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Chapter 1 Resource Masters Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters are available as consumable workbooks in both English and Spanish. Study Guide and Intervention Workbook Skills Practice Workbook Practice Workbook Word Problem Practice Workbook MHID 0-07-878882-X 0-07-878884-6 0-07-878886-2 0-07-878888-9 ISBN 978-0-07-878882-6 978-0-07-878884-0 978-0-07-878886-4 978-0-07-878888-8 0-07-878883-8 0-07-878885-4 0-07-878887-0 0-07-878889-7 978-0-07-878883-3 978-0-07-878885-7 978-0-07-878887-1 978-0-07-878889-7 Spanish Versions Study Guide and Intervention Workbook Skills Practice Workbook Practice Workbook Word Problem Practice Workbook Answers for Workbooks The answers for Chapter 1 of these workbooks can be found in the back of this Chapter Resource Masters booklet. StudentWorks PlusTM This CD-ROM includes the entire Student Edition test along with the English workbooks listed above. TeacherWorks PlusTM All of the materials found in this booklet are included for viewing, printing, and editing in this CD-ROM. Spanish Assessment Masters MHID: 0-07-878890-0 ISBN: 978-0-07-878890-1 These masters contain a Spanish version of Chapter 1 Test Form 2A and Form 2C. Copyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe California Mathematics, Grade 7. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240 ISBN: 978-0-07-878308-1 MHID: 0-07-878308-9 Printed in the United States of America 1 2 3 4 5 6 7 8 9 10 079 14 13 12 11 10 09 08 07 CAGR7 CRM1 CONTENTS Teacher’s Guide to Using the Chapter 1 Resource Masters .........................................iv Chapter Resources Chapter Chapter Chapter Chapter Chapter Chapter Chapter 1 1 1 1 1 1 1 Student-Made Glossary ...................1 Family Letter (English) .....................3 Family Activity (English) ...................4 Family Letter (Spanish) ....................5 Family Activity (Spanish)..................6 Anticipation Guide (English).............7 Anticipation Guide (Spanish) ...........8 Lesson 1-1 A Plan for Problem Solving Lesson Reading Guide ......................................9 Study Guide and Intervention ..........................10 Skills Practice...................................................11 Practice ............................................................12 Word Problem Practice ....................................13 Enrichment .......................................................14 Lesson 1-2 Variables, Expressions, and Properties Lesson Reading Guide ....................................15 Study Guide and Intervention ..........................16 Skills Practice...................................................17 Practice ............................................................18 Word Problem Practice ....................................19 Enrichment .......................................................20 TI-73 Activity ....................................................21 Lesson 1-3 Integers and Absolute Value Lesson Reading Guide ....................................22 Study Guide and Intervention ..........................23 Skills Practice...................................................24 Practice ............................................................25 Word Problem Practice ....................................26 Enrichment .......................................................27 TI-83/84 Plus Activity .......................................28 Study Guide and Intervention ..........................42 Skills Practice...................................................43 Practice ............................................................44 Word Problem Practice ....................................45 Enrichment .......................................................46 TI-83/84 Plus Activity .......................................47 Lesson 1-7 Writing Equations Lesson Reading Guide ....................................48 Study Guide and Intervention ..........................49 Skills Practice...................................................50 Practice ............................................................51 Word Problem Practice ....................................52 Enrichment .......................................................53 Lesson 1-8 Problem-Solving Investigation: Work Backward Study Guide and Intervention ..........................54 Skills Practice...................................................55 Practice ............................................................56 Word Problem Practice ....................................57 Lesson 1-9 Solving Addition and Subtraction Equations Lesson Reading Guide ....................................58 Study Guide and Intervention ..........................59 Skills Practice...................................................60 Practice ............................................................61 Word Problem Practice ....................................62 Enrichment .......................................................63 Lesson 1-10 Solving Multiplication and Division Equations Lesson Reading Guide ....................................64 Study Guide and Intervention ..........................65 Skills Practice...................................................66 Practice ............................................................67 Word Problem Practice ....................................68 Enrichment .......................................................69 Lesson 1-4 Adding Integers Assessment Lesson Reading Guide ....................................29 Study Guide and Intervention ..........................30 Skills Practice...................................................31 Practice ............................................................32 Word Problem Practice ....................................33 Enrichment .......................................................34 Student Recording Sheet ................................71 Rubric for Scoring Pre-AP................................72 Chapter 1 Quizzes 1 and 2 .............................73 Chapter 1 Quizzes 3 and 4 .............................74 Chapter 1 Mid-Chapter Test............................75 Chapter 1 Vocabulary Test ..............................76 Chapter 1 Test, Form 1 ...................................77 Chapter 1 Test, Form 2A.................................79 Chapter 1 Test, Form 2B.................................81 Chapter 1 Test, Form 2C.................................83 Chapter 1 Test, Form 2D.................................85 Chapter 1 Test, Form 3 ...................................87 Chapter 1 Extended-Response Test ...............89 Chapter 1 Standardized Test Practice ............90 ANSWERS ...............................................A1-A41 Lesson 1-5 Subtracting Integers Lesson Reading Guide ....................................35 Study Guide and Intervention ..........................36 Skills Practice...................................................37 Practice ............................................................38 Word Problem Practice ....................................39 Enrichment .......................................................40 Lesson 1-6 Multiplying and Dividing Integers Lesson Reading Guide ....................................41 iii Teacher’s Guide to Using the Chapter 1 Resource Masters The Chapter 1 Resource Masters includes the core materials needed for Chapter 1. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing on the TeacherWorks PlusTM CD-ROM. Chapter Resources Lesson Resources Student-Built Glossary (pages 1-2) These masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. Give this to students before beginning Lesson 1-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson. Lesson Reading Guide Get Ready for the Lesson reiterates the questions from the beginning of the Student Edition lesson. Read the Lesson asks students to interpret the context of and relationships among terms in the lesson. Finally, Remember What You Learned asks students to summarize what they have learned using various representation techniques. Use as a study tool for note taking or as an informal reading assignment. It is also a helpful tool for ELL (English Language Learners). Study Guide and Intervention This master provides vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. Family Letter and Family Activity (pages 3-6) The letter informs your students’ families of the mathematics they will be learning in this chapter. The family activity helps them to practice problems that are similar to those on the state test. A full solution for each problem is included. Spanish versions of these pages are also included. Give these to students to take home before beginning the chapter. Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson. Anticipation Guide (pages 7-8) This master, presented in both English and Spanish, is a survey used before beginning the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed. Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for secondday teaching of the lesson. iv Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 10 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests. Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson. Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. They are written for use with all levels of students. Leveled Chapter Tests • Form 1 contains multiple-choice questions and is intended for use with below grade level students. • Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations. Graphing Calculator, Scientific Calculator, or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation. • Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations. • Form 3 is a free-response test for use with above grade level students. Assessment Options All of the above mentioned tests include a free-response Bonus question. The assessment masters in the Chapter 1 Resources Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment. Extended-Response Test Performance assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation. Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter. Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and shortanswer free-response questions. Pre-AP Rubric This master provides information for teachers and students on how to assess performance on open-ended questions. Answers • The answers for the Anticipation Guide and Lesson Resources are provided as reduced pages with answers appearing in red. Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter. • Full-size answer keys are provided for the assessment masters. Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and freeresponse questions. v NAME ________________________________________ DATE ______________ PERIOD _____ Student-Built Glossary This is an alphabetical list of new vocabulary terms you will learn in Chapter 1. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term Found on Page Definition/Description/Example absolute value additive inverse algebra [AL-juh-brah] Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. algebraic [AL-juh-BRAY-ihk] expression conjecture coordinate counterexample equation [ih-KWAY-zhuhn] evaluate inequality integer [IHN-tih-juhr] Chapter 1 1 Glencoe California Mathematics, Grade 7 Chapter Resources 1 NAME ________________________________________ DATE ______________ PERIOD _____ 1 Student-Built Glossary Vocabulary Term Found on Page (continued) Definition/Description/Example inverse operations negative number numerical expression opposites Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. order of operations positive number powers property solution solve variable Chapter 1 2 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ Family Letter Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Dear Parent or Guardian: relate concepts learned in One of the goals of this class is to example, integers are a the classroom to the real world. For used to describe things part of our daily lives. They are often e, and money. Knowing such as sports scores, temperature, tim make important decisions how to work with integers helps us at work and at home. r child will learn about In Chapter 1, Algebra: Integers, you g, about variables, developing a plan for problem solvin phing data, and about expressions, and properties, about gra dividing integers. Your adding, subtracting, multiplying, and absolute value of child will also learn how to find the ns. In the study of this integers, and write and solve equatio iety of daily classroom chapter, your child will complete a var ly produce a chapter assignments and activities and possib project . it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that practices how the an activity you can do with your chi 1 might be tested. You math we will be learning in Chapter th.com for self-check may also wish to log on to ca.gr7ma have any questions or quizzes and other study help. If you school. comments, feel free to contact me at Sincerely, Signature of Parent or Guardian ______________________________________ Date ________ Chapter 1 3 Glencoe California Mathematics, Grade 7 Chapter Resources 1 NAME ________________________________________ DATE ______________ PERIOD _____ 1 Family Activity Standards Practice Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 2. Jarred has five fewer model cars than Cammie. Half of the sum of their combined model cars is equal to 10. How many model cars does Cammie have? 1. Evan stepped into an elevator in a very tall building in downtown New York City. The buttons he could choose from ranged from Basement Level D (4) to 64. 