First Edition. Extending the Number System
|
|
- Diana Caren Terry
- 5 years ago
- Views:
Transcription
1 First Edition Extending the Number System
2 Understanding Integers Understanding integers on a number line.
3 Attributions : Say Thanks to the Authors Click Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution/Non- Commercial/Share Alike 3.0 Unported (CC BY-NC-SA) License ( as amended and updated by Creative Commons from time to time (the CC License ), which is incorporated herein by this reference. Helpful Websites and Apps LearnZillion AAAMath APlusClick Khan Academy App 2
4 Section 1 Integers Key Terms integer - a whole number and its opposite negative number - a number to the left of zero on a number line, written with a (-) sign. opposite - a pair of numbers that are the same distance from zero; a pair of numbers when added together equal zero (also called additive inverses) positive number - a number to the right of zero on a number line. whole number - a number without fractions; integer. z Integers in the Real World Have you ever heard a weather report that talked about temperatures below zero, like the cold front will produce temperatures of 10 below zero. What does that mean? Look at the thermometer. Notice that there are is a 10 above zero and one below zero. The one below zero is written with a (-) sign to show that it is less than zero. Do you notice that both of the 10 s are the same distance from zero? They go in opposite directions, but are the same distance. Numbers with the same value that are on opposite sides of zero are called opposite numbers What is the opposite of 50 F? What is the opposite of -1 F?
5 Think about this: On the same winter morning, the temperature is -28 in Anchorage, Alaska and in 65 Miami, Florida. How many degrees warmer was it in Miami than in Anchorage on that morning? Click here LearnZillion Video Temperature Where else can you find use for integers? You use integers to determine how much money is in your pocket, account or wallet. You have $10.00 in your pocket.!!! $10.00 You owe your sister $5.00.!!!! -$5.00 How much money do you have to spend AND be able to pay your sister back. Money that you owe is a negative amount. Money you have is a positive amount. At a bank there are special words that describe your negative and positive money amount. A checkbook register is one way to keep track of your spendings and earnings. A place for the check number, date and description of a transaction are given to keep your organized. If you have a balance of $ and need to pay your phone bill of $100.00, how much would you withdraw to pay the bill? How much would you have left? Click here LearnZillion Video Money INTERACTIVE 1.1 Check Register Number Date Transaction Withdrawal Deposit $ Withdrawal Deposit Checkbook A withdrawal is money you take out of your account, or spend. It is a negative amount. A deposit is money you put into your account, or save. It is a positive amount. 4
6 You also use integers in football. Have you ever heard of a 15 yard penalty? If so, what does that mean? It means you have to move back 15 yards in the opposite direction you want to go, or -15 yards from the line of scrimmage. Let s try writing a few integers and phrases that would represent them using the real world examples you have read about. Integer phrases practice: match the integer with the phrase Question 1 of 5 minus 10 degrees Fahrenheit a five yard penalty!!!!! -5 yds a gain of 10 yards!!!! 10 yds a loss of 12 yards!!!!! -12 yds A. -10 F B. +10 F a 10 degree dip in the temperature!! a 20 degree rise in the temperature!! -10 degrees 20 degrees C. -10 C D. 0 F a deposit of $300.00!!!! $ a withdrawal of $75.00!!!! -$75.00 earning $15.00!!!!! $15.00 Check Answer you owe $3.00!!!!!! -$3.00 5
7 We can use integers when we talk about elevation. On Earth, sea level is often treated like 0 on a number line. Objects above that level are considered positive values. Objects below that level are considered negative values. Click Here Learnzillion Video Elevation Think about this: Denver, Colorado is called The Mile High City because its elevation is 5280 feet above sea level. Someone tells you that the elevation of Death Valley, California is -282 feet. a. Is Death Valley located above or below sea level? Explain. b. How many feet higher is Denver than Death Valley? c. What would your elevation be if you were standing near the ocean? 6
