# 1.2. Adding and Subtracting Integers Changing Elevations. My Notes ACTIVITY

Save this PDF as:

Size: px
Start display at page:

Download "1.2. Adding and Subtracting Integers Changing Elevations. My Notes ACTIVITY"

## Transcription

1 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 trip for her students every year. On the first day of school, each student recommends a place where the class should go on the annual trip. 1. If your teacher were to plan a field trip for your class this year, where would you like to go? Write your choice below and explain why this would be a good choice for your class trip. ACTIVITY 1.2 When the students report to math class, many have ideas about where they would like to go. Marcus wants the class to go to Death Valley this year. The other students think that Death Valley would not be a pleasant place to visit so they tell Marcus to convince them this is a good choice. In his research, Marcus finds that Death Valley is very interesting and could be called a land of extremes. He was surprised to learn that Death Valley has some high mountains and some very low canyons. He noticed that some elevations in Death Valley are above sea level and are listed as positive numbers, while some are below sea level and are listed as negative numbers. He also noticed that the online atlas listed sea level as 0 feet. For a moment he was confused about what these numbers meant, but then remembered that last year he learned that these numbers are called integers. 2. In the chart below, list what you already know about integers and what more you would like to learn about them. When you are finished, your class will make a chart showing everyone s information. What I know about integers: What I want to learn about integers: Unit 1 Integers and Rational Numbers 11

2 ACTIVITY 1.2 Adding and Subtracting Integers SUGGESTED LEARNING STRATEGIES: Visualize, Create Representations, Quickwrite, Look for a Pattern, Group Presentation, Think/Pair/Share 3. Marcus found that one of the lowest elevation points on Earth is in Death Valley. Some of Earth s lowest locations and their elevations are listed below. Lake Assal (Africa): -509 ft. Qattara Depression (Egypt): -435 ft. Laguna del Carbón (Argentina): -344 ft. Death Valley (United States): -282 ft. Valdes Peninsula (Argentina): -131 ft. Graph the integer for each elevation on this number line Death Valley also has some higher points of elevation. They include: Shoshone, with an elevation of 1585 feet Dante s View, with an elevation of 5500 feet Butte Valley, with an elevation of 4400 feet Graph the integer for each elevation on this number line Look back at the number lines in Questions 3 and 4. What do you notice about the order of the integers on the number line? 6. Using your generalization from Question 5, order the integers in each set from least to greatest. a , -282, -435 b. -410, -505, -509, -180 c. -266, -227, -410, SpringBoard Mathematics with Meaning TM Level 2

3 Adding and Subtracting Integers ACTIVITY 1.2 SUGGESTED LEARNING STRATEGIES: Quickwrite, Look for a Pattern, Interactive Word Wall, KWL, Think/Pair/Share The students began thinking about elevation. They reasoned that there must be places as far above sea level as there are below sea level. 7. For example, the elevation of the Salton Sea in California is -227 feet and Jamestown, Louisiana is approximately 227 feet above sea level. Graph the integer for each location Describe the position of these two integers in relationship to zero. 9. Telescope Peak is the highest point in Death Valley. Its elevation is 11,049 feet. a. If a student begins a hike at sea level, and hikes to the top of Telescope Peak, how far above sea level will he be? b. If a diving bell begins a dive at sea level, and dives to a point below sea level that is as far from sea level as Telescope Peak, how far below sea level would it be? c. What are the two distances in questions 8 and 9 called? 10. Why are the distances of the hike and the dive with their changes in elevation an example of two integers with the same absolute value? 11. Write the absolute value of each integer. Integer ,865 Absolute Value Unit 1 Integers and Rational Numbers 13

4 ACTIVITY 1.2 Adding and Subtracting Integers MATH TERMS The absolute value of a number is its distance from zero on a number line. Distance or absolute value is always positive, so -6 = 6 and 6 = 6. SUGGESTED LEARNING STRATEGIES: Think Aloud, Summarize/Paraphrase/Retell, Think/Pair/Share, Quickwrite 12. Evaluate each expression. a b. 56 c. 0 The students in Ms. Flower s class were starting to get excited about their field trip, but Lindsay was concerned that they would not be able to stay warm at night. When camping, even when it is very hot during the day, it can be very cold at night. Lindsay decided to do some research on sleeping bags. The temperature rating of a sleeping bag describes the lowest outside temperature at which the bag will keep a sleeper warm. 13. Look at each situation below and decide if the sleeping bag is the correct bag for the temperature of the camping location based on the rating of the bag. Location Alamosa, Colorado Yellowstone National Park St. Cloud, Minnesota Bartlett, New Hampshire Fairbanks, Alaska Sleeping Bag Rating Outside Temperature º 0-10º -10-3º º +15-4º Will sleeper be warm? 14. List the locations for which the sleeping bags are not rated for the temperature and explain why. 15. How did being able to compare integers help you know which sleeping bag would keep a sleeper warm? Explain below. 14 SpringBoard Mathematics with Meaning TM Level 2