64 Which equation can be used to find the number of model cars Cammie has? c5 A 10 0 street level 1 2 3 D 4 B 2 c c 5 2 10 C c c 5 10 2 D c 5 10 How many stories high is this building (including its basements)? A 60 stories high B 68 stories high C 67 stories high D 61 stories high Fold here Solution Solution 2. Hint: A letter (or variable) is used to represent a number that we do not know, in this case the number of cars Cammie has. In order to solve the problem, you also will need to write an expression for the number of cars that Jared has based on the number Cammie has. 1. There are 64 stories above ground and 4 stories below ground, which means there are 64 4, or 68 stories. The number of cars that Cammie has can be represented by the letter c. We know that Jared has 5 less cars than Cammie, or c 5. If we add their cars together (c c 5) and divide by 2, the number should equal 10. The answer is B. Chapter 1 The answer is B. 4 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2 NOMBRE ______________________________________ FECHA ____________ PERÍODO Carta a la familia Chapter Resources 1 ___ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Estimado padre o apoderado: relacionar los conceptos Uno de los objetivos de esta clase es real. Por ejemplo, los aprendidos en el salón con el mundo Se usan para describir enteros son parte de la vida cotidiana. tro deportivo, la tempecosas como el marcador de un encuen saber usar los enteros ratura, la hora, el dinero, etcétera. Al en el trabajo y en el podemos tomar importantes decisiones hogar. su hijo(a) aprenderá a En el Capítulo 1, Álgebra: Enteros, blemas, aprenderá sobre desarrollar un plan para resolver pro así como a graficar datos y variables, expresiones y propiedades, nes y divisiones de enteros. a realizar sumas, restas, multiplicacio ar el valor absoluto de Su hijo(a) aprenderá también a calcul ones. En este capítulo, él o enteros y escribirá y resolverá ecuaci eas y actividades diarias y es ella completará una variedad de tar del capítulo. posible que trabaje en un proyecto su hijo(a), usted se comAl firmar esta carta y devolverla con en su aprendizaje. Junto con promete a ayudarlo(a) a participar que puede realizar con esta carta, va incluida una actividad rían encontrar en las prueél(ella) y la cual practica lo que pod aprenderán en el bas de los conceptos matemáticos que th.com para ver autoCapítulo 1. Además, visiten ca.gr7ma o. Si tiene cualquier precontroles y otras ayudas para el estudi teme en la escuela. gunta o comentario, por favor contác Cordialmente, Firma del padre o apoderado Capítulo 1 ________________________________________ Fecha 5 ______ Glencoe California Mathematics, Grade 7 NOMBRE ______________________________________ FECHA ____________ PERÍODO 1 ___ Actividad en familia Práctica de estándares Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas. 2. Jarred tiene cinco autos a escala más que Cammie. La mitad de la suma de los autos a escala que tienen entre los dos es igual a 10. ¿Cuántos autos a escala tiene Cammie? 1. Evan se subió al elevador de un edificio muy alto en el centro de la ciudad de Nueva York. Los botones que podía elegir variaban de sótano nivel D (4) a 64. 64 ¿Qué ecuación sirve para calcular el número de autos a escala que tiene Cammie? 0 nivel de la calle c5 A 10 ¿Cuántos pisos tiene este edificio, incluyendo los sótanos? A 60 pisos B 68 pisos C 67 pisos D 61 pisos B 2 c c 5 2 10 C c c 5 10 2 D c 5 10 Doblen aquí Solución Solución 1. Hay 64 pisos sobre el suelo y 4 niveles en el sótano. Esto significa que hay 64 4 ó 68 pisos. 2. Ayuda: Para representar un número cuyo valor se desconoce se usa una letra (o variable). En este caso, el número de autos de Cammie. Para resolver este problema, también tienen que escribir una expresión que represente el número de autos de Jared, en base al número de autos de Cammie. Los autos de Cammie se pueden representar con la letra c. Sabemos que Jared tiene 5 autos menos que Cammie o c 5. Si sumamos ambas cantidades (c c 5) y dividimos entre 2, el resultado deberá ser 10. La respuesta es B. La respuesta es B. Capítulo 1 6 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2 NAME ________________________________________ DATE ______________ PERIOD _____ 1 Anticipation Guide Step 1 Before you begin Chapter 1 • Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS STEP 2 A or D Statement 1. A conjecture is a statement proven to be true. 2. Algebraic expressions are any mathematical expressions that contain at least one operation symbol. 3. According to the Order of Operations, all operations within grouping symbols must be completed first. 4. According to the Order of Operations, all addition and subtraction should be done before multiplication and division. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 5. The Commutative Property is true only for addition and multiplication. 6. Negative integers can be used to express values less than zero. 7. When comparing two negative integers, the greater integer is the one with the greater absolute value. 8. The sum of a positive integer and a negative integer is always negative. 9. When subtracting a negative integer, add its opposite. 10. The product of two negative integers is always positive. 11. The quotient of two negative integers is always negative. 12. Any letter can be used to represent an unknown in an expression or equation. Step 2 After you complete Chapter 1 • Reread each statement and complete the last column by entering an A or a D. • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a piece of paper to write an example of why you disagree. Chapter 1 7 Glencoe California Mathematics, Grade 7 Chapter Resources Algebra: Integers NOMBRE ______________________________________ FECHA ____________ PERÍODO 1 ___ Ejercicios preparatorios Álgebra: Enteros Paso 1 Antes de comenzar el Capítulo 1 • Lee cada enunciado. • Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado. • Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)). PASO 1 A, D o NS PASO 2 AoD Enunciado 1. Una conjetura es un enunciado que se ha probado como verdadero. 2. Las expresiones matemáticas son cualesquiera expresiones matemáticas que contengan por lo menos un símbolo de operación. 3. Según el orden de las operaciones, todas las operaciones dentro de signos de agrupación deben completarse primero. 5. La propiedad conmutativa es verdadera solo para la adición y la multiplicación. 6. Se pueden usar los números enteros negativos para expresar valores menores que cero. 7. Cuando se comparan dos enteros negativos, el entero mayor es aquél con el mayor valor absoluto. 8. La suma de un entero positivo y un entero negativo es siempre negativa. 9. Cuando se sustrae un entero negativo, se suma su opuesto. 10. El producto de dos enteros negativos es siempre positivo. 11. El cociente de dos enteros negativos es siempre negativo. 12. Cualquier letra puede usarse para representar una incógnita en una expresión o ecuación. Paso 2 Después de completar el Capítulo 1 • Vuelve a leer cada enunciado y completa la última columna con una A o una D. • ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna? • En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D. Capítulo 1 8 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4. De acuerdo con el orden de las operaciones, toda adición y sustracción debe efectuarse antes que la multiplicación y división. NAME ________________________________________ DATE ______________ PERIOD _____ 1-1 Lesson Reading Guide 7MR1.1, 6AF2.3 A Plan for Problem Solving Get Ready for the Lesson Complete the Mini Lab at the top of page 24 in your textbook. Write your answers below. 1. How many white tiles does it take to border each of these three gardens? 2. Predict how many white tiles it will take to border the next-largest garden. Check your answer by modeling the garden. Lesson 1–1 3. How many tiles will it take to border a garden that is 6 tiles long? Explain your reasoning. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Read the Lesson 4. Read the Check section in Example 1 at the bottom of page 25. In the equation 8 18 26, what does the 8 stand for? What does the 18 stand for? 5. Look at the Explore section in Example 2 on page 26. What does the word “difference” mean? Now read the Plan section. Explain how to find the distance traveled in 1 minute when you know the distance per second. 6. Look at the graph in Example 2 on page 26. Explain how the animals in the chart are listed. Why is the cheetah first? Remember What You Learned 7. Early problem solvers care is a mnemonic aid to remember the first letters of the steps in the problem-solving plan. Write a mnemonic aid of your own using the first letters of the steps. Chapter 1 9 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1-1 Study Guide and Intervention 7MR1.1, 6AF2.3 A Plan for Problem Solving You can always use the four-step plan to solve a problem. Explore Determine what information is given in the problem and what you need to find. Plan Select a strategy including a possible estimate. Solve Solve the problem by carrying out your plan. Check Examine your answer to see if it seems reasonable. Example 1 Plant A and Plant B are two new experimental apple trees being grown in a laboratory. The table displays their heights, in millimeters, when they are 5 to 10 days old. Day 5 6 7 8 9 10 Plant A 36 39 42 45 48 51 Plant B 32 36 40 44 48 52 Explore You know their heights for days 5 to 10. You need to determine their heights in two more days. Plan Determine whether there is a pattern and extend that pattern to day 12. Solve Comparing each plant’s heights on consecutive days, we see that Plant A’s height increases by 3 millimeters each day, while Plant B’s height increases by 4 millimeters each day. To estimate Plant A’s height on day 12, assume that it will grow 3 millimeters each day past day 10, so it will be 51 3 3 or 57 millimeters. To estimate Plant B’s height on day 12, assume that it will grow 4 millimeters each day past day 10, so it will be 52 4 4 or 60 millimeters. Check Given what we know about each plant’s height and how plants grow in general, both estimates seem reasonable. Exercises Use the four-step plan to solve each problem. 1. MOVIES A movie ticket costs $3.50. A large popcorn costs $3.75 and a large soda costs $3.00. How much will it cost two friends to go to a movie if they share a popcorn and each has a large soda? 2. FLOUR BEETLES The population of a flour beetle doubles in about a week. How long would it take for the population to grow to eight times its original size? Chapter 1 10 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Estimate the height of each plant on day 12. NAME ________________________________________ DATE ______________ PERIOD _____ 1-1 Skills Practice 7MR1.1, 6AF2.3 A Plan for Problem Solving Use the four-step plan to solve each problem. 1. GAS MILEAGE Each day Ernesto drives 52 miles. If he can drive 26 miles on one gallon of gasoline, how many days can he drive on 14 gallons of gasoline? 