8 Integers in Math Now that you have an idea of where we use integers in the real world, we will consider how to use them in the math world. A number line is a great place to start - think of it as a sideways thermometer. In math, opposites are a pair of numbers that are the same distance from zero going in opposite directions. Much of the time in math you will refer to opposites as negative and positive numbers. However, sometimes the (-) negative sign is read as the opposite of the number it is naming. -3 would be read as the opposite of 3-16 would be read as the opposite of 16 Opposites: translate the opposites Question 1 of 3 the opposite of 12 What about 0 (zero)? Zero is neither negative or positive. Notice how the numbers match up. Move one space to the right of zero and your are at 1. Move the same one space in the opposite direction and you are at and -1 are opposites. 15 and -15 are opposites A. -12 B. 12 C. 21 D. 0 Check Answer 7
9 Independent Practice Directions: Write an integer to represent each situation. 1. A loss of 20 points 2. A gain of 14 points 3. A profit of $ A loss of $ An elevation of 500 ft feet below sea level 7. 8 degrees below zero degrees 9. A decrease of $ An increase of $55.00 Challenge problems Directions: Write the opposite of each integer described or written 11. A loss of A gain of feet below the surface of the ocean Extra practice 8
10 Absolute Value and Ordering integers
11 Section 1 Absolute Value Absolute value is always a positive number. Absolute value is written as x The number is enclosed between two lines. Using this notation can be translated as the positive value of. Absolute value The absolute value of a number is its distance from zero. Example A -7 = 7 Solution: The absolute value of a number or an expression is ALWAYS positive or 0 The absolute values of opposite numbers are equal Example: -4 = 4 = 4 because both -4 and 4 are 4 units away from 0 Example B With absolute value the direction does not matter, only the distance. 10
12 **Important note!!! When a negative sign is written within the vertical lines, the answer will be positive -8 = 8 Fill in the rest of the chart, then answer the True False questions below. (Hint: think opposites)!! When a negative sign is written outside the vertical lines, the answer will be negative - 5 = -5 City State Elevation above sea level Elevation below sea level Example C - The opposite of the absolute value of 75, which is -75. The opposite of the absolute value of -25 is -25. Denver Colorado 5130? New Orleans Louisiana -8? Seattle Washington 0? Elevation True or False? Question 1 of 8 New Orleans is feet below sea level. Evaluate the following absolute values. a) c) b) d) A. True B. False Check you your Khan Academy App - Absolute Value Check Answer 11
13 Section 2 Ordering Integers The same applies when you have both +/- numbers in a group to be ordered. -12, 3, -4, 6 becomes -12, -4, 3, 6 in order from least to greatest Ordering integers You would have not problem if you were asked to put the numbers 13, 1, 15 and 8 in order from least to greatest. But, what if you needed to put -13, -1, -15 and -8 in order from least to greatest. What would you do? A number line would be a good place to start. Remember the farther to the left a number is, the smaller it is. The farther to the right a number is the larger it is. Draw the number line above on your own. Label the locations of -2 and -4. Remember the idea of opposites and that the farther to the left you go the smaller your value. Next, write the number is order from least to greatest. 0, 2, 4, -2, -4!!! Comparing Integers From least to greatest: -15, -13, -8, is farthest to the left so it is the smallest number In addition to ordering numbers in a set, you can use the number line to help you compare numbers using inequality signs (, ) How do we compare integers? -1 is the farthest to right so it is the greatest 12
14 rg/video/ordering-negativenumbers? There are a couple of important things to consider when comparing integers. 1. A positive number is ALWAYS greater than a negative number. The more positive a number, the greater it is. Let s look at an example. Example -6 2 Negative six is below zero. Two is above zero. Two is greater than negative six. -6 < 2 2. If two numbers are positive, the larger number is greater. Example Seventeen is greater than > If two numbers are negative, the number closer to zero is greater than the other. For two negative numbers, you have to think backwards. The larger the number the greater the loss is. The greater the loss, the smaller the number. Think about the number and its relationship to zero. Example Negative 25 is closer to zero than -36. It is the greater number. -25 > -36 Check out your Khan Academy App - negative number basics Ordering integers practice: 1. 3, 0, -2, , -3, 0, 2, 5, , 4, 2, -19, 0, -12, , -4, 5, 7, 0, 10, -7 Comparing integer practice:
15 Think about this: You can use what you have just learned to organize data from the real world. REVIEW 2.1 Ordering and Comparing Integers Question 1 of 5 Which statement is true Mon Tues Wed Thurs Fri Sat Sun Look at the low temperature in Juneau, Alaska for one week. a. Arrange them in order from coldest to warmest temperature. b. On a winter day, the low temperature in Anchorage was 23 degrees below zero (in C ) and the low temperature in Minneapolis was 14 degrees below zero (in C ). Sophia wrote, A B C Minneapolis was colder because Is Sophia correct? Explain your answer. c. The lowest temperature ever recorded on earth was -89 C in Antarctica. The average temperature on Mars is about -55 C. Which is warmer, the coldest temperature on earth or the average temperature on Mars? Write an inequality to support your answer. Check Answer Need more help? Click on this Learnzillion Video series (Click on any of the videos on the left side of the screen) 14
16 Section 3 Ordering Rational Numbers What is a rational number? A rational number is a number that can be written as a fraction; or p/q where q is not zero. Think to yourself: When moving to the RIGHT of zero, count UP. When moving to the LEFT of zero, count BACKWARD! -3 1/2 or -3.5! 1/2 or 0.5 Rational numbers include integers,simple fractions, mixed numbers, decimals and percents. Examples 1,2,3,4, 1/2, 1/3, 6/7, 1 3/5, 2 1/3 2.35, 5.5, 10.3, 60%, 125% Like whole numbers, fractions and decimals can have negative values. BUT, they are not considered integers. Remember integers are WHOLE numbers and their opposites. Ordering rational numbers is just like ordering integers. Tips for Ordering If you have fractions, percents and decimals in the same group of numbers to be orders, change them to all one type. Example: Change all numbers to decimals 3.5, 75%, -0.28, 1 1/3 3.5, 0.75, -0.28, 1.33 Now they can be put in order easily. 15
17 **Reminders Ascending order is another way to say from least to greatest (going up) Descending order is from greatest to least (going down) Ordering rational numbers Question 1 of 3 Which group of numbers is in ascending order? A. -1 1/2, -1/2, 0, 1, 4 B. 0, -1/2, 1, -1 1/2, 4 C. 4, 1, 0, -1/2, -1 1/2 Check Answer 16
18 Absolute value absolute value; noun 1 Mathematics the magnitude of a real number without regard to its sign. Also called modulus. Related Glossary Terms Drag related terms here Index Find Term
19 Integer ˈintijər noun 1 a whole number; a number that is not a fraction. 2 a thing complete in itself. Related Glossary Terms Drag related terms here Index Find Term
20 Negative number A negative number is a real number that is less than zero. Such numbers are often used to represent the amount of a loss or absence. For example, a debt that is owed may be thought of as a negative asset, or a decrease in some quantity may be thought of as a negative increase. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. Related Glossary Terms Drag related terms here Index Find Term
21 Opposites a pair of numbers that are the same distance from zero; a pair of numbers when added together equal zero (also called additive inverses) Related Glossary Terms Drag related terms here Index Find Term
22 Positive number A positive number is a real number that is greater than zero. Such numbers are often used to represent the amount of a gain or increase. Related Glossary Terms Drag related terms here Index Find Term
23 Rational number In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number. Related Glossary Terms Drag related terms here Index Find Term
ABSOLUTE VALUE Judo Math Inc.
ABSOLUTE VALUE 2013 Judo Math Inc. 6 th grade Number Sense Discipline: Orange Belt Training Order of Mastery: Absolute Value (6NS7-8) 1. Inequality to show position 2. Explain statements of order in the
More informationIntroduction to Integers
Introduction to Integers Get the Point? Lesson 7-1 Integers and the Number Line Lesson Targets: Use integers to represent quantities in real-world contexts. Position and identify integers on a number line.
More informationGrade 6. The Number System & Mathematical Operations.
1 Grade 6 The Number System & Mathematical Operations 2015 10 20 www.njctl.org 2 Table of Contents Addition, Natural Numbers & Whole Numbers Addition, Subtraction and Integers Multiplication, Division
More informationMATH STUDENT BOOK. 6th Grade Unit 9
MATH STUDENT BOOK 6th Grade Unit 9 Unit 9 Integers and Transformations MATH 609 Integers and Transformations 1. INTEGERS 5 INTEGERS 6 COMPARING AND ORDERING INTEGERS 12 ABSOLUTE VALUE 16 COORDINATE PLANE
More informationGrade 6 The Number System & Mathematical Operations
Slide 1 / 206 Slide 2 / 206 Grade 6 The Number System & Mathematical Operations 2015-10-20 www.njctl.org Slide 3 / 206 Table of Contents Addition, Natural Numbers & Whole Numbers Addition, Subtraction
More informationACTIVITY: Reading Thermometers. Work with a partner. The thermometers show the temperatures in four cities.