5 Adding and Subtracting Integers ACTIVITY 1.2 SUGGESTED LEARNING STRATEGIES: Close Reading, Visualize, Group Presentation, Create Representations You can use inequalities to compare integers. 16. For each pair of integers, write two inequalities comparing the integers using the given inequality symbol. Integers < > 35, 60 0, , -3 15, , -4 Inequalities can also be graphed on a number line. READING MATH Read the symbol > as greater than. Read the symbol < as less than. Read the symbol as greater than or equal to. Read the symbol as less than or equal to. EXAMPLE 1 Graph the inequality: x < 2. Step 1: Step 2: Graph the integer in the inequality on the number line. Since 2 is the integer, locate 2 on the number line. If the inequality sign is < or >, graph the point as an open circle because the integer is not part of the solution. If the inequality sign is or, graph the point as a closed circle because the integer is part of the solution Think about the group of numbers the inequality is describing and draw an arrow on the number line to represent them. Since the numbers described in the inequality are less than 2, the arrow goes to the left because that is where all numbers less than 2 are Solution: The number line above is the graph of x < 2. Unit 1 Integers and Rational Numbers 15

6 ACTIVITY 1.2 Adding and Subtracting Integers TRY THESE A SUGGESTED LEARNING STRATEGIES: KWL, Group Presentation, Think/Pair/Share, Close Reading Graph each inequality. a. y < 6 b. s > -5 c. b -2 d. a 7 Integers without signs are considered to be positive. Some of the students were excited about going hiking on their field trip. Ms. Flowers knew that thinking about hiking could help the students understand adding and subtracting integers. She explained adding and subtracting integers using ideas related to hiking. The first number in a problem is where you start your hike. The operation sign in the middle of the problem tells you whether you are going to face in the positive direction or the negative direction. The sign of the second number tells you if you are going to step backward (-) or forward (+). The answer to the integer problem is where your hike ends. EXAMPLE 2 Find the sum: -4 + (-2) Use this number line to follow along with this example. Step 1: Start at -4. Step 2: Face the positive direction (right). Step 3: Since the 2 is negative, take 2 steps backward (to the left). Solution: The answer is SpringBoard Mathematics with Meaning TM Level 2

7 Adding and Subtracting Integers ACTIVITY 1.2 SUGGESTED LEARNING STRATEGIES: Create Representations, Use Manipulatives TRY THESE B Illustrate the move for each problem. Then record your answer: a (-3) = b. 6 + (-6) = c. 5 + (-3) = d = 17. Work with a partner. For each problem, roll a number cube twice. Use the numbers you roll to make a problem. Then use the number line to solve the problem. Look for patterns while you work. a. - + (- ) = WRITING MATH Parentheses are placed around a signed number to make a problem easier to read. b. - + = c. + (- ) = d. + = 18. What patterns did you notice about integer addition as you worked? Unit 1 Integers and Rational Numbers 17

8 ACTIVITY 1.2 Adding and Subtracting Integers SUGGESTED LEARNING STRATEGIES: Self Revision/Peer Revision, Look for a Pattern, KWL, Group Presentation 19. Use the patterns that you noticed to write rules about adding integers. Include an example in your explanation. a. A positive integer plus a positive integer. b. A negative integer plus a negative integer. c. A negative integer plus a positive integer. d. A positive integer plus a negative integer. e. An integer and its opposite Now consider subtracting integers. EXAMPLE 3 Find the difference: -4 - (-2) Use this number line to follow along with this example. Step 1: Start at -4. Step 2: Face the negative direction (left). Step 3: Since the 2 is negative, take 2 steps backward (to the right). Solution: The answer is SpringBoard Mathematics with Meaning TM Level 2