2. FIELD TRIP A school policy requires that there be at least one chaperone for every 8 students on a field trip. How many chaperones are required for a field trip with 67 students? Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4. PRODUCE At the local grocery store, lemons are 52 cents each and limes are 21 cents each. How many lemons and limes can you buy for exactly $3.75? 5. PIZZA The Chess Club sold 2,116 pizzas during a fundraiser that lasted for all of March, April, and May. How many pizzas did they sell per day? 6. GUPPIES In January, Tate’s fish tank had 12 guppies. In February, it had 18, and in March it had 24. How many guppies do you expect to be in Tate’s fish tank in May? Find a pattern in the list of numbers. Then find the next number in the list. 7. 1860, 1890, 1920, 1950, 1980 8. 1024, 256, 64, 16, 4 Draw the next two figures in each of the patterns below. 9. 10. Chapter 1 11 Glencoe California Mathematics, Grade 7 Lesson 1–1 3. EXERCISE Trevor jogs every 3 days and swims every 4 days. How often does he jog and swim on the same day? NAME ________________________________________ DATE ______________ PERIOD _____ 1-1 Practice 7MR1.1, 6AF2.3 A Plan for Problem Solving Use the four-step plan to solve each problem. 1. FOOD The table shows a portion of the price list for a local pizzeria. Tony has $17 that he can spend to buy one large pizza. If the pattern in the prices continues, what is the greatest number of toppings that Tony can order on his pizza? What is the cost of that pizza? Toppings Price 1 $12.99 2 $13.79 3 $14.59 4 $15.39 2. MOVIES Mr. Sedgwick paid $13 for one adult ticket and one child ticket for a movie. Mrs. Wong paid $18 for one adult ticket two child tickets to see the same movie, and Mr. Gomez paid $23 for one adult ticket and three child tickets. If the pattern continues, how much should Mrs. Beauregard expect to pay for one adult ticket and four child tickets? 4. GEOGRAPHY The land area of Washington, D.C., is 61 square miles. In 2003, the population of Washington, D.C., was 563,384. If one square mile is equal to 640 acres, about how many people per acre were there in Washington, D.C., in 2003? 5. ART SUPPLIES At the craft store, a paint brush costs $0.79, and a small bottle of paint costs $0.89. What combination of paint brushes and bottles of paint could you buy for exactly $4.15? 6. GEOMETRY Draw the next two figures in the pattern. Chapter 1 12 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 3. SPORTS The track coach must buy at least two bottles of water for each participant in a track meet. One team has 35 members, and the other team has 28 members. If each case of water contains 24 bottles, what is the fewest number of full cases that the coach can buy? NAME ________________________________________ DATE ______________ PERIOD _____ 1-1 Word Problem Practice 7MR1.1, 6AF2.3 A Plan for Problem Solving Use the four-step plan to solve each problem. SKATEBOARDING For Exercises 1 and 2, use the table at the right. It shows the results of a recent survey in which teenagers were asked who the best professional skateboarder is. Skater Votes Bob Burnquist 18 Danny Way 15 Bam Margera 11 Arto Saari 9 2. How many more teenagers preferred Burnquist to Saari? 3. HISTORY The area of Manhattan Island is 641,000,000 square feet. According to legend, the Native Americans sold it to the Dutch for $24. Estimate the area that was purchased for one cent. 4. TRAVEL Britney’s flight to Rome leaves New York City at 5:15 P.M. on Wednesday. The flight time is 7.5 hours. If Rome is 6 hours ahead of New York City, use Rome time to determine when she is scheduled to arrive. 5. OFFICE SUPPLIES At an office supply store, pens are $1.69 per dozen and note pads are $4.59 per dozen. Can Shirley buy 108 pens and 108 note pads for $50? Explain your reasoning. 6. SHOPPING Yoshi bought two pairs of shoes. The regular price of each pair was $108. With the purchase of one pair of shoes at regular price, the second pair was half price. How much did Yoshi pay altogether for the two pairs of shoes? Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Lesson 1–1 1. Estimate the total number of teenagers who voted. Chapter 1 13 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1-1 Enrichment 7MR2.3 Logical Reasoning When planning how to solve problems, it is helpful to be familiar with a number of problem-solving strategies. When a problem presents a large amount of information, one strategy that can be effective is logical reasoning combined with the use of a table to organize the information. Holly, Keisha, Sandra, and Jamal are Bexley Middle School’s student council officers. The offices they hold are president, vice-president, secretary, and treasurer. Sandra is the president, Holly is not the treasurer, and Keisha is the vice-president. What office does Jamal hold? Holly President Vice President Secretary Treasurer Keisha Sandra Jamal N N N Y N N Y N N N N N Using the table, mark Y for relationships that are true, and N for relationships that are not true. For example, since you know that Sandra is the president, put a Y in that cell and put an N in each of the other cells of that column and in the president row. Fill in the remaining cells to show that Jamal must be the treasurer. Five male athletes won events in the district track and field meet. Each boy won exactly one event. From the clues below, find each boy’s name, school name, and the event he won. • • • • • • • • Two boys competed in the field events and three boys competed in the three track events. No boy participated in both track events and field events. The athlete from North Middle School, who is not Mitch, placed last in the 100-meter. The 100-meter winner lost to the South Middle School student in another event. The boy from Wilson Academy, who placed second in the discus throw, was not in any event with Mitch or Rob. The South Middle School boy and Kyle, who is not from Wilson, were not in any of the same events. The student from Taft Junior High did not participate in any field events. In one event Nick beat the student from North Middle School and the 400-meter winner. Vine Field Track Chapter 1 North South Taft Shot Put Discus 400-m 100-m Hurdles Mitch Kyle Rob Nick Cory Shot Put Discus 400-m 100-m Hurdles 14 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Use the process of logical reasoning and the table below to answer the following question. NAME ________________________________________ DATE ______________ PERIOD _____ 1-2 Lesson Reading Guide 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties Get Ready for the Lesson Complete the Mini Lab at the top of page 29 in your textbook. Write your answers below. 1. Complete the table below. Figure Number 1 2 Perimeter 4 8 3 4 5 6 What is the relationship between the figure number and the perimeter of the figure? 2. What would be the perimeter of Figure 10? Read the Lesson ____ Addition ____ Multiplication ____ Subtraction ____ Division For Exercises 4–8, describe how each pair of numerical expressions is different. Then determine whether the two expressions are equal to each other. If the expressions are equal, name the property that says they are equal. 4. 2 5, 5 2 5. (6 4) 1, 6 (4 1) 6. 2(5 3), 2 5 2 3 7. 5 (4 7), (5 4) 7 8. 10 2, 2 10 Remember What You Learned 9. The word counter has several meanings in the English language. Use a dictionary to find the meaning of counter when it is used as a prefix in the word counterexample. Then write your own definition of counterexample. Chapter 1 15 Glencoe California Mathematics, Grade 7 Lesson 1–2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 3. Number the operations in the correct order for simplifying 2 4(9 6 3). Then simplify the expression. NAME ________________________________________ DATE ______________ PERIOD _____ 1-2 Study Guide and Intervention 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties When finding the value of an expression with more than one operation, perform the operations in the order specified by the order of operations. Order of Operations 1. Perform all operations within grouping symbols first; start with the innermost grouping symbols. 2. Evaluate all powers before other operations. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. Evaluate the expression (5 7) 2 3 (8 1). (5 7) 2 3 (8 1) 12 2 3 (8 1) 12 2 3 9 639 18 9 9 Example 2 Add inside the left parentheses. Add inside the remaining parentheses. Divide. Multiply. Subtract. Evaluate the expression 3x2 4y if x 3 and y 2. 3x2 4y 3(3)2 4(2) 3(9) 4(2) 27 8 19 Replace x with 3 and y with 2. Evaluate the power first. Do all multiplications. Subtract. Exercises Evaluate each expression. 1. 4 5 8 2. 16 12 4 3. 14 2 3(5) 4. 5 6 2 3 5. 2 32 10 14 6. 22 32 8 5 7. (10 5) 3 8. 52 (8 6) 9. (17 5)(6 5) 10. 3 7(14 8 2) 14 3 2 11. 5[24 (6 8)] 12. 2 Evaluate each expression if a 3, b 5, and c 6. 13. a 3b 14. 4b 3c 15. 2a b 5c 16. (ab)2 17. a(b c) 18. 3(bc 8) a Chapter 1 16 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Example 1 NAME ________________________________________ DATE ______________ PERIOD _____ 1-2 Skills Practice 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties Evaluate each expression. 1. 10 2 8 2. 4(9) 36 3 3. 24 12 4 4. 25 2 8 4 5. 49 (32 8 3) 6. 2(20 5) 7. (27 24)(27 24) 8. 23 4 3 6 9. (4 4) 4 4 4 28 7 11. 42 13 34 14 4 10. 3[(8 2) 5] 7 12. (15 9)2 (5 4) 13. 3n p 14. t 2p 15. 3p n 4 16. (np)2 17. np2 18. 5(2t n) 19. p(n t) 20. 6t2 t npt 21. 22. 4(pt 3) n p2 4 23. pn 24. 25. n2 3n 8 26. 2t2 t 9 3 3t 5 2 t 10 Name the property shown by each statement. 27. (4 5)3 4(3) 5(3) 28. 1 x2 x2 29. 2(bc) (2b)c 30. (6 2) 5 6 (2 5) 31. 2(bc) 2(cb) 32. (4 5) 0 4 5 33. 13 (5 10) (5 10) 13 34. 3(7 2) 3(7) 3(2) Chapter 1 17 Glencoe California Mathematics, Grade 7 Lesson 1–2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Evaluate each expression if n 4, p 3, and t 6. NAME ________________________________________ DATE ______________ PERIOD _____ 1-2 Practice 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties Evaluate each expression if r = 3, s = 5, and t = 2. 1. 3r s 2. 4s 5t 3. 8 6t r 4. rs2 5. (st)2 r2 1 6. t 3 7. s(7 t) r 8. 2s2 8s 3 Name the property shown by each statement. 9. 6(5 1) 6(5) 6(1) 11. (10 7) 4 10 (7 4) 10. 1(2 3) 2 3 12. 5 (1 9) 5 (9 1) State whether each conjecture is true or false. If false, provide a counter example. 13. The sum of an even number and an odd number is always even. Rewrite each expression using the indicated property. 15. (x 7) 3, Associative Property 16. 5(3) 5(4), Distributive Property 17. INTERNET A bookstore offers wireless Internet access to its customers for a charge. The m cost of using this service is given by the expression $1.50 , where m is the number 20 of minutes online. How much would it cost to be online 40 minutes? 18. TEMPERATURE When a temperature in degrees Celsius C is known, the expression 9C 160 can be used to find the temperature in degrees Fahrenheit. If a thermometer 5 shows that a temperature is 20C, what is the temperature in degrees Fahrenheit? Chapter 1 18 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 14. Multiplication of whole numbers is associative. NAME ________________________________________ DATE ______________ PERIOD _____ 1-2 Word Problem Practice 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties FOOTBALL For Exercises 1 and 2, use the table that shows statistics from the 2006 Super Bowl. Touchdowns Extra Points Field Goals Pittsburgh 3 3 0 Seattle 1 1 1 1. Each team’s final score for a football game can be found using the expression 6t e 3f, where t is the number of touchdowns, e is the number of extra points, and f is the number of field goals. Find Pittsburgh’s final score in the 2006 Super Bowl. 2. Use the expression 6t e 3f to find Seattle’s final score in the 2006 Super Bowl. 3. GEOMETRY The expression 6s2 can be used to find the surface area of a cube, where s is the length of an edge of the cube. Find the surface area of a cube with an edge of length 10 centimeters. 4. VERTICAL MOTION The height of an object dropped from the top of a 300foot tall building can be described by the expression 300 16t2, where t is the time, in seconds, after the ball is dropped. Find the height of the object 3 seconds after it is dropped. 