6. Integers less than? How can you represent numbers that are ACTIVITY: Reading Thermometers Work with a partner. The thermometers show the temperatures in four cities. Honolulu, Hawaii Death Valley, California
More informationIntegers and Absolute Value
Practice A Integers and Absolute Value Circle the letter that best represents each situation. 1. a gain of 5 yards in football A 5 B +5 C 50 D +50 3. an elevation of 9 feet below sea level A 9 B 1 + 9
More information3 or ; 4 1 or 4
LESSON 98 Temperature Power Up facts mental math Power Up I a. Number Sense: Simplify the improper fractions 6 4, 7 4, and 8 4. 11 2, 1 4, 2 b. Number Sense: What is the reciprocal of 4?... of 1 4? 4 or
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 informationIntegers. Domain 1 Lesson 3. Getting the Idea. Example 1. Strategy. Step 1. Step 2
Domain 1 Lesson 3 Integers Common Core Standards: 6.NS.5, 6.NS.6.a, 6.NS.6.c Getting the Idea Integers include the counting numbers (1, 2, 3, ), their opposites (21, 22, 23, ), and zero. The number line
More informationThe Celsius temperature scale is based on the freezing point and the boiling point of water. 12 degrees Celsius below zero would be written as
Prealgebra, Chapter 2 - Integers, Introductory Algebra 2.1 Integers In the real world, numbers are used to represent real things, such as the height of a building, the cost of a car, the temperature of
More informationIntroduction to Negative Numbers and Computing with Signed Numbers
Section 6. PRE-ACTIVITY PREPARATION Introduction to Negative Numbers and Computing with Signed Numbers In the previous five chapters of this book, your computations only involved zero and the whole numbers,
More informationCH 17 INTRO TO SIGNED NUMBERS
101 CH 17 INTRO TO SIGNED NUMBERS Positive and Negative Numbers Have you ever owed someone money? Then you already know all about negative numbers. Let s begin with a picture of the positive and negative
More information1 Monday s low temperature was -6. The high for the day was 11. How many degrees did the temperature rise?
1 Monday s low temperature was -6. The high for the day was 11. How many degrees did the temperature rise? 2 The temperature for seven days were recorded in degrees Fahrenheit as follows: -5, 10, 3, -6,
More informationCH 10 INTRO TO SIGNED NUMBERS
87 CH 10 INTRO TO SIGNED NUMBERS Positive and Negative Numbers W e just saw equations like x + 2 = 10, and we know that we can subtract 2 from each side of the equation to get the solution x = 8. But what
More informationReview for Test #1 over Ch 1. Work all the problems on a separate piece of paper showing all steps.
109 Review for Test #1 over Ch 1 Work all the problems on a separate piece of paper showing all steps. Define each of the following: 1) a) Natural Numbers b) Whole Numbers c) Integers d) Rational Numbers
More informationReal Numbers and an Introduction to Algebra
ChaPter 1 Real Numbers and an Introduction to Algebra Objectives In this chapter you will learn how to do the following: 1. Read mathematical symbols. 2. Distinguish between different sets of numbers.
More informationChapter 4 Formulas and Negative Numbers
Chapter 4 Formulas and Negative Numbers Section 4A Negative Quantities and Absolute Value Introduction: Negative numbers are very useful in our world today. In the stock market, a loss of $2400 can be
More informationMath 6 Notes Integers
We use positive and negative numbers dail in real life. Positive numbers are those numbers greater than zero. The can be written with a positive (+) sign in front of them, but we usuall write a positive
More informationIntegers and Absolute Value (Pages 56 61)
2-1 Integers and Absolute Value (Pages 56 61) An integer is a number that is a whole number of units from zero on the number line. Integers to the left of zero are less than zero. They are negative. The
More informationAssignment. I Love New York Negative Numbers in the Real World
Assignment Assignment for Lesson 7.1 Name I Love New York Negative Numbers in the Real World Date 1. The highest temperature ever recorded on Earth was 136 F at Al Aziziyah, Libya, in Africa. The lowest
More informationDraw a horizontal line. Place a point on the line and label it 0.