9 Adding and Subtracting Integers ACTIVITY 1.2 SUGGESTED LEARNING STRATEGIES: Create Representations, Use Manipulatives TRY THESE C Illustrate the move for each problem. Then record your answer. a (-3) = b = c. 5 - (-3) = d. 6-2 = 20. For each move that you illustrated in Try These C, show a different move that starts at the same integer and has the same answer as the original problem. The first one is done for you. a (-3) = -5 + (+3) = -2 b = c. 5 - (-3) = d. 6-2 = Unit 1 Integers and Rational Numbers 19

10 ACTIVITY 1.2 Adding and Subtracting Integers SUGGESTED LEARNING STRATEGIES: Self Revision/Peer Revision, Group Presentation, Look for a Pattern, Use Manipulatives 21. How did you find each move in Question 20? 22. Use the patterns that you noticed to write rules about subtracting integers. Include an example in your explanation. a. A positive integer minus a positive integer. b. A negative integer minus a positive integer. c. A negative integer minus a negative integer. d. A positive integer minus a negative integer. 20 SpringBoard Mathematics with Meaning TM Level 2

11 Adding and Subtracting Integers ACTIVITY 1.2 SUGGESTED LEARNING STRATEGIES: Use Manipulatives, Group Presentation, Think/Pair/Share 23. Work with a partner. For each problem, roll a number cube twice. Use the numbers you roll to make a problem. Then use the number line to solve the problem. a. - - (- ) = b. - - = c. - (- ) = d. - = 24. For each problem, you will need to add and subtract. You can use the rules you found or number lines to help you add and subtract the integers. a (-3) = b (-6) = c (-2) - 2 = 25. Describe a situation that matches each equation. a = 0 b. \$75 + (-\$75) = \$0 Unit 1 Integers and Rational Numbers 21

12 ACTIVITY 1.2 Adding and Subtracting Integers CHECK YOUR UNDERSTANDING Write your answers on notebook paper. Show your work. 1. Give a real world situation for the integer Order these integers from least to greatest: 3. Evaluate 36. 0, -132, 458, -789, Give two values that make these inequalities true. a. 0 < d b. z < 37 c. -12 > f 5. If p stands for any positive integer and t stands for any negative integer, write two inequalities comparing p and t. 6. Graph the inequality y < 5 on a number line. 7. Simplify each problem. Use a number line if necessary. a (-8) b c. 6 - (-6) d a. Use a number line to illustrate this problem and find its solution. b. Write a problem for a different move that begins at the same integer and has the same answer. 9. Describe a situation that matches this equation = MATHEMATICAL What relationship exists REFLECTION between addition and subtraction? Explain using integer models. 22 SpringBoard Mathematics with Meaning TM Level 2

### Adding and Subtracting Integers

Adding and Subtracting Integers What s the Temperature? Lesson 8-1 Using Models to Add Integers ACTIVITY 8 Learning Targets: Using models, create several representations of a given integer. Using models,

More information

### For 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 information

### https://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...

of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach Bell-Ringer Activity Students

More information

### UNIT 3 VOCABULARY: INTEGERS

1º ESO Bilingüe Page 1 UNIT 3 VOCABULARY: INTEGERS 3.1. Some uses of negative numbers There are many situations in which you need to use negative numbers. POSITIONS A submarine which is sailing 700 m below

More information

### My Notes CONNECT TO SCIENCE

Mood Rings, Part SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/ Retell, Vocabulary Organizer Tyrell and four of his friends from West Middle School went to a craft fair and they all decided to buy

More information

### Positive and Negative Integers

0.4 Positive and Negative Integers 0.4 OBJECTIVES 1. Represent integers on a number line 2. Order signed numbers 3. Evaluate numerical expressions involving absolute value When numbers are used to represent

More information

### 25 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 information

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

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

More information

### Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 5 Subtracting Integers

Supplemental Worksheet Problems To Accompany: The Pre-Algebra 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 information

### Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

More information

### Using Algebra Tiles for Adding/Subtracting Integers and to Solve 2-step Equations Grade 7 By Rich Butera

Using Algebra Tiles for Adding/Subtracting Integers and to Solve 2-step Equations Grade 7 By Rich Butera 1 Overall Unit Objective I am currently student teaching Seventh grade at Springville Griffith Middle

More information

### Adding 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 information

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

More information

### Listen 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 information

### Expressions and Equations

Expressions and Equations Standard: CC.6.EE.2 Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y.