10 cm 5. MOVIE RENTALS Mario intends to rent 10 movies for his birthday party. He can rent new releases for $4 each, while older ones are $2 each. If he rents n new releases, the total cost, in dollars, of the 10 movies is represented by the expression 4n 2(10 n). Evaluate the expression to find the total cost if he rents 7 new releases. 6. CIRCULAR MOTION Pelipa is able to spin her yo-yo along a circular path. The yo-yo is kept in this path by a force which can be described by the mv2 r expression . Evaluate the expression to find the force when m 12, v 4, and r 8. r Chapter 1 19 Glencoe California Mathematics, Grade 7 Lesson 1–2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Team NAME ________________________________________ DATE ______________ PERIOD _____ 1-2 Enrichment 7AF1.3 Division by Zero? Some interesting things happen when you try to divide by zero. For example, look at these two equations. 5 x 0 0 y 0 Because multiplication “undoes” division, you can write two equivalent equations for the ones above. 0x5 0y0 There is no number that will make the left equation true. This equation has no solution. For the right equation, every number will make it true. The solution set for this equation is “all numbers.” Because division by zero leads to impossible situations, it is not a “legal” step in solving a problem. People say that division by zero is undefined, or not possible, or simply not allowed. Explain what is wrong with each of these “proofs.” 0 1 0 and 0 2 0 Step 2 Therefore, 0 1 and 0 2. Step 3 Therefore, 1 2. 0 0 But, 1 2 is a contradiction. 2. Step 1 Assume a b. Step 2 0 a 0 and 0 b 0 Step 3 Therefore, 0 a and 0 b. Step 4 Therefore, a b. 0 0 But, a b contradicts a b. Describe the solution set for each equation. 3. 4x 0 4. x 0 0 5. x 0 x 6. 0 0 7. 0 x 8. 0 0 x Chapter 1 x x 20 y Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1. Step 1 NAME ________________________________________ DATE ______________ PERIOD _____ 1-2 TI-73 Activity Evaluating Expressions Graphing calculators follow the order of operations. So there is no need to perform each operation separately. To evaluate an expression, enter it just as it is written. If an expression contains parentheses, enter them in the calculator just as they are written. Example Evaluate 3(x 6) 2 (x2 15) for x 8 and for x 12. You could enter the expression, replacing the x with 8 and then enter it again, replacing x with 12. But it is easier to enter the expression just once and store the values for x. Step 1 Evaluate the expression for x 8. 8 STO 3 ENTER 6 ( 2 ( 15 Step 2 ) ) ENTER Evaluate the same expression for x 12. You do not need to reenter the expression. 2nd [ENTRY] to redisplay the previous entries you made. Press 2nd [ENTRY] to redisplay the line that stores the value for x. Use the cursor keys to move to the 8. Insert 12 in place of the 8. DEL 2nd Press 2nd Press ENTER [INS] 12 [ENTRY] ENTER 2nd [ENTRY] to redisplay the expression. to reevaluate the expression. Exercises Use a graphing calculator to evaluate each expression for x 3, x 6, and x 15. 1. x2 9 2. 2x2 10 16x2 3. 4. x(20 x) 3 5. How would you evaluate xy2 for x 4 and y 7 on a TI-73 graphing calculator? (Hint: Enter Y by pressing 2nd [TEXT] and using the cursor keys to select Y and then Done.) Chapter 1 21 Glencoe California Mathematics, Grade 7 Lesson 1–2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Use NAME ________________________________________ DATE ______________ PERIOD _____ 1-3 Lesson Reading Guide 7NS2.5 Integers and Absolute Value Get Ready for the Lesson Read the introduction at the top of page 35 in your textbook. Write your answers below. 1. What does an elevation of 86 meters represent? 2. What does a temperature of 35º represent? Read the Lesson The symbol ... is called an ellipsis. 3. Look on page 35 in your textbook to find the meaning of the ellipsis as it is used in the list 1, 4, 7, 10,... . 4. Use a dictionary to find the meaning of the ellipsis as it is used in the sentence The marathon began...downtown. 6. Look at the number line on page 35 of your textbook. How are the ellipses (plural of ellipsis) in the set of integers {...,4, 3, 2, 1, 0, 1, 2, 3, 4,...} represented on the number line? Complete each sentence with either left or right to make a true sentence. Then write a statement comparing the two numbers with either or . 7. 45 lies to the ________ of 0 on a number line. 8. 72 lies to the ________ of 0 on a number line. 9. 3 lies to the ________ of 95 on a number line. 10. 6 lies to the ________ of 7 on a number line. 11. Describe the symbol for the absolute value of 3. Then write the symbol. Remember What You Learned 12. Write a mathematical expression that represents the following sentence. (Hint: Let f represent the 49ers’ score and s represent the Seahawks’ score.) The Seahawks and the 49ers scored within 3 points of each other. Chapter 1 22 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 5. How can you explain the usage of the ellipsis in the list in Exercise 3 in terms of the meaning for the ellipsis in the sentence in Exercise 4? NAME ________________________________________ DATE ______________ PERIOD _____ 1-3 Study Guide and Intervention 7NS2.5 Integers and Absolute Value A number line can help you order a set of integers. When graphed on a number line, the smaller of two integers is always to the left of the greater integer. Example 1 Order the set of integers {10, 3, 9, 4, 0} from least to greatest. Graph each integer on a number line. 10 8 6 4 2 0 2 4 6 8 10 The numbers from left to right are {9, 3, 0, 4, 10}. The absolute value of a number is the distance of that number from 0 on a number line. Example 2 Evaluate the expression |20| |10|. |20| |10| 20 |10| 20 10 30 The absolute value of 220 is 20. The absolute value of 10 is 10. Simplify. Order each set of integers in each set from least to greatest. 1. {3, 0,5, 1, 4} 2. {6,8, 3,1,4} 3. {2, 13,11,21, 5} 4. {31, 0,34,9, 7} Evaluate each expression. 7. |3| |5| 5. |13| 6. |21| 8. |9| |8| 9. |13| |15| 11. |11| |5| 12. |4| |4| 10. |21 18| 13. |23 15| Evaluate each expression if a 6, b 4, and c 5. 14. |a| 14 15. |c b| 16. b |c| 17. |3b| 18. 2|a| c 19. |2b c| Chapter 1 23 Glencoe California Mathematics, Grade 7 Lesson 1–3 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Exercises NAME ________________________________________ DATE ______________ PERIOD _____ 1-3 Skills Practice 7NS2.5 Integers and Absolute Value Write an integer for each situation. 1. 3 strokes below par 2. 10 strokes above par 3. a 6-yard loss 4. an 8-yard gain 5. 12 centimeters longer 6. 7 inches below normal 7. $5 off the original price 8. a gain of 6 hours 9. 2° above zero 10. a loss of 15 pounds 11. a $35 withdrawal 12. a $75 deposit 13. 1 mile above sea level 14. 20 fathoms below the surface 15. 12 4 16. 4 5 17. 10 8 18. 3 13 19. |6| |6| 20. |4| |5| Order each set of integers in each set from least to greatest. 21. {0, 6, 7, 2, 4} 22. {1, 2, 3, 3, 2, 1} Evaluate each expression. 23. |8| 24. |31| 25. |1| 26. |256| 27. |3| |19| 28. |12| |13| 29. |28| |26| 30. |28| |26| 31. |24| |15| Evaluate each expression if a 3, b 8, and c 5. 32. |a| 5 33. |b| 2 34. 2|c| b 35. a |a| 36. |3b| 37. |a 16| Chapter 1 24 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Replace each with , , or to make a true sentence. NAME ________________________________________ DATE ______________ PERIOD _____ 1-3 Practice 7NS2.5 Integers and Absolute Value Replace each with , , or to make a true sentence. 1. 0 8 2. 5 3 3. 1 7 4. 4 4 5. 12 10 6. 5 6 7. 6 7 8. 0 8 9. 10 10 Order each set of integers from least to greatest. 10. {5, 7, 0, 5, 7} 11. {1, 2, 3, 4} 12. {2, 4, 6, 8, 10, 12} 13. {0, 9, 3, 7, 1, 1} Evaluate each expression. 14. |19| 15. |15| 16. |0| 17. |1||3| 18. |19||8| 19. |12||4| 20. |m| 6 21. n |p| 22. k |p| 23. 5|n| k 24. |n| 4 25. 9|m| 14 TEMPERATURE For Exercises 26 and 28, use the following information. During a five-day cold spell, Jose recorded the temperature each day at noon. The temperature was 3F on Monday, 5F on Tuesday, 4F on Wednesday, 1F on Thursday, and 0F on Friday. 26. On which day was it the coldest at noon? 27. On which day was it the warmest at noon? 28. The temperature at noon on Saturday was 25 warmer than the temperature on Tuesday. What was the temperature on Saturday? Justify your answer using a number line. Chapter 1 25 Glencoe California Mathematics, Grade 7 Lesson 1–3 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Evaluate each expression if k 4, m 2, n 7, and p 5. NAME ________________________________________ DATE ______________ PERIOD _____ 1-3 Word Problem Practice 7NS2.5 Integers and Absolute Value GOLF For Exercises 1 and 2, use the table that lists ten players and their scores in Round 3 of the 2005 60th U.S. Women’s Open. Gulbis, Natalie Score 0 Player Kim, Birdie Score 2 Icher, Karine 1 Kung, Candie Jo, Young 1 Lang, Brittany 1 Kane, Lorie 5 Pressel, Morgan 1 Kerr, Cristie 1 Ochoa, Lorena 6 0 1. Order the scores in the table from least to greatest. 2. Who had the lowest score? 3. LONGITUDE London, England, is located at 0° longitude. Write integers for the locations of New York City whose longitude is 74° west and Tokyo whose longitude is 140° east. Assume that east is the positive direction. 4. STOCK MARKET Your stock loses 53 points on Monday and 23 points on Tuesday, but gains 67 points on Wednesday. Write an integer for each day's change. 5. SOLAR SYSTEM The average temperature of Saturn is 218°F, while the average temperature of Jupiter is 162°F. Which planet has the lower average temperature? 6. OCEAN TRENCHES The elevation of the Puerto Rican Trench in the Atlantic Ocean is 8,605 meters, the elevation of the Mariana Trench in the Pacific Ocean is 10,924 meters, and the elevation of the Java Trench in the Indian Ocean is 7,125 meters. Which trench has the the lowest elevation? Chapter 1 26 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Player NAME ________________________________________ DATE ______________ PERIOD _____ 1-3 Enrichment 7AF1.3 When You Want to Be Negative Many symbols and signs use a slash mark such as /, \, or | to mean is not or no. For example, the symbol means is not equal to. Which of the symbols, , , and will make the statement true? Some problems have more than one correct answer. 1. 2 ____ 0 2. |4| ____ |4| 3. For any number x, |x| ____ x. 4. For any nonzero integer n, n ____ n. 5. A number x is either greater than 0 or less than 0. So, x ____ 0. 6. ____ means the same as . 7. 8. 9. 10. 11. 12. Lesson 1–3 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. What does each of these signs mean? 13. Create three different “no” signs of your own. Chapter 1 27 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1-3 TI-83/84 Plus Activity Absolute Value A graphing calculator can be used to evaluate problems containing absolute value. The absolute value function on the TI-83/84 Plus is found in the MATH (NUM) menu. Example 1 Simplify |17|. Enter: MATH 1 (–) ) ENTER 3 + 8 ) 17 17 So, |17| 17. Example 2 Simplify |3 8|. Enter: MATH 1 (–) ENTER 5 So, |3 8| 5. Example 3 Simplify |5| |14|. Enter: MATH 1 (–) 5 ) — MATH 1 14 ) ENTER 9 Exercises Simplify. 1. ⏐4⏐ 2. ⏐8⏐ 3. ⏐12⏐ 4. ⏐10⏐ 5. ⏐7⏐ 6. ⏐25⏐ 7. ⏐6 4⏐ 8. ⏐15 8⏐ 9. ⏐3 14⏐ 10. ⏐1 4⏐ 11. ⏐7 9⏐ 12. ⏐2 (5)⏐ 13. ⏐7⏐ ⏐15⏐ 14. ⏐14⏐ ⏐5⏐ 15. ⏐8⏐ ⏐12⏐ 16. ⏐3⏐ ⏐9⏐ 17. ⏐11⏐ ⏐8⏐ 18. ⏐6⏐ ⏐7⏐ Chapter 1 28 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. So, |5| |14| 9. NAME ________________________________________ DATE ______________ PERIOD _____ 1-4 Lesson Reading Guide 7NS1.2, 7AF1.3 Adding Integers Get Ready for the Lesson Read the introduction at the top of page 41 in your textbook. Write your answers below. 1. Write an integer that describes the game show host’s statement. 2. Write an addition sentence that describes this situation. Read the Lesson 3. Look at your answer for Exercise 2. Identify each number in the addition sentence as either an addend or a sum. 4. 4, 8 5. 3, 5 6. 9, 12 7. 23, 16 Determine whether you add or subtract the absolute values of the numbers to find the sum. Give a reason for your answer. 8. 4 8 9. 3 5 10. 9 (12) 11. 23 (16) Determine whether the sum is positive or negative. Then find the sum. 12. 4 8 13. 3 5 14. 9 (12) 15. 23 (16) Add. 16. 3 (4) 17. 3 4 18. 6 (4) 19. 7 8 20. 25 (17) 21. 34 (17) 22. 43 4 23. 11 (30) 24. 81 (63) 25. 39 124 26. 