Lesson 1 Materials: Paper, Ruler, Compass Activity: Constructing the Number Line: Draw a horizontal line. Place a point on the line and label it 0. Use a compass to locate and label the next point 1, thus
More informationII COMMON Lesson 1: Positive and Negative Numbers on the Number line opposite. enaaae. Lesson 1: Positive and Negative Numbers on the Number Line
II COMMON Lesson 1: Positive and Negative Numbers on the Number line opposite ny Direion and Value enaaae 51 Date: 10/7/13 Which group had the opposite of the number on your index card? Choose a group
More informationInequalities. CK12 Editor. Say Thanks to the Authors Click (No sign in required)
Inequalities CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org
More informationMath 7 Notes Unit Two: Integers
Math 7 Notes Unit Two: Integers Syllabus Objective: 2.1 The student will solve problems using operations on positive and negative numbers, including rationals. Integers the set of whole numbers and their
More informationI will understand absolute value and use it to find magnitude of a positive or negative quantity.
Today's Objective: I will understand absolute value and use it to find magnitude of a positive or negative quantity. 1 Lesson 11: Absolute Value Magnitude and Distance Opening Exercise: 2 Example 1: The
More informationSection 1 - Introduction to Integers
Pre Algebra Unit 1 Unit 1 Integers Objective Overview The following is a small subset of possible problems that could represent each objective. Refer to notes, homework and reviews for a more complete
More information{ }. 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 informationIntegers What, Me Negative? 10.2 Number Sets Ordering and Absolute Value
Integers At 282 feet below sea level, Badwater Basin in Death Valley, California, is the lowest spot in the United States. Since terrain elevation is measured in comparison with sea level, Death Valley's
More informationLesson 2: Real-World Positive and Negative Numbers and Zero
Lesson 2: Real-World Positive and Negative Numbers and Zero Classwork Example 1: Take it to the Bank For Tim s 13 th birthday, he received $150 in cash from his mom. His dad took him to the bank to open
More informationComparing and Ordering Integers
6.2 Comparing and Ordering Integers to order real-life events? How can you use a number line 1 ACTIVITY: Seconds to Takeoff Work with a partner. You are listening to a command center before the of a rocket.
More informationContents. Positive and Negative. Additional Practice Answers to Check Your Work. Section A
Contents Section A Positive and Negative What Time Is It There? 1 World Time Zones 3 Below and Above Sea Level 6 Summary 10 Check Your Work 10 Additional Practice Answers to Check Your Work Student Activity
More informationA C E. Answers Investigation 3. Applications. 2 are equivalent. It takes 3 thirds to. 1 or 1. 4 or. 2 or
Applications Answers Investigation. and are equivalent. It takes thirds to make whole, so thirds is equivalent to wholes and one third.. B. (See Figure.). Answers will vary. (See Figure.) Pay attention
More informationElectron Arrangement
Electron Arrangement Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org
More information{ }. The dots mean they continue in that pattern to both
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 to both positive and negative infinity. Before starting
More informationHW: page 168 (12-24 evens, 25-28) Extra Credit # 29 & 31
Lesson 5-1 Rational Numbers pages 166-168 Review our number system and real numbers. Our Number System Real Complex Rational Irrational # Integers # Whole # Natural Rational Numbers the word "rational"
More informationSAMPLE: DO NOT REPRODUCE IN2 STUDENT PACKET INTEGERS STUDENT PACKET 2: INTEGER CONCEPTS. Name Period Date
Name Period Date INTEGERS STUDENT PACKET 2: INTEGER CONCEPTS IN2.1 IN2.2 IN2.3 Temperature and Number Lines Represent integers on a number line. Explore integer addition on the number line. Use integers
More informationG6-M3-Lesson 1: Positive and Negative Numbers on the Number Line Opposite Direction and Value
G6-M3-Lesson 1: Positive and Negative Numbers on the Number Line Opposite Direction and Value 1. Draw a number line, and create a scale for the number line in order to plot the points 1, 3, and 5. a. Graph
More informationNorth Seattle Community College Math 084 Chapter 1 Review. Perform the operation. Write the product using exponents.
North Seattle Community College Math 084 Chapter 1 Review For the test, be sure to show all work! Turn off cell phones. Perform the operation. Perform the operation. Write the product using exponents.