More information

### 1.5. Solving Multi-Step Equations Field Trip Fundraiser. My Notes ACTIVITY

Solving Multi-Step Equations SUGGESTED LEARNING STRATEGIES: KWL, Question the Text, Create Representations, Quickwrite The Future Engineers of America Club (FEA) wants to raise money for a field trip to

More information

### Integers. 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 information

### Title: Integers: Quick, Fun and Easy To Learn

Title: Integers: Quick, Fun and Easy To Learn Brief Overview Students will identify and understand positive and negative integers. Using this understanding, the students will use the number line, study

More information

### PURPOSE: 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 information

### MATH 65 NOTEBOOK CERTIFICATIONS

MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1

More information

### Rules 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 information

### 3.1. Angle Pairs. What s Your Angle? Angle Pairs. ACTIVITY 3.1 Investigative. Activity Focus Measuring angles Angle pairs

SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Use Manipulatives Two rays with a common endpoint form an angle. The common endpoint is called the vertex. You can use a protractor to draw and measure

More information

### TYPES 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 information

### Answers Teacher Copy. Systems of Linear Equations Monetary Systems Overload. Activity 3. Solving Systems of Two Equations in Two Variables

of 26 8/20/2014 2:00 PM Answers Teacher Copy Activity 3 Lesson 3-1 Systems of Linear Equations Monetary Systems Overload Solving Systems of Two Equations in Two Variables Plan Pacing: 1 class period Chunking

More information

### Grade 7 Mathematics. Unit 2. Integers. Estimated Time: 15 Hours

Grade 7 Mathematics Integers Estimated Time: 15 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade

More information

### Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations.

Section 1 Mathematics has a language all its own. In order to be able to solve many types of word problems, we need to be able to translate the English Language into Math Language. is the process of translating

More information

### Rational Numbers. Say Thanks to the Authors Click (No sign in required)

Rational Numbers 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

### Adding Integers on a Number Line

NS7-5 Adding Integers on a Number Line Pages 36 37 Standards: 7.NS.A.1b Goals: Students will add integers using a number line. Students will interpret addition of integers when the integers are written

More information

### 3.1. 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 information

### 5 1 d. 2.5? t. 10 more than the. the sum of 10x and 7z quotient of x and 4. product of 3 and x

- Practice Form G Variables and Expressions Write an algebraic expression for each word phrase.. 0 less than x. 5 more than d x 0 5 d. 7 minus f. the sum of and k 7 f k 5. x multiplied by 6 6. a number

More information

### 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.

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 information

### Addition and Subtraction of Integers

Addition and Subtraction of Integers Integers are the negative numbers, zero, and positive numbers Addition of integers An integer can be represented or graphed on a number line by an arrow. An arrow pointing

More information

### Lesson 18: Introduction to Algebra: Expressions and Variables

LESSON 18: Algebra Expressions and Variables Weekly Focus: expressions Weekly Skill: write and evaluate Lesson Summary: For the Warm Up, students will solve a problem about movie tickets sold. In Activity

More information

### Chapter 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 information

### Absolute Value of Reasoning

About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection

More information

### Unit 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 information

### Adding & Subtracting Integers

WARDEN AVE P.S. Adding & Subtracting Integers Number Sense & Numeration Unit #1 Grade 7 Math 2014-2015 School Year This mini-unit will run from September 15-26 and must be handed in on Friday Sept. 26th

More information

### 1.6 The Order of Operations

1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

More information

### Accuplacer Elementary Algebra Study Guide for Screen Readers

Accuplacer Elementary Algebra Study Guide for Screen Readers The following sample questions are similar to the format and content of questions on the Accuplacer Elementary Algebra test. Reviewing these

More information

### Current California Math Standards Balanced Equations

Balanced Equations Current California Math Standards Balanced Equations Grade Three Number Sense 1.0 Students understand the place value of whole numbers: 1.1 Count, read, and write whole numbers to 10,000.

More information

### Objectives. By the time the student is finished with this section of the workbook, he/she should be able

QUADRATIC FUNCTIONS Completing the Square..95 The Quadratic Formula....99 The Discriminant... 0 Equations in Quadratic Form.. 04 The Standard Form of a Parabola...06 Working with the Standard Form of a

More information

### POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

More information

### Accentuate the Negative: Homework Examples from ACE

Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 12-15, 47, 49-52 Investigation 2: Adding and Subtracting Rational Numbers, ACE 18-22, 38(a),

More information

### Adding Integers Using a Number Line

Adding Integers The addition of integers can be done in a variety of ways, such as using number lines, manipulatives and a T-chart, calculators or shortcuts. Parentheses (or brackets) are often used around