97 (165) 27. 49 (75) Remember What You Learned 28. You have seen what a negative number means in terms of weather or money. Describe what a negative number means on a video cassette recorder. Chapter 1 29 Glencoe California Mathematics, Grade 7 Lesson 1–4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Identify the number with the greater absolute value. NAME ________________________________________ DATE ______________ PERIOD _____ 1-4 Study Guide and Intervention 7NS1.2, 7AF1.3 Adding Integers To add integers with the same sign, add their absolute values. The sum has the same sign as the integers. Example 1 Find 3 (4). 3 (4) 7 Add |3| |4|. Both numbers are negative, so the sum is negative. To add integers with different signs, subtract their absolute values. The sum has the same sign as the integer with the greater absolute value. Example 2 Find 16 12. 16 12 4 Subtract |12| from |16|. The sum is negative because |16| |12|. Exercises 1. 9 16 2. 10 (10) 3. 18 (26) 4. 23 (15) 5. 45 35 6. 39 (38) 7. 55 81 8. 61 (39) 9. 74 36 10. 5 (4) 8 11. 3 10 (6) 13. 3 (10) (16) 11 12. 13 (8) (12) 14. 17 31 (14) 26 Evaluate each expression if x 4 and y 3. 15. 11 y 16. x (6) 17. y 2 18. |x y| 19. |x| y 20. x |y| Chapter 1 30 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Add. NAME ________________________________________ DATE ______________ PERIOD _____ 1-4 Skills Practice 7NS1.2, 7AF1.3 Adding Integers Add. 1. 2 (3) 2. 4 7 3. 8 9 4. 12 (3) 5. 27 18 6. 11 (13) 7. 44 26 8. 44 (26) 9. 15 (51) 11. 53 (28) 12. 86 77 13. 10 (4) 6 14. 16 (5) 12 15. 2 17 (12) 16. 35 (31) (39) 17. 8 (12) 15 (13) 18. 23 (18) 41 (17) Evaluate each expression if a 9, b 12, and c 8. 19. 3 a 20. b 8 21. 6 c 22. |a| b 23. |a| |c| 24. |b c| Chapter 1 31 Glencoe California Mathematics, Grade 7 Lesson 1–4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 10. (17) (13) NAME ________________________________________ DATE ______________ PERIOD _____ 1-4 Practice 7NS1.2, 7AF1.3 Adding Integers Find each sum. 1. 1 (8) 2. 13 15 3. 19 (7) 4. 14 (14) 5. 12 10 6. 5 (26) 7. 46 27 8. 33 55 9. 29 (25) 10. 6 14 (12) 11. 15 (17) 10 12. 13 (13) (18) 13. 5 8 (1) (6) 14. 8 (7) (8) (9) 15. 15 10 (16) 12 POPULATION For Exercises 16 and 17, use the table below that shows the change in population for four cities between 2000 and 2005. 2000 Population (thousands) 589 Change as of 2005 (thousands) Las Vegas, Nevada 478 67 Pittsburgh, Pennsylvania 335 18 Rochester, New York 220 8 Boston, Massachusetts 30 Source: U.S. Census Bureau 16. What is the population of each of these cities as of 2005? 17. What was the total population change for these four cities? Write an addition expression to describe each situation. Then find each sum and explain its meaning. 18. GAMES On one turn, you move 10 spaces forward around the game board. On the next turn, you move 4 spaces backward. 19. CAMPING While hiking down into a canyon, Manuel passed a sign stating that the elevation was 100 feet below sea level. He descended another 56 feet before reaching his campsite. 20. WEATHER Before you went to sleep last night, the temperature was 3F. During the night the temperature dropped by 5. 21. ELEVATOR Mrs. Brown parked in the parking garage 30 feet below street level. She then got in an elevator and went up 80 feet to her office. Chapter 1 32 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. City NAME ________________________________________ DATE ______________ PERIOD _____ 1-4 Word Problem Practice 7NS1.2, 7AF1.3 1. FOOTBALL A football team loses 5 yards on one play and then loses 8 yards on the next play. Write an addition expression that represents the change in position of the team for the two plays. Then find the sum. 2. ELEVATOR You park in a garage 3 floors below ground level. Then you get in the elevator and go up 12 floors. Write an addition expression to represent this situation. Then find the sum. 3. GOLF In 2005, Tiger Woods won the Masters Tournament. His scores were 2, 6, 7, and 1 for four rounds. Write an addition expression that represents his final score. Then find the sum. 4. INVENTORY A local bookstore has 30 copies of a bestseller when it opens Monday morning. On Monday, it sells 6 copies of the book. On Tuesday, it sells 3 copies. On Wednesday, it receives a shipment containing 24 copies of the book and also sells 8 copies. Write an addition expression that represents the number of copies of the book that store has at the end of the day on Wednesday. Then find the sum. 5. OCEANOGRAPHY A research team aboard an underwater research vessel descends 1,500 feet beneath the surface of the water. They then rise 525 feet and descend again 350 feet. Write an addition expression to represent this situation. Then find the sum. 6. SPORTS Peter weighs 156 pounds, but he would like to wrestle in a lower weight class. He loses 4 pounds one week, gains back 2 pounds the next week, loses 5 pounds the third week, and loses 3 pounds the fourth week. Write an addition expression to represent this situation. Then find the sum. Lesson 1–4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Adding Integers Chapter 1 33 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1-4 Enrichment 7NS1.2 Adding Integers Listed below are the scores for a game of cards in which the highest score wins. The three players recorded their scores for each hand, but did not total the scores until they were done playing. Hand Micah Juanita Taylor 1 125 30 68 2 72 54 0 3 15 105 95 4 0 5 20 5 146 37 110 6 82 15 62 7 25 130 47 8 40 0 12 1. Who had the highest total score after round 3? How many points did this player have? 2. Who had the lowest score after round 5? What was his or her score at this point in the game? 3. What was each player’s score after round 6? 4. Who was in second place after round 7? How many points did this player have? 5. Who won the game? 6. What was each player’s final score at the end of the game? Chapter 1 34 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Refer to the table above to answer the following questions. NAME ________________________________________ DATE ______________ PERIOD _____ 1-5 Lesson Reading Guide 7NS1.2 Get Ready for the Lesson Complete the Mini Lab at the top of page 46 in your textbook. Write your answers below. 1. How does this result compare with the result of 3 (5)? 2. Use algebra tiles to find 4 2. 3. How does this result compare to 4 (2)? 4. Use algebra tiles to find each difference and sum. Compare the results in each group. a. 1 5; 1 (5) b. 6 4; 6 (4) Read the Lesson 5. Find the opposite of 7. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 6. Find the additive inverse of 7. 7. How is the opposite of a number different from the additive inverse of the number? Rewrite each difference as a sum. Then find the sum. 9. 3 8 8. 2 9 10. 10 (12) 11. 5 (16) Subtract. 12. 3 (5) 13. 3 5 14. 7 (3) 15. 6 8 16. 23 (17) 17. 24 (12) 18. 41 4 19. 31 (26) 20. 81 (33) 21. 139 134 22. 97 (265) 23. 59 (77) 24. Describe the method for subtracting integers. Remember What You Learned 25. Subtraction and addition are often referred to as opposite operations. Explain in your own words the relationship between addition and subtraction. Chapter 1 35 Glencoe California Mathematics, Grade 7 Lesson 1–5 Subtracting Integers NAME ________________________________________ DATE ______________ PERIOD _____ 1-5 Study Guide and Intervention 7NS1.2 Subtracting Integers To subtract an integer, add its opposite or additive inverse. Example 1 Find 8 15. 8 15 8 (15) 7 Example 2 To subtract 15, add 15. Add. Find 13 (22). 13 (22) 13 22 35 To subtract 22, add 22. Add. Exercises 1. 3 4 2. 5 (2) 3. 10 8 4. 15 (12) 5. 23 (28) 6. 16 9 7. 9 16 8. 21 16 9. 28 37 11. 65 (6) 12. 19 |29| 10. 34 (46) Evaluate each expression if a 7, b 3, and c 5. 13. a 8 14. 20 b 15. a c 16. c b 17. b a c 18. c b a Chapter 1 36 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Subtract. NAME ________________________________________ DATE ______________ PERIOD _____ 1-5 Skills Practice 7NS1.2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Subtract. 1. 6 7 2. 12 8 3. 9 9 4. 17 18 5. 13 (25) 6. 14 (19) 7. 25 15 8. 21 (23) 9. 34 (11) 10. 56 94 11. 38 (39) 12. 72 27 13. 36 47 14. 33 (68) 15. 76 18 16. 4 |6| 17. |10| |7| 18. |52| 49 Evaluate each expression if k 8, m 7, and p 10. 19. k 19 20. 19 m 21. p 11 22. k m 23. p m 24. m 3 25. m k 26. k m 16 27. k m p Chapter 1 37 Glencoe California Mathematics, Grade 7 Lesson 1–5 Subtracting Integers NAME ________________________________________ DATE ______________ PERIOD _____ 1-5 Practice 7NS1.2 Subtracting Integers Subtract. 1. 15 7 2. 3 12 3. 8 9 4. 4 (12) 5. 18 (7) 6. 8 (9) 7. 14 (18) 8. 19 (13) 9. 8 (22) 10. 1 15 11. 12 19 12. 10 (5) 13. d 10 14. g 15 15. d g 16. d f 17. d f g 18. g d f GEOGRAPHY For Exercises 1921, use the table that shows the elevations above sea level of the lowest and highest points on six continents. 19. How far below the highest point in Australia is the lowest point in Australia? 20. How far below the highest point in North America is the lowest point in Asia? 21. Find the difference between the lowest point in South America and the lowest point in Africa. Lowest Point (m) Africa 156 Highest Point (m) 5,895 Asia 400 8,850 Australia 12 2,228 Europe 28 5,642 North America 86 6,194 South America 42 6,960 Continent Source: www.worldoffacts.com Simplify. 22. 29 (4) (15) 23. 10 [8 (16)] 24. 25 [16 (9)] 25. [22 (18)] (5 11) 26. (5 9) (20 12) 27. [15 (7)] (8 11) Chapter 1 38 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Evaluate each expression if d 4, f 7, and g 11. NAME ________________________________________ DATE ______________ PERIOD _____ 1-5 Word Problem Practice 7NS1.2 GEOGRAPHY For Exercises 1 and 2, use the table. The table shows the elevations of several places on Earth. Place Elevation (feet) Mt. McKinley 20,320 Puerto Rican Trench 28,232 Mt. Everest 29,035 1,348 Dead Sea 282 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Death Valley 1. Find the difference in elevation between the top of Mt. McKinley and and the top of Mt. Everest. 2. Find the difference in elevation between Death Valley and the Dead Sea. 3. TEMPERATURE The highest recorded temperature on Earth was recorded in Africa at 136°F, while the lowest was 129°F in Antarctica. What is the range of temperatures recorded on Earth? 4. WEATHER If the overnight temperature at the Arctic Circle was 14°F, but the temperature rose to 8°F during the day, what was the difference between these high and low temperatures? 5. WATER The boiling point of water is 212°F, while 460°F is its absolute lowest temperature. Find the difference between these two temperatures. 6. STOCK MARKET During the course of one day, the price of a stock fluctuated between a high of $3 above the previous day’s closing price and a low of $2 below the previous day’s closing price. What was the difference between the high and low prices for that day? Chapter 1 39 Glencoe California Mathematics, Grade 7 Lesson 1–5 Subtracting Integers NAME ________________________________________ DATE ______________ PERIOD _____ 1-5 Enrichment 7NS2.5 Distance on the Number Line The absolute value of the difference between two integers can be interpreted as the distance between two points on a number line. That is, if point A has a as a coordinate and point B has b as a coordinate, then |a b| is the distance between points A and B. Graph each pair of points on the number line. Then write an expression using absolute value to find the distance between the points. 1. H at 4 and G at 2 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 3 2 1 0 1 2 3 4 5 6 7 8 3 2 1 0 1 2 3 4 5 6 7 8 6 7 8 6 7 8 8 7 6 5 4 3. A at 5 and B at 5 8 7 6 5 4 Use the number lines to solve the problems. 4. Graph two points, M and N, that are each 5 units from 2. Make M N. 8 7 6 5 4 3 2 1 0 1 2 3 4 5 5. Graph the two solutions to the equation |y 2| 3. Call the points y1 and y2. 8 7 Chapter 1 6 5 4 3 2 1 0 40 1 2 3 4 5 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2. X at 7 and Y at 1 NAME ________________________________________ DATE ______________ PERIOD _____ 1-6 Lesson Reading Guide 7NS1.2, 7AF1.3 Multiplying and Dividing Integers Get Ready for the Lesson Read the introduction at the top of page 51 in your textbook. Write your answers below. 