More informationApply Properties of 1.1 Real Numbers
TEKS Apply Properties of 1.1 Real Numbers a.1, a.6 Before Now You performed operations with real numbers. You will study properties of real numbers. Why? So you can order elevations, as in Ex. 58. Key
More informationRational Numbers. Chapter GOALS
Chapter Rational Numbers GOALS You will be able to interpret, compare, and order rational numbers add, subtract, multiply, and divide rational numbers using the correct order of operations solve problems
More informationI.E.S. Andrés de Vandelvira - Sección Europea
1 The negative numbers. 6 Integers There are many situations in which you need to use numbers below zero, one of these is temperature, others are money that you can deposit (positive) or withdraw (negative)
More informationBeginning Algebra. v. 1.0
Beginning Algebra v. 1.0 Table of Contents About the Author... 1 Acknowledgments... 2 Preface... 3 Chapter 1: Real Numbers and Their Operations... 5 Real Numbers and the Number Line... 6 Adding and Subtracting
More informationMath 90 Lecture Notes Chapter 1
Math 90 Lecture Notes Chapter 1 Section 1.1: Introduction to Algebra This textbook stresses Problem Solving! Solving problems is one of the main goals of mathematics. Think of mathematics as a language,
More informationLesson 1: Positive and Negative Numbers on the Number Line Opposite Direction and Value
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 6 3 Lesson 1: Positive and Negative Numbers on the Number Line Opposite Direction and Value 1. If zero lies between aa and dd, give one set of possible values
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 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 informationHonors Math 2 Unit 5 Exponential Functions. *Quiz* Common Logs Solving for Exponents Review and Practice
Honors Math 2 Unit 5 Exponential Functions Notes and Activities Name: Date: Pd: Unit Objectives: Objectives: N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
More informationAppendix B Lesson 1: What Is Weather Exit Ticket
Appendix B Lesson 1: What Is Weather Exit Ticket Name Date Period What is Weather? Exit Ticket List 3 things that you learned during the demonstrations today. What are two questions that you still have?
More informationSignificant Figures. CK12 Editor. Say Thanks to the Authors Click (No sign in required)
Significant Figures CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,
More informationWork with a partner. Write an integer that represents the elevation of each object. How far is each object from sea level? Explain your reasoning.
6.4 Absolute Value from sea level? How can you describe how far an object is ACTIVITY: Sea Level Work with a partner. Write an integer that represents the elevation of each object. How far is each object
More informationMath 8 Ms. Campos Unit 1- Integers
Math 8 Ms. Campos Unit 1- Integers 2017-2018 Day Test Date: Lesson Topic Homework Schedule Sept W 6 First Day Return Signed Contract T 7 1 Introduction to Integers Lesson 1- page 4 F 8 2 Add and Subtract
More informationIntegers. Academic Vocabulary elevation
Integers Unit Overview In this unit, you will study negative numbers, and you will learn to add, subtract, multiply and divide them. You will graph positive and negative numbers on number lines and on
More informationGRE Workshop Quantitative Reasoning. February 13 and 20, 2018
GRE Workshop Quantitative Reasoning February 13 and 20, 2018 Overview Welcome and introduction Tonight: arithmetic and algebra 6-7:15 arithmetic 7:15 break 7:30-8:45 algebra Time permitting, we ll start
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 informationComplex Numbers CK-12. Say Thanks to the Authors Click (No sign in required)
Complex Numbers CK-12 Say Thanks to the Authors Click http://www.ck12.org/saythanks No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org
More informationPolynomials. Eve Rawley, (EveR) Anne Gloag, (AnneG) Andrew Gloag, (AndrewG)
Polynomials Eve Rawley, (EveR) Anne Gloag, (AnneG) Andrew Gloag, (AndrewG) Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book,
More informationMath 7 Notes Unit 1: Integers
Integers are defined as the set of whole numbers {0, 1, 2, } and their opposites. One way to show this is listing its members like this {...,, 2, 1, 0, 1, 2,, } or more simply {, -1, 0 +1, } or describing
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 informationVectors (Trigonometry Explanation)
Vectors (Trigonometry Explanation) CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive
More informationWhen any two whole numbers are added we always get another whole number
UNIT 5 INTEGERS IES CASTILBLANCO DE LOS ARROYOS 1. MENTAL CALCULATION INTRODUCING INTEGERS 2. HOW MANY DIFFERENTS NUMBERS CAN I REMEMBER? Please listen these ten different situations and decide with your
More informationUnit 1 Writing and Evaluating Algebraic Expressions
CC Math 1A Name Unit 1 Writing and Evaluating Algebraic Expressions Day Date Lesson Assignment Mon 8/25 Lesson 1 Writing and Evaluating Algebraic Expressions Tues 8/26 Lesson 2 Combining Like Terms & Distributive
More informationIntegers. number AnD AlgebrA NuMber ANd place value
2 2A Adding and subtracting integers 2B Multiplying integers 2C Dividing integers 2D Combined operations on integers WhAT Do You know? Integers 1 List what you know about positive and negative integers.