More information

### EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING Revised For ACCESS TO APPRENTICESHIP

EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING For ACCESS TO APPRENTICESHIP MATHEMATICS SKILL OPERATIONS WITH INTEGERS AN ACADEMIC SKILLS MANUAL for The Precision Machining And Tooling Trades

More information

### Definition 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 information

### 47 Numerator Denominator

JH WEEKLIES ISSUE #22 2012-2013 Mathematics Fractions Mathematicians often have to deal with numbers that are not whole numbers (1, 2, 3 etc.). The preferred way to represent these partial numbers (rational

More information

### parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE FIVE

TM parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE FIVE 5 America s schools are working to provide higher quality instruction than ever before. The way we taught students in the past simply does

More information

### T. H. Rogers School Summer Math Assignment

T. H. Rogers School Summer Math Assignment Mastery of all these skills is extremely important in order to develop a solid math foundation. I believe each year builds upon the previous year s skills in

More information

### Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section What is algebra? Operations with algebraic terms Mathematical properties of real numbers Order of operations What is Algebra? Algebra is

More information

### Lesson 3: Using Inequalities to Problem Solve

Lesson 3: Using Inequalities to Problem Solve Selected Content Standards Benchmarks Addressed: N-1-M Demonstrating that a rational number can be expressed in many forms, and selecting an appropriate form

More information

### Objective. Materials. TI-73 Calculator

0. Objective To explore subtraction of integers using a number line. Activity 2 To develop strategies for subtracting integers. Materials TI-73 Calculator Integer Subtraction What s the Difference? Teacher

More information

### Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

More information

### UNIT TWO POLYNOMIALS MATH 421A 22 HOURS. Revised May 2, 00

UNIT TWO POLYNOMIALS MATH 421A 22 HOURS Revised May 2, 00 38 UNIT 2: POLYNOMIALS Previous Knowledge: With the implementation of APEF Mathematics at the intermediate level, students should be able to: -

More information

### Adding 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 information

### Square Roots. Learning Objectives. Pre-Activity

Section 1. Pre-Activity Preparation Square Roots Our number system has two important sets of numbers: rational and irrational. The most common irrational numbers result from taking the square root of non-perfect

More information

### MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

More information

### HFCC Math Lab Beginning Algebra 13 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES

HFCC Math Lab Beginning Algebra 1 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES Before being able to solve word problems in algebra, you must be able to change words, phrases, and sentences

More information

### Integers (pages 294 298)

A Integers (pages 294 298) An integer is any number from this set of the whole numbers and their opposites: { 3, 2,, 0,, 2, 3, }. Integers that are greater than zero are positive integers. You can write

More information

### Subtracting 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 information

### Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego

Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego Courtney O Donovan Class: Algebra 1 Day #: 6-7 Grade: 8th Number of Students: 25 Date: May 12-13, 2011 Goal: Students will

More information

### Subtraction 1.3. Overcoming Math Anxiety

1.3 Subtraction 1.3 OBJECTIVES 1. Use the language of subtraction 2. Subtract whole numbers without borrowing 3. Solve applications of simple subtraction 4. Use borrowing in subtracting whole numbers 5.

More information

### The Properties of Signed Numbers Section 1.2 The Commutative Properties If a and b are any numbers,

1 Summary DEFINITION/PROCEDURE EXAMPLE REFERENCE From Arithmetic to Algebra Section 1.1 Addition x y means the sum of x and y or x plus y. Some other words The sum of x and 5 is x 5. indicating addition

More information

### Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER

Rules of Exponents CHAPTER 5 Math at Work: Motorcycle Customization OUTLINE Study Strategies: Taking Math Tests 5. Basic Rules of Exponents Part A: The Product Rule and Power Rules Part B: Combining the

More information

### Operations and Algebraic Thinking Represent and solve problems involving multiplication and division.

Performance Assessment Task The Answer is 36 Grade 3 The task challenges a student to use knowledge of operations and their inverses to complete number sentences that equal a given quantity. A student

More information

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

More information

### Prentice Hall Mathematics: Algebra 1 2007 Correlated to: Michigan Merit Curriculum for Algebra 1

STRAND 1: QUANTITATIVE LITERACY AND LOGIC STANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONS Based on their knowledge of the properties of arithmetic, students understand and reason

More information

### Multiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20

SECTION.4 Multiplying and Dividing Signed Numbers.4 OBJECTIVES 1. Multiply signed numbers 2. Use the commutative property of multiplication 3. Use the associative property of multiplication 4. Divide signed

