall that multiplication is defined as repeated addition from elementary school. For example, 5 6 = 6 5 = 30, since:
2.4 Multiplication of Integers Recall that multiplication is defined as repeated addition from elementary school. For example, 5 6 = 6 5 = 30, since: 5 6=6+6+6+6+6=30 6 5=5+5+5+5+5+5=30 To develop a rule
More informationAdding and Subtracting Integers Unit. Grade 7 Math. 5 Days. Tools: Algebra Tiles. FourPan Algebra Balance. Playing Cards
Adding and Subtracting Integers Unit Grade 7 Math 5 Days Tools: Algebra Tiles FourPan Algebra Balance Playing Cards By Dawn Meginley 1 Objectives and Standards Objectives: Students will be able to add
More informationMathematics Success Grade 8
T92 Mathematics Success Grade 8 [OBJECTIVE] The student will create rational approximations of irrational numbers in order to compare and order them on a number line. [PREREQUISITE SKILLS] rational numbers,
More information1.2. Adding and Subtracting Integers Changing Elevations. My Notes ACTIVITY
Adding and Subtracting Integers SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge, Think/Pair/Share, Interactive Word Wall Ms. Flowers, a math teacher at Rachel Carson Middle School, plans a field
More informationReview: Addition and Subtraction of Positive and Negative Numbers
Review: Addition and Subtraction of Positive and Negative Numbers Objective To practice adding and subtracting positive and negative numbers. www.everydaymathonline.com epresentations etoolkit Algorithms
More informationUsing Algebra Tiles for Adding/Subtracting Integers and to Solve 2step Equations Grade 7 By Rich Butera
Using Algebra Tiles for Adding/Subtracting Integers and to Solve 2step Equations Grade 7 By Rich Butera 1 Overall Unit Objective I am currently student teaching Seventh grade at Springville Griffith Middle
More informationThese sample questions, selected from state endofcourse exams, cover the same algebraic concepts explored in the Math in Fashion lesson.
Math in Fashion: Sample Related EndofCourse (EOC) Questions These sample questions, selected from state endofcourse exams, cover the same algebraic concepts explored in the Math in Fashion lesson.
More informationVerbal Phrases to Algebraic Expressions
Student Name: Date: Contact Person Name: Phone Number: Lesson 13 Verbal Phrases to s Objectives Translate verbal phrases into algebraic expressions Solve word problems by translating sentences into equations
More informationTeaching & Learning Plans. Quadratic Equations. Junior Certificate Syllabus
Teaching & Learning Plans Quadratic Equations Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.
More informationCurriculum Alignment Project
Curriculum Alignment Project Math Unit Date: Unit Details Title: Solving Linear Equations Level: Developmental Algebra Team Members: Michael Guy Mathematics, Queensborough Community College, CUNY Jonathan
More informationMultiplying Integers. Lesson Plan
Lesson Plan Video: 12 minutes Lesson: 38 minutes Previewing :00 Warm up: Write 5 + 5 + 5 + 5 = on the board. Ask students for the answer. Then write 5 x 4 = on the board. Ask the students for the answer.
More informationELEMENTARY NUMBER THEORY AND METHODS OF PROOF
CHAPTER 4 ELEMENTARY NUMBER THEORY AND METHODS OF PROOF SECTION 4.4 Direct Proof and Counterexample IV: Division into Cases and the QuotientRemainder Theorem Copyright Cengage Learning. All rights reserved.
More informationUnit 3: Algebra. Date Topic Page (s) Algebra Terminology 2. Variables and Algebra Tiles 3 5. Like Terms 6 8. Adding/Subtracting Polynomials 9 12
Unit 3: Algebra Date Topic Page (s) Algebra Terminology Variables and Algebra Tiles 3 5 Like Terms 6 8 Adding/Subtracting Polynomials 9 1 Expanding Polynomials 13 15 Introduction to Equations 16 17 One
More informationUsing the Properties in Computation. a) 347 35 65 b) 3 435 c) 6 28 4 28
(1) Chapter 1 Real Numbers and Their Properties In this section 1.8 USING THE PROPERTIES TO SIMPLIFY EXPRESSIONS The properties of the real numbers can be helpful when we are doing computations. In this
More informationInteger Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions
Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.
More informationPicture. Right Triangle. Acute Triangle. Obtuse Triangle
Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from
More informationPicture. Right Triangle. Acute Triangle. Obtuse Triangle
Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from
More informationIntroduction to Fractions, Equivalent and Simplifying (12 days)
Introduction to Fractions, Equivalent and Simplifying (12 days) 1. Fraction 2. Numerator 3. Denominator 4. Equivalent 5. Simplest form Real World Examples: 1. Fractions in general, why and where we use
More informationTom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.
Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find
More informationModule 2 Rational Numbers
Module 2 Rational Numbers ENY Lesson 2 Using a Number Line to Add Integers 1 positive integers What is an integer? What do you know about: negative numbers Let's Make a Number Line Use the number line
More informationAddition of Two Negative Numbers. Sum of Two Numbers with Like Signs
.3 Addition and Subtraction of Real Numbers (9) 9 In this section Addition of Two Negative Numbers Addition of Numbers with Unlike Signs Subtraction of Signed Numbers.3 ADDITION AND SUBTRACTION OF REAL
More informationClifton High School Mathematics Summer Workbook Algebra 1
1 Clifton High School Mathematics Summer Workbook Algebra 1 Completion of this summer work is required on the first day of the school year. Date Received: Date Completed: Student Signature: Parent Signature:
More informationPreAlgebra Curriculum Map 8 th Grade Unit 1 Integers, Equations, and Inequalities
Key Skills and Concepts Common Core Math Standards Unit 1 Integers, Equations, and Inequalities Chapter 1 Variables, Expressions, and Integers 12 days Add, subtract, multiply, and divide integers. Make
More informationOperations on Decimals
Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers. Then write the decimal
More informationLesson 6 Rational Functions. Topics OUTLINE. Introduction
Lesson 6 Rational Functions Introduction In the last lesson we discussed polynomials and looked at how to add, subtract and multiply polynomials, but what happens when we divide polynomials? When we divide
More informationIII BACKGROUND KNOWLEDGE
Algebra Made Easy Grade Level: 6 th Presented by: Julia Daniely and Pat Graham, Miller Magnet School, Macon, Georgia Length of Unit: Five math lessons (10 days) I. ABSTRACT As we enter the 21 st century,
More informationTYPES OF NUMBERS. Example 2. Example 1. Problems. Answers
TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime
More informationNote: Remember you can always add zeros, after the decimal point, to the back of a number, if needed. $4.35 $5.68 $10.03
5.2 Adding and Subtracting Decimals Adding/Subtracting Decimals. Stack the numbers (one digit on top of another digit). Make sure the decimal points align. 2. Add/Subtract the numbers as if they were whole
More informationMonomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial
9.1 Add and Subtract Polynomials Before You added and subtracted integers. Now You will add and subtract polynomials. Why? So you can model trends in recreation, as in Ex. 37. Key Vocabulary monomial degree
More information