More informationFair Game Review. Chapter. Order the integers from least to greatest. 1. 9, 8, 0, 3, , 4, 1, 2, , 6, 8, 5, 9 4.
Name Date Chapter 1 Fair Game Review Order the integers from least to greatest. 1. 9, 8, 0, 3, 7.,, 1,, 1 3. 11, 6, 8, 5, 9.,, 5, 0, 7 Use the graph to write an ordered pair corresponding to the point.
More informationBuilding Concepts: What is an Equation?
Lesson Overview Algebraic Focus: How do equations differ from expressions? What does it mean to have a solution to an equation? In this lesson students begin by establishing the difference between an expression
More informationThis is Solving Linear Systems, chapter 4 from the book Beginning Algebra (index.html) (v. 1.0).
This is Solving Linear Systems, chapter 4 from the book Beginning Algebra (index.html) (v. 1.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
More informationUnit 5, Lesson 1: Interpreting Negative Numbers
Unit 5, Lesson 1: Interpreting Negative Numbers Lesson Goals Locate rational numbers on the number line. Interpret positive and negative numbers in context. Compare rational numbers. Required Materials
More informationReady to Go On? Skills Intervention Integers in Real-World Situations
11-1 Ready to Go On? Skills Intervention Integers in Real-World Situations Positive numbers are greater than 0. They can be shown with or without the positive sign. For example: 25 or 25 Negative numbers
More informationAdding Integers with Different Signs. ESSENTIAL QUESTION How do you add integers with different signs? COMMON CORE. 7.NS.1, 7.NS.
? LESSON 1.2 Adding Integers with Different Signs ESSENTIAL QUESTION How do you add integers with different signs? 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and
More informationOperations with Integers
Operations with Integers Integers and Absolute Values Solve multi step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals),
More informationName: Date: Core: Rational Numbers. Opposite and Absolute Value of Integers. Comparing and Ordering Rational Numbers
Name: Date: Core: Rational Numbers Comparing and Ordering Integers Opposite and Absolute Value of Integers Intro to Rational Numbers Comparing and Ordering Rational Numbers Rational Numbers on Coordinate
More information{...- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4,...}
Introduction to Integers (2.1) Integers are the set of whole numbers and their opposites. {...- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4,...} Example: The highest elevation in North America is Mt. McKinley, which
More informationSolving Absolute Value Equations and Inequalities
Solving Absolute Value Equations and Inequalities Say Thanks to the Authors Click http://www.ck1.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive
More informationNumber System Chapter Questions
Number System Chapter Questions. What is an integer?. Explain what absolute value represents.. Create an owing money example for comparing two negative numbers.. What is the Cartesian (Coordinate) plane?
More informationChapter 1. Exercise Set 1.1
Chapter Exercise Set.. To prepare properly for this class, you need to do all the homework carefully and preview the new material that is to be covered in class.. At least hours of study and homework time
More informationLesson Rules for Dividing Integers (and Rational Numbers)
Lesson: Lesson 3.3.2 Rules for Dividing Integers (and Rational Numbers) 3.3.2 Supplement Rules for Dividing Integers (and Rational Numbers) Teacher Lesson Plan CC Standards 7.NS.2 Apply and extend previous
More informationMATHS QUEST 8 for the Australian Curriculum
MATHS QUEST 8 for the Australian Curriculum 2 2A Adding and subtracting integers 2B Multiplying integers 2C Dividing integers 2D Combined operations on integers WHAT DO YOU KNOW? Integers 1 List what you
More informationChapter 2: Linear Functions
Chapter 2: Linear Functions Chapter one was a window that gave us a peek into the entire course. Our goal was to understand the basic structure of functions and function notation, the toolkit functions,
More informationIntermediate Algebra
Intermediate Algebra Anne Gloag Andrew Gloag Mara Landers Remixed by James Sousa Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org To access a customizable
More informationMath 7 Notes Unit 02: Rational Numbers
As we begin this unit it s a good idea to have an overview. When we look at the subsets of the real numbers it helps us organize the groups of numbers students have been exposed to and those that are soon
More informationAdding and Subtracting Integers. How can you use addition and subtraction of integers to solve real-world problems?