More information

### CAHSEE on Target UC Davis, School and University Partnerships

UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

More information

### PREPARATION FOR MATH TESTING at CityLab Academy

PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRE-TEST

More information

### P.E.R.T. Math Study Guide

A guide to help you prepare for the Math subtest of Florida s Postsecondary Education Readiness Test or P.E.R.T. P.E.R.T. Math Study Guide www.perttest.com PERT - A Math Study Guide 1. Linear Equations

More information

### CAHSEE on Target UC Davis, School and University Partnerships

UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

More information

### 2 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 information

### Session 7 Fractions and Decimals

Key Terms in This Session Session 7 Fractions and Decimals Previously Introduced prime number rational numbers New in This Session period repeating decimal terminating decimal Introduction In this session,

More information

### Lesson 2. Operations with Integers. Objectives

Student Name: Date: Contact Person Name: Phone Number: Lesson 2 Operations with Integers Objectives Add and subtract integers Determine the absolute value of a number Solve word problems that involve adding

More information

### Solving 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 information

### Lesson 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 information

### Mathematics Task Arcs

Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number

More information

### Measurement with Ratios

Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical

More information

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

More information

### MATH 90 CHAPTER 1 Name:.

MATH 90 CHAPTER 1 Name:. 1.1 Introduction to Algebra Need To Know What are Algebraic Expressions? Translating Expressions Equations What is Algebra? They say the only thing that stays the same is change.

More information

### Shake, Rattle and Roll

00 College Board. All rights reserved. 00 College Board. All rights reserved. SUGGESTED LEARNING STRATEGIES: Shared Reading, Marking the Tet, Visualization, Interactive Word Wall Roller coasters are scar

More information

### Mathematics. Mathematical Practices

Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with

More information

### (- 7) + 4 = (-9) = - 3 (- 3) + 7 = ( -3) = 2

WORKING WITH INTEGERS: 1. Adding Rules: Positive + Positive = Positive: 5 + 4 = 9 Negative + Negative = Negative: (- 7) + (- 2) = - 9 The sum of a negative and a positive number: First subtract: The answer

More information

### TEACHER S GUIDE: ORDER OF OPERATIONS

TEACHER S GUIDE: ORDER OF OPERATIONS LEARNING OBJECTIVES Students will learn the order of operations (PEMDAS). Students will solve simple expressions by following the order of operations. Students will

More information

### Year 9 set 1 Mathematics notes, to accompany the 9H book.

Part 1: Year 9 set 1 Mathematics notes, to accompany the 9H book. equations 1. (p.1), 1.6 (p. 44), 4.6 (p.196) sequences 3. (p.115) Pupils use the Elmwood Press Essential Maths book by David Raymer (9H

More information

### MATH 111. 3. Numbers & Operations

MATH 111 3. Numbers & Operations Chapter 3 - Numbers & Operations 2013 Michelle Manes, University of Hawaii Department of Mathematics These materials are intended for use with the University of Hawaii

More information

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

More information

### Solving Quadratic Equations

9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation

More information

### Lesson Plan -- Integers, Opposites, Absolute Value

Lesson Plan -- Integers, Opposites, Absolute Value Chapter Resources - Lesson 3-1 Integers and the Number Line - Lesson 3-1 Integers and the Number Line Answers - Lesson 3-2 Opposites and Absolute Value

More information

### Integer Instruction That Works: Best Practices for Instruction of Integers for All Students Including LEP Learners Math, LEP Grades 5-8

Integer Instruction That Works: Best Practices for Instruction of Integers for All Students Including LEP Learners Math, LEP Grades 5-8 Frustrated by the fact that your students incorrectly apply the rule

More information

### Algebra 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 information

### Guide to SRW Section 1.7: Solving inequalities

Guide to SRW Section 1.7: Solving inequalities When you solve the equation x 2 = 9, the answer is written as two very simple equations: x = 3 (or) x = 3 The diagram of the solution is -6-5 -4-3 -2-1 0

More information

### Fry Instant Word List

First 100 Instant Words the had out than of by many first and words then water a but them been to not these called in what so who is all some oil you were her sit that we would now it when make find he

More information

### Grade 4 Mathematics Measurement: Lesson 2

Grade 4 Mathematics Measurement: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

More information

### Lesson 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 information

### Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

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 information

### 1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?

Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.

More information

### 2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses

College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2

More information