2. Write a multiplication sentence that could be used to find this same depth. Explain your reasoning. 3. Write a multiplication sentence that could be used to find the submersible’s depth after 10 minutes. Then find the product. Read the Lesson 4. Identify each number in the multiplication sentence 3(120) 360 as either a factor or a product. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Complete each sentence with either positive or negative. 5. The product of two integers with different signs is __________ . 6. The product of two integers with the same signs is __________ . 7. The quotient of two integers with different signs is __________ . 8. The quotient of two integers with the same signs is __________ . Determine whether each product or quotient is positive or negative. Then evaluate the expression. 9. 4 8 10. 3 5 11. 9(2) 12. 6(7) 13. 12 (4) 14. 35 (7) 21 15. 64 16. 3 8 Remember What You Learned 17. Explain how to find the mean of a set of numbers. What is another name for the mean? Chapter 1 41 Glencoe California Mathematics, Grade 7 Lesson 1–6 1. Write two different addition sentences that could be used to find the submersible’s depth after 3 minutes. Then find their sums. NAME ________________________________________ DATE ______________ PERIOD _____ 1-6 Study Guide and Intervention 7NS1.2, 7AF1.3 Multiplying and Dividing Integers Use the following rules to determine whether the product or quotient of two integers is positive or negative. • The product of two integers with different signs is negative. • The product of two integers with the same sign is positive. • The quotient of two integers with different signs is negative. • The quotient of two integers with the same sign is positive. 7(4) 28 Example 2 5(6) 30 Example 3 15 (3) 5 Example 4 54 (6) 9 Find 7(4). The factors have different signs. The product is negative. Find 5(6). The factors have the same sign. The product is positive. Find 15 (3). The dividend and divisor have different signs. The quotient is negative. Find 54 (6). The dividend and divisor have the same sign. The quotient is positive. Exercises Multiply or divide. 1. 8(8) 2. 3(7) 3. 9(4) 4. 12(8) 5. 33 (3) 6. 25 5 7. 48 4 8. 63 (7) 9. (4)2 75 10. 15 11. 6(3)(5) 143 12. 13 Evaluate each expression if a 1, b 4, and c 7. 13. 3c b Chapter 1 14. a(b c) 15. c2 5b 42 a6 16. c Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Example 1 NAME ________________________________________ DATE ______________ PERIOD _____ 1-6 Skills Practice 7NS1.2, 7AF1.3 Multiplying and Dividing Integers 1. 2 3 2. 3(3) 3. 4(2) 4. 5 7 5. 9(8) 6. 11 12 7. 15(3) 8. 7(13) 10. (10)2 11. 6(8)(3) 12. (4)3 14. 1(3)(4) 15. (10)3 16. 3(4)(7) 17. 15 3 18. 40 (5) 19. 63 (7) 20. 76 4 56 21. 48 22. 57 23. 75 24. 9. 5(2)(7) Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 13. (9)2 Divide. 4 16 19 5 Evaluate each expression if a 2, b 5, and c 6. 25. abc 26. 2b c 2b c 27. 28. ab c 29. c 2a c 30. 31. b2 5a 32. (c)2 ab Chapter 1 b a 43 Glencoe California Mathematics, Grade 7 Lesson 1–6 Multiply. NAME ________________________________________ DATE ______________ PERIOD _____ 1-6 Practice 7NS1.2, 7AF1.3 Multiplying and Dividing Integers Multiply. 1. 5(7) 2. 3 12 3. 8(9) 4. 4(12) 5. (7)2 6. 2(5)(3) 8. 35 (7) 9. 48 (6) Divide. 7. 14 2 66 10. 6 80 12. 5 56 11. 7 13. s + 5t 14. 10 rt 5s 15. t4 42 16. rt 17. r2 16 18. (2t 4)2 4 Find the mean of each set of integers. 19. 8, 5, 3, 9, 5, 2 20. 11, 15, 16, 17, 20, 18, 22 21. 5, 4, 8, 12, 10 22. 22, 19, 14, 17, 18 Find each product or quotient. 23. (3)2 (4)2 24. 3(5)2 10(15) 26. 6 27. 25. 5(2)(4)(3) 4 12 28. 8 122 12 29. MONEY If you have $216 and you spend $12 each day, how long would it be until you had no money left? 30. WEATHER During a six hour period, the temperature dropped 18F. Find the average hourly change in the temperature. Chapter 1 44 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Evaluate each expression if r 4, s 11, and t 7. NAME ________________________________________ DATE ______________ PERIOD _____ 1-6 Word Problem Practice 7NS1.2, 7AF1.3 1. STOCK MARKET The price of a stock decreased $2 per day for four consecutive days. What was the total change in value of the stock over the four-day period? 2. EVAPORATION The height of the water in a tank decreases 3 inches each week due to evaporation. What is the change in the height of the water over a fiveweek period due to evaporation? 3. FOOTBALL A football team lost 9 yards on each of three consecutive plays. What was the team’s total change in position for the three plays? 4. HIKING A group of hikers is descending a mountain at a rate of 400 feet per hour. What is the change in the elevation of the hikers after 6 hours? Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. G 10 20 30 40 50 40 30 20 10 G 5. WEATHER On a certain day, the temperature changed at a rate of 2ºF per hour. How long did it take for the change in temperature to be 14ºF? 6. GEOLOGY The length of an island is changing at the rate of 17 inches per year. How long will it take for the change in the length of the island to be 255 inches? 14 F 7. DEPRECIATION The value of a piece of office equipment is changing at a rate of $175 per year. How long will it take for the change in value to be $1,050? Chapter 1 45 8. POPULATION The population of a small town is changing at a rate of 255 people per year. How long will it take for the change in population to be 2,040 people? Glencoe California Mathematics, Grade 7 Lesson 1–6 Multiplying and Dividing Integers NAME ________________________________________ DATE ______________ PERIOD _____ 1-6 Enrichment 7NS1.2, 7AF1.3 Doubles and Halves Most numbers are easy to double or halve mentally. And, many types of multiplication problems can be done mentally by using doubling and halving. In working problems of this type, it is helpful to remember that 5 equals 10 divided by 2. And, dividing by 2 is the same as multiplying by one-half. So, multiplying by 5 is the same as first multiplying by 10 and then halving. 10 1 5 ; 5 10 ; 87 5 87 10 2 870 2 435 2 2 Double each number. Use mental math. 1. 13 2. 214 3. 48 4. 2,512 5. 57 6. 609 7. 383 8. 6,523 10. 468 11. 690 12. 1,484 13. 72 14. 56 15. 38 16. 54 17. 116 18. 364 19. 5,296 20. 7,436 9. 64 Compute mentally. 21. 5 126 22. 5 234 23. 5 (872) 24. 20 93 25. 20 361 26. 20 317 Transform each product into an expression that uses doubling or halving. Change only the second factor. 27. 256 20 28. 613 5 29. 472 50 30. 57 40 31. 138 25 32. 93 125 Chapter 1 46 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Halve each number. Use mental math. NAME ________________________________________ DATE ______________ PERIOD _____ 1-6 TI-83/84 Plus Activity Calculating with Integers You can solve problems involving integers on a graphing calculator. When a number is positive, you do not need to enter a sign. But when a number is negative, use the (–) key before you enter the number. Example 1 Find 6 (10). Enter: 6 + (–) 10 ENTER 4 Example 2 1–6 Lesson X–6 So, 6 (10) 5 (4). Find 24 (3). Enter: (–) 24 3 (–) 8 ENTER So, 24 (3) 8. Example 3 Evaluate g t if g 4 and t 1. Enter: (–) 4 — (–) 1 ENTER 3 So, g t 3 when g 4 and t 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Exercises Perform the indicated operation. 1. 8 16 2. 4 (11) 3. 5 17 4. 6 12 5. 48 (3) 6. 3 (9) 7. 12 (11) 8. 36 (11) 9. 84 (3) Evaluate each expression if x 4, y 5, and z 1. 10. 15 x 11. y (4) 12. 10 z 13. 0 y 14. z (6) 15. 14 (z) 16. x y 17. y z 18. x y z 19. x (z) 20. x y (2) 21. x y z Chapter 1 47 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1-7 Lesson Reading Guide 7AF1.1, 7AF1.4 Writing Equations Get Ready for the Lesson Read the introduction at the top of page 57 in your textbook. Write your answers below. 1. What is the relationship between the number of guests and the cost of the party? 2. Write an expression representing the cost of a party with g guests. 3. What does the equation g 8 120 represent in this situation? Read the Lesson Look at the steps for writing an algebraic equation on page 57. Then determine whether each situation requires addition, subtraction, multiplication, or division. 5. Find the cost per person when the price of a pizza is split among several people. 6. Find the price of an airline ticket after the price has been decreased by $50. 7. Find how much an executive spent on breakfast, lunch, and dinner. 8. Find the flight time after the time has been increased by 15 minutes. 9. Find the product of the price of a calculator and the number of students in the class. 10. Find the high temperature on Wednesday if this temperature is 3º less than the high temperature on Tuesday. 11. Find the ratio of the amount of gasoline used and the distance traveled. Remember What You Learned 12. Devise your own way to determine how a verbal description should be translated as an algebraic equation. Chapter 1 48 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4. Find the difference between the cost of a gallon of premium gasoline and the cost of a gallon of regular gasoline. NAME ________________________________________ DATE ______________ PERIOD _____ 1-7 Study Guide and Intervention 7AF1.1, 7AF1.4 Writing Equations The table shows several verbal phrases for each algebraic expression. Phrases Expression Phrases Expression 8 more than a number the sum of 8 and a number x plus 8 x increased by 8 x8 the difference of r and 6 6 subtracted from a number 6 less than a number r minus 6 r6 Phrases Expression Phrases Expression 4 multiplied by n 4 times a number the product of 4 and n a number divided by 3 the quotient of z and 3 the ratio of z and 3 4n z 3 Sentences Equation Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 9 less than a number is equal to 45. The difference of a number and 9 is 45. A number decreased by 9 is 45. 45 is equal to a number minus 9. n 9 45 Exercises Write each verbal phrase as an algebraic expression. 1. the sum of 8 and t 2. the quotient of g and 15 3. the product of 5 and b 4. p increased by 10 5. 14 less than f 6. the difference of 32 and x Write each verbal sentence as an algebraic equation. 7. 5 more than a number is 6. 8. The product of 7 and b is equal to 63. 9. The sum of r and 45 is 79. 10. The quotient of x and 7 is equal to 13. 11. The original price decreased by $5 is $34. 12. 5 shirts at $d each is $105.65. Chapter 1 49 Glencoe California Mathematics, Grade 7 Lesson 1-7 The table shows several verbal sentences that represent the same equation. NAME ________________________________________ DATE ______________ PERIOD _____ 1-7 Skills Practice 7AF1.1, 7AF1.4 Writing Equations Write each verbal phrase as an algebraic expression. 1. a number divided by 5 2. the sum of d and 7 3. the product of 10 and c 4. the difference of t and 1 5. the score increased by 8 points 6. the cost split among 4 people 7. the cost of 7 CDs at $d each 8. the height decreased by 2 inches 9. $500 less than the sticker price 11. 2 hours more than the estimate 10. the total of Ben’s score and 75 12. 25 times the number of students Write each verbal sentence as an algebraic equation. 13. The sum of a number and 16 is equal to 45. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 14. The product of 6 and m is 216. 15. The difference of 100 and x is 57. 16. The quotient of z and 10 is equal to 32. 17. $12 less than the original price is $48. 18. 17 more than some number is equal to 85. 19. The number of members divided by 6 is 15. 20. The total of Joshua’s savings and $350 is $925. 21. 65 is 5 times a number. 22. The total area decreased by 75 square feet is 250 square feet. 23. The cost of 10 books at $d each is $159.50. 24. Carla’s height plus 4 inches is 68 inches. Chapter 1 50 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1-7 Practice 7AF1.1, 7AF1.4 Writing Equations Define a variable. Then write an equation to model each situation. 1. After receiving $25 for her birthday, Latisha had $115. 2. At 14 years old, Adam is 3 years younger than his brother Michael. 3. A class of 30 students separated into equal sized teams results in 5 students per team. 4. When the bananas were divided evenly among the 6 monkeys, each monkey received 4 bananas. 5. GRADES Kelly’s test score was 6 points higher than Michelle’s. If Kelly’s test score was 88, what was Michelle’s test score? Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 6. GEOMETRY A rectangle's width is one-third its length. If the width is 8 inches, what is the length of the rectangle? 7. FOOTBALL A team had a total gain of 15 yards over several plays with an average gain of 5 yards per play. How many plays are represented? Write an equation to model the relationship between the quantities in each table. 8. 9. Feet, f Yards, y 1,000 3 1 2 2,000 6 2 3 3,000 9 3 4 4,000 12 4 k g f y Kilograms, k Grams, g 1 10. MONEY Carlotta earns $3 for every hour that she baby sits. Complete the table of values showing the amount she earns for baby sitting 1, 2, 3, 4, and h hours. Given h, a number of hours, write an equation to find a, the amount that Carlotta earns. Chapter 1 51 Hours, h Amount, a Glencoe California Mathematics, Grade 7 Lesson 1-7 Define a variable. Then write an equation that could be used to solve each problem. NAME ________________________________________ DATE ______________ PERIOD _____ 1-7 Word Problem Practice 7AF1.1, 7AF1.4 1. AGE Julia is 3 years younger than Kevin. Kevin is 13. Define a variable and write an equation to find Julia’s age. 2. CIVICS In the 2004 presidential election, Texas had 23 more electoral votes than Tennessee. Define a variable and write an equation to find the number of Tennessee’s electoral votes if Texas had 34 votes. 3. ENERGY One year, China consumed 4 times as much energy as Brazil. Define a variable and write an equation to find the amount of energy Brazil used that year if China used 12,000 kilowatt-hours. 4. CHEMISTRY The atomic number of cadmium is half the atomic number of curium. The atomic number for cadmium is 48. Define a variable and write an equation to find the atomic number of curium. 5. LIBRARIES The San Diego Public Library has 44 fewer branches than the Chicago Public Library. Define a variable and write an equation for the number of branches in the San Diego Public Library if Chicago has 79 branches. 6. ASTRONOMY Saturn is 6 times farther from the Sun than Mars. Define a variable and write an equation to find the distance of Mars from the Sun if Saturn is about 1,429,400,000 km from the sun. 7. POPULATION The population of Oakland, California, is 9,477 more than the population of Omaha, Nebraska. Omaha has a population of 390,007. Define a variable and write an equation to find the population of Oakland. 8. GEOGRAPHY Kings Peak in Utah is 8,667 feet taller than Spruce Knob in West Virginia. Spruce Knob is 4,861 feet tall. Define a variable and write an equation to find the height of Kings Peak. Chapter 1 52 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Writing Equations NAME ________________________________________ DATE ______________ PERIOD _____ 1-7 Enrichment 7AF1.1 Writing Equations to Describe Sequences A sequence can be extended by finding the pattern, describing it, and then applying the description to produce successive terms. To describe the pattern in words, we could write, “Add four to the previous term to find the next term.” Determine the pattern rule for the sequence below. What are the next three terms? Position Term 1 4 2 8 3 12 4 16 5 20 6 7 8 A. 2, 4, 6, 8, 10, 12, ___, ___, ___ B. 3, 6, 9,12, 15, 18, ___, ___, ___ C. 3, 5, 7, 9, 11, 13, ___, ___, ___ D. 3, 9, 27, 81, 243, ___, ___, ___ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. E. 6,230, 623, 62.3, 6.23, 0.623, ___, ___, ___ F. 1, 4, 9, 16, 25, 36, ___, ___, ___ The rule of a sequence can be generalized into an equation so that it is possible to find the 10th term, 100th term, or nth term without writing out of the terms in between. The rule of the sequence shows the relationship between a term and its position number. Look again at the beginning example. The rule is multiply the position number by four. If we call the position numbers n, the algebraic expression for the rule is 4n. For each term t 4n. Write an equation rule for each of the sequences in exercises 1–6. Be careful that your rule gives the correct first term. 1. Sequence A 2. Sequence B 3. Sequence C 4. Sequence D 5. Sequence E 6. Sequence F Write an equation rule for each of the sequences below. Then use the equation to find the 100th term. 7. 4, 7, 10, 13, 16, … 9. 0, 2, 4, 6, 8, … 8. 2, 5, 10, 17, 26, … 10. 0.75, 1.5, 2.25, 3, 3.75, … 11. 11, 12, 13, 14, 15, … 12. Write your own sequence rule and find the first 5 terms. Chapter 1 53 Glencoe California Mathematics, Grade 7 Lesson 1-7 Pattern 4 4 4 4 Describe the pattern in words and write the next three terms in each of the following sequences. NAME ________________________________________ DATE ______________ PERIOD _____ 1-8 Study Guide and Intervention 7MR1.1, 7NS1.2 Problem-Solving Investigation: Work Backward You may need to work backward to solve a problems. Explore • Determine what information is given in the problem and what you need to find. Plan • Select a strategy including a possible estimate. Solve • Solve the problem by carrying out your plan. Check • Examine your answer to see if it seems reasonable. Example 1 Explore You know that Mari put $200 in the bank on the fourth week. You need to know how much money she put in the bank on the first week. Plan Start with the amount she put in the bank on the last week and work backward. Solve Start with the $200 Mari put in the bank on the fourth week. Fourth Week $200 This is $20 more than the third week. Check Third Week Second Week $180 $40 $220 Work This is $40 less Work This is twice as backward. than the second backward. much as the Subtract week. Add $40. first week. $20. $20 2 First Week $110 Work backward. Divide by 2. Start with $110 for the first week and work forward. On the second week she deposited twice as much money in the bank than on the first week, which is $220. On the third week, she deposited $40 less than the second week, which is $180. On the fourth week she deposited $20 more than on the third week, or $200. This is what you know she deposited on the fourth week. Exercises Use the work backward strategy to solve each problem. 1. SHOPPING Jack spent a total of $87.58 when he went shopping for camping supplies. He spent $36.89 on food, $23.24 on a sleeping bag, and bought lunch. When he got home, he had $15.70. How much did he spend on lunch? 2. AGE Sam is 4 years older than Eliot. Eliot is 9 years younger than Xing. Xing is 3 years older than Damien. If Damien is 15 years old, how old are each of the other boys? Chapter 1 54 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Mari put money in her savings account each week. She put a certain amount of money in the bank on the first week. On the second week she put twice as much money in the bank as the first week. On the third week, she put $40 less in the bank than on the second week. On the fourth week, she put $20 more in the bank than on the third week. Mari put $200 in the bank on the fourth week. How much money did Mari put in the bank on the first week? NAME ________________________________________ DATE ______________ PERIOD _____ 1-8 Skills Practice 7MR1.1, 7NS1.2 Problem-Solving Investigation: Work Backward Use the work backward strategy to solve each problem. 1. SKATEBOARDS On Monday, David’s skateboard shop received its first shipment of skateboards. David sold 12 skateboards that day. On Thursday, he sold 9 skateboards. On Friday, he received a shipment of 30 more skateboards and sold 10 skateboards. He then had a total of 32 skateboards in his shop. How many skateboards were delivered on Monday? 2. SHIPPING An overseas cargo ship was being loaded. At the end of each day, a scale showed the total weight of the ship’s cargo. On Monday, 48 tons of cargo were loaded onto the ship. On Tuesday, three times as much cargo was loaded on to the ship as on Monday. On Wednesday, 68 tons of cargo were loaded onto the ship. On Thursday, 0.75 as much cargo was loaded onto the ship as on Wednesday. On Friday, 120 tons of cargo were loaded onto the ship. At the end of the day on Friday, the scale showed that the ship was carrying 690 tons of cargo. How much cargo was the ship carrying when it first came into port on Monday? 4. JOGGING Edmund is training for a marathon. He ran a certain number of miles on Monday. On Wednesday, he ran 2 more miles than on Monday. On Saturday, he ran twice as far as on Wednesday. On Sunday, he ran 6 miles less than on Saturday. He ran 8 miles on Sunday. How many miles did Edmund run on Monday? Use the table to solve each problem. Flight Number 253 142 295 Airline Schedule Minneapolis, MN to Dallas, TX Departure Time 8:20 A.M. 11:52 A.M. 12:00 P.M. Arrival Time 10:37 A.M. 1:45 P.M. 3:30 P.M. 5. Charles needs to take Flight 295. He needs 45 minutes to eat breakfast and pack. It takes 25 minutes to get to the airport. To be at the airport 90 minutes early, what is the latest time he can start eating breakfast? 6. Mrs. Gonzales left her office at 7:25 a.m. She planned that it would take her 30 minutes to get to the airport, but the traffic was so heavy it took an additional 20 minutes. It takes 30 minutes to check her baggage and walk to the boarding gate. What is the first flight she can take to Dallas? Chapter 1 55 Glencoe California Mathematics, Grade 7 Lesson 1-8 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 3. NUMBERS Jana is thinking of a number. If she divides her number by 12 and then multiplies the quotient by 8, the result is 520. What number is Jana thinking of? NAME ________________________________________ DATE ______________ PERIOD _____ 1-8 Practice 7MR1.1, 7NS1.2 Problem-Solving Investigation: Work Backward 4. ANALYZE TABLES The table below gives the results from a poll taken at school about the times in minutes that boys and girls spend using the Internet for school work and the total time spent using the Internet each week. Mixed Problem Solving Use the work backward strategy to solve Exercises 1 and 2. 1. TRAVEL Rajiv and his family left home on a trip and drove for 2 hours before they stopped to eat. After 1.5 hours, they were back on the road. They arrived at their destination 3 hours later at 5:00 P.M. What time did they leave home? Gender Time Used for Total Time School Work per Week Boys Girls 33 min 72 min 255 min 213 min How many more minutes per week do boys spend using the Internet for purposes other than school work than girls? 2. GRADES Kumiko had an average of 92 on her first three math tests. Her scores on the second and third tests were 97 and 89. What was her score on the first test? Use any strategy to solve Exercises 3 and 4. Some strategies are shown below. For Exercises 5 and 6, select an appropriate operation to solve the problem. Justify your solution and solve the problem. 5. MOVIES The two animated films with the highest box office receipts brought in a total of $775 million. If one film brought in $97 million more than the other, how much did the film with the highest receipts bring in? Problem-Solving Strategies • Use the four-step plan. • Work backward. 3. BAKING Isabel doubled her recipe for chocolate chip cookies. After her brothers ate 8 cookies, she set aside half of the remaining cookies for a school party. Isabel then gave 2 dozen cookies to her neighbor. She had 12 cookies left over. How many cookies does one recipe make? Chapter 1 6. U.S. PRESIDENTS Harry S Truman was elected president in 1944. He died in 1972 at the age of 88. How old was he at the time he was elected? 56 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Select the Operation NAME ________________________________________ DATE ______________ PERIOD _____ 1-8 Word Problem Practice 7MR1.1, 7NS1.2 Problem-Solving Investigation: Work Backward Use the work backward strategy to solve each problem. CLARINET PRACTICE For Exercises 1 and 2, use the table at the right. It is a record of the amount of time Elena practiced her clarinet in a week. Tuesday 20 minutes more than Monday Thursday 10 minutes less than Tuesday Saturday Twice as long as Thursday Sunday 15 minutes less than Saturday– 45 minutes 1. How many minutes did Elena practice the clarinet on Thursday? 2. How many minutes did Elena practice on Monday? 