UNIT 1 Study Guide Review? MODULE 1 ESSENTIAL QUESTION Adding and Subtracting Integers How can you use addition and subtraction of integers to solve real-world problems? Key Vocabulary additive inverse
More informationSUMMER PACKET FOR HONORS ALGEBRA ONE
SUMMER PACKET FOR HONORS ALGEBRA ONE Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Write an algebraic expression for the phrase.. the sum
More information8.1 Apply Exponent Properties Involving Products. Learning Outcome To use properties of exponents involving products
8.1 Apply Exponent Properties Involving Products Learning Outcome To use properties of exponents involving products Product of Powers Property Let a be a real number, and let m and n be positive integers.
More informationWork with a partner. How can you show that ( 1)( 1) = 1?
. Multiplying and Dividing Rational Numbers numbers positive? Why is the product of two negative rational In Section., you used a table to see that the product of two negative integers is a positive integer.
More informationLesson 1. Problem 1. Solution. Problem 2. Solution. Problem 3
Lesson 1 Tyler reads of a book on Monday, of it on Tuesday, of it on Wednesday, and of the remainder on Thursday. If he still has 14 pages left to read on Friday, how many pages are there in the book?
More informationHow can you use a number line to compare positive and negative fractions and decimals? ACTIVITY: Locating Fractions on a Number Line
. Fractions and Decimals on the Number Line How can you use a number line to compare positive and negative fractions and decimals? ACTIVITY: Locating Fractions on a Number Line On your time line for A
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 informationAlgebra SECTION 1: THE MEANING AND USE OF SIGNED NUMBERS; THE SET OF INTEGERS
Algebra Introduction: About how many days each year does the temperature in Oklahoma City drop below zero? Water freezes at 0ϒC. How would you write a temperature below zero? You can write 1ϒC above zero
More informationStudy Guide and Intervention
NAME DATE PERIOD Study Guide and Intervention Adding Integers For integers with the same sign: the sum of two positive integers is positive. the sum of two negative integers is negative. For integers with
More informationHave fun & we ll see you in August!
Kids Information Page We re so proud of you for taking the time to work on math over the summer! Here are some helpful hints for success: Find a quiet work space where you can get organized and stay focused.
More informationMTH 05 Lecture Notes. Andrew McInerney
MTH 05 Lecture Notes Andrew McInerney Fall 2016 c 2016 Andrew McInerney All rights reserved. This work may be distributed and/or modified under the conditions of the Copyleft License. Andrew McInerney
More informationWhy is the product of two negative rational numbers positive?
. Multiplying and Dividing Rational Numbers Why is the product of two negative rational numbers positive? In Section., you used a table to see that the product of two negative integers is a positive integer.
More information6 th Grade Re-engagement ADDITIONAL RE-ENGAGEMENT AND PRACTICE 6.NS.6C
6 th Grade Re-engagement ADDITIONAL RE-ENGAGEMENT AND PRACTICE 6.NS.6C 6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs
More informationSt. Ann s Academy - Mathematics
St. Ann s Academy - Mathematics Students at St. Ann s Academy will be able to reason abstractly and quantitatively. Students will define, explain, and understand different types of word problems (simple
More informationGrade 6 - SBA Claim 1 Example Stems
Grade 6 - SBA Claim 1 Example Stems This document takes publicly available information about the Smarter Balanced Assessment (SBA) in Mathematics, namely the Claim 1 Item Specifications, and combines and
More informationMath Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities)
Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities) By Scott Fallstrom and Brent Pickett The How and Whys Guys This work is licensed under a Creative Commons
More informationInteresting Integers!
Interesting Integers! What You Will Learn n Some definitions related to integers. n Rules for adding and subtracting integers. n A method for proving that a rule is true. Are you ready?? Definition n Positive
More informationAsk questions such as If you ate a total of 30 cookies, some in the morning and 12 in the afternoon, how many crackers did you eat in the morning?
Welcome to Summer Vacation! Your child has worked hard this school year to strengthen their ability as a young Mathematician. Remember that learning does not stop outside the classroom. Daily routines
More informationReteaching Using Deductive and Inductive Reasoning
Name Date Class Reteaching Using Deductive and Inductive Reasoning INV There are two types of basic reasoning in mathematics: deductive reasoning and inductive reasoning. Deductive reasoning bases a conclusion
More informationFourth Grade Number Sense and Algebraic Concepts
Slide 1 / 308 Slide 2 / 308 Fourth Grade Number Sense and Algebraic Concepts 2015-11-23 www.njctl.org Compare numbers Round Numbers Patterns Slide 3 / 308 Table of Contents Algebraic Equations/Number Sentences
More information