3. HOCKEY During a hockey game, Brandon played 7 less minutes than Nick. Zach played 12 minutes more than Brandon. Hunter played twice as long as Zach. Hunter played for 44 minutes. How many minutes did Nick play in the hockey game? 4. PACKAGES In the morning, a delivery truck delivers 24 of it packages to a factory. It then goes to a distribution lot, where the remaining packages are separated into 4 equal groups and put on other trucks. There were 18 packages in each of the groups. How many packages were on the delivery truck to begin with? 5. WEATHER On Monday, Eliza read her book. On Tuesday, she read three times as long as she read on Monday. On Wednesday she read 20 minutes less than Tuesday. On Thursday she read for 20 minutes, which was half as long as she read on Wednesday How many minutes did Eliza read over the 4-day period? 6. STAMPS Zoe added 23 stamps to her collection. Three months later her collection had tripled in number to a total of 159 stamps. How many stamp did Zoe have to start her collection? Chapter 1 57 Glencoe California Mathematics, Grade 7 Lesson 1-8 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Monday ? NAME ________________________________________ DATE ______________ PERIOD _____ 1-9 Lesson Reading Guide 6AF1.1 Solving Addition and Subtraction Equations Get Ready for the Lesson Complete the Mini Lab at the top of page 65 in your textbook. Write your answers below. Solve each equation using algebra tiles. 1. x 1 4 2. x 3 7 3. x (4) 5 4. Explain how you would find a value of x that makes x (3) 8 true without using models. Read the Lesson x69 _____ a. Subtract 11 from each side. s 5 14 _____ b. Subtract 6 from each side. 4 3 p _____ c. Add 3 to each side. 11 m 33 _____ d. Add 5 to each side. For Exercises 6–8, explain how to solve each equation. 6. w 7 2 _________________________ 7. c 3 9 _________________________ 8. 17 11 k _________________________ Solve each equation. 9. z 8 2 10. 3 7 r 11. 9 g 14 Remember What You Learned 12. Write two addition and two subtraction equations of your own. Trade your equations with a partner and solve. Explain to each other the method you used to solve the equations. Chapter 1 58 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 5. Match the method of solving with the appropriate equation. NAME ________________________________________ DATE ______________ PERIOD _____ 1-9 Study Guide and Intervention 6AF1.1 Solving Addition and Subtraction Equations You can use the following properties to solve addition and subtraction equations. • Addition Property of Equality — If you add the same number to each side of an equation, the two sides remain equal. • Subtraction Property of Equality — If you subtract the same number from each side of an equation, the two sides remain equal. Example 1 Solve w 19 45. Check your solution. w 19 45 w 19 19 45 19 w 26 w 19¬ 45 26 19¬ 45 45¬ 45 ✓ Check 19 19 0 and 45 19 26. w is by itself. Write the original equation. Replace w with 26. Is this sentence true? 26 19 45 Solve h 25 76. Check your solution. h 25¬ 76 h 25 25¬ 76 25 h¬ 51 Check Subtract 19 from each side. h 25¬ 76 51 25¬ 76 76¬ 76 ✓ Write the equation. Add 25 to each side. 25 25 0 and 76 25 51. h is by itself. Write the original equation. Replace h with 51. Is this sentence true? 51 25 51 (25) or 76 Exercises Solve each equation. Check your solution. 1. s 4 12 2. d 2 21 3. h 6 15 4. x 5 8 5. b 10 34 6. f 22 6 7. 17 c 41 8. v 36 25 9. y 29 51 10. 19 z 32 11. 13 t 29 12. 55 39 k 13. 62 b 45 14. x 39 65 15. 56 47 n Chapter 1 59 Glencoe California Mathematics, Grade 7 Lesson 1-9 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Example 2 Write the equation. NAME ________________________________________ DATE ______________ PERIOD _____ 1-9 Skills Practice 6AF1.1 Solving Addition and Subtraction Equations 1. x 3 4 2. y 6 5 3. t 2 2 4. z 5 1 5. a 4 3 6. h 3 6 7. u 4 1 8. 8 d 14 9. 19 x 7 10. 17 b 8 11. 19 z 21 12. 22 y 29 13. 16 24 p 14. 17 19 x 15. f 25 35 16. y 37 59 17. s 46 72 18. m 65 11 19. r 53 19 20. n 75 42 21. g 35 62 22. 111 x 68 23. 54 32 w 24. 27 z 47 Chapter 1 60 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Solve each equation. Check your solution. NAME ________________________________________ DATE ______________ PERIOD _____ 1-9 Practice 6AF1.1 Solving Addition and Subtraction Equations Solve each equation. Check your solution. 1. t 7 12 2. h 3 8 3. 8 b 9 4. k 4 14 5. m 9 7 6. y 10 3 7. 14 2 d 8. 15 n 10 9. 8 r 6 10. 11 w 5 11. 9 g 9 12. 12 c 16 13. GEOMETRY Two angles are supplementary if the sum of their measures is 180. The two angles shown are supplementary. Write and solve an equation to find the measure of angle R. 140 R S 15. FUND RAISING During a five-day fund raiser, Shantell sold 8 boxes of greeting cards the first day, 6 boxes the second day, 10 boxes the third day, and 7 boxes the fourth day. If she sold a total of 45 boxes of greeting cards during the five days, write an equation that can be used to find the number of boxes Shantell sold the fifth day. Explain two methods of solving this equation. Then solve the equation. 16. ANALYZE TABLES The total points scored by both teams in the 2006 Super Bowl was 14 less than the total points for 2005. Write and solve an equation to find the total points for 2005. Total Points Scored by Both Teams in Super Bowl Year Points 2005 p 2006 31 Source: www.superbowl.com Chapter 1 61 Glencoe California Mathematics, Grade 7 Lesson 1-9 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 14. ARCHITECTURE The Sears Tower in Chicago was the tallest building in the world when it was completed. Twenty-three years later, a taller building was completed in 1996 on Taiwan. Write and solve an equation to find the year that the Sears Tower was completed. NAME ________________________________________ DATE ______________ PERIOD _____ 1-9 Word Problem Practice 6AF1.1 1. AGE Walter lived 2 years longer than his brother Martin. Walter was 79 at the time of his death. Write and solve an addition equation to find Martin’s age at the time of his death. 2. CIVICS New York has 24 fewer members in the House of Representatives than California. New York has 29 representatives. Write and solve a subtraction equation to find the number of California representatives. 3. GEOMETRY Two angles are supplementary if the sum of their measures is 180°. Angles A and B are supplementary. If the measure of angle A is 78°, write and solve an addition equation to find the measure of angle B. 4. BANKING After you withdraw $40 from your checking account, the balance is $287. Write and solve a subtraction equation to find your balance before this withdrawal. mA ⫽ 78˚ 180˚ B A 5. WEATHER After the temperature had risen 12°F, the temperature was 7°F. Write and solve an addition equation to find the 7 F starting temperature. 6. CHEMISTRY The atomic number of mercury is the sum of the atomic number of aluminum and 67. The atomic number of mercury is 80. Write and solve an addition equation to find the atomic number of aluminum. 7. ELEVATION The lowest point in Louisiana is 543 feet lower than the highest point in Louisiana. The elevation of the lowest point is 8 feet. Write and solve a subtraction equation to find the elevation of the highest point in Louisiana. 8. POPULATION In 2005, the population of Honduras is the population of Haiti decreased by 832,598. The population of Honduras is 6,823,568. Write and solve a subtraction equation to find the population of Haiti. Chapter 1 62 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Solving Addition and Subtraction Equations NAME ________________________________________ DATE ______________ PERIOD _____ 1-9 Enrichment 7AF1.1 Geometric Equations Equations are often used to solve geometric problems. To work the problems on this page, you will need to use the following facts. Angles are complementary if their measures add to 90°. If their measures add to 180°, they are supplementary. The total number of degrees in the measures of the central angles of a circle is 360°. The sum of the measures of the angles in a triangle is 180°. A straight angle measures 180°. Match each equation in the chart at the bottom of the page with a figure that could be used to solve for the missing angle measurement. Then solve for that measurement. A. B. C. 20˚ x˚ 90˚ x˚ x˚ 150˚ 72˚ D. E. x˚ 45˚ F. x˚ 45˚ x˚ Equation 15˚ 30˚ 15˚ Letter of Figure Angle Measurement (x) 35° 20° x° 180° 90° x° 15° x° 72° 180° 360° x° 150° 90° 2(45°) x° 180° 30° x° 15° 90° Chapter 1 63 Glencoe California Mathematics, Grade 7 Lesson 1-9 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 35˚ NAME ________________________________________ DATE ______________ PERIOD _____ 1-10 Lesson Reading Guide 6AF1.1 Solving Multiplication and Division Equations Get Ready for the Lesson Read the introduction at the top of page 70 in your textbook. Write your answers below. 1. If d represents the number of days the bamboo has been growing, write a multiplication equation you could use to find how long it would take for the bamboo to reach a height of 210 inches. Read the Lesson Complete each sentence. 2. To solve 3x 51, __________ each side by 3. 3. To solve b 4, __________ each side by 2. 2 5. To solve 7 d, __________ each side by 6. 6 Explain how to solve each equation. 6. u 13 _________________________ 7. 2c 14 _________________________ 8. 64 16k _________________________ 6 Solve each equation. 9. 8r 32 10. 3 x 11. 9 9g 7 Remember What You Learned 12. Write two multiplication and two division equations of your own. Trade your equations with a partner and solve. Explain to each other the method you used to solve the equations. Chapter 1 64 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4. To solve 65 5t, __________ each side by 5. NAME ________________________________________ DATE ______________ PERIOD _____ 1-10 Study Guide and Intervention 6AF1.1 Solving Multiplication and Division Equations You can use the following properties to solve multiplication and division equations. • Multiplication Property of Equality — If you multiply each side of an equation by the same number, the two sides remain equal. • Division Property of Equality — If you divide each side of an equation by the same nonzero number, the two sides remain equal. Example 1 Solve 19w 104. Check your solution. 19w 114 Write the equation. 19w 114 19 19 Divide each side of the equation by 19. 1w 6 19 19 1 and 114 19 6. w6 19w¬ 114 Check Write the original equation. 19(6)¬ 114 Replace w with 6. This sentence is true. Solve d 9. Check your solution. 15 d 9 15 d (15) 9(15) 15 Multiply each side of the equation by 15. d 135 Check d ¬ 9 15 135 ¬ 9 15 9¬ 9 ✓ Write the original equation. Replace d with 135. 135 15 9 Exercises Solve each equation. Check your solution. 1. r 6 2. 2d 12 3. 7h 21 4. 8x 40 5. f 6 6. x 7 7. 17c 68 8. h 12 9. 29t 145 11. 13t 182 12. 117 39k 5 10. 125 5z Chapter 1 10 8 11 65 Glencoe California Mathematics, Grade 7 Lesson 1-10 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 114¬ 114 ✓ Example 2 Identity Property; 1w w NAME ________________________________________ DATE ______________ PERIOD _____ 1-10 Skills Practice 6AF1.1 Solving Multiplication and Division Equations Solve each equation. Check your solution. 1. u 3 2. 3c 12 3. 5x 15 4. 7z 49 5. n 7 6. a 11 7. 14g 56 8. t 11 9. 18y 144 10. 135 9z 11. 11d 143 12. 116 29k 13. w 17 14. 14 15. 112 8v 16. 17c 136 17. 21a 126 18. s 9 19. m 7 20. 16q 272 21. 15 z 9 31 g 22 22. 23 Chapter 1 9 3 12 y 7 y 25 23. 16 19 14 24. 47k 517 66 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1-10 Practice 6AF1.1 Solving Multiplication and Division Equations Solve each equation. Check your solution. 1. 5s 45 2. 8h 64 3. 36 9b 4. 3p 24 5. 12m 72 6. 56 7d x 7. 11 5 v 8. 20 4 c 9. 43 2 y 10. 16 3 n 11. 9 8 a 12. 3 25 14. POPULATION The population of South Africa is four times the population of Greece. If the population of South Africa is 44 million, write and solve a multiplication equation to find the population of Greece. MEASUREMENT For Exercises 15 and 16, refer to the table. Write and solve an equation to find each quantity. Customary System 15. the number of quarts in 24 pints Conversions (capacity) 1 pint 2 cups 1 quart 2 pints 1 quart 4 cups 16. the number of gallons in 104 pints 1 gallon 4 quarts 1 gallon 8 pints Solve each equation. 84 17. 3 g Chapter 1 4 18. 8 x 144 19. 16 r 67 Glencoe California Mathematics, Grade 7 Lesson Lesson 1-10 X–4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 13. CARS Mrs. Alvarez bought a new car. Her monthly payments are $525. If she will pay a total of $25,200 in payments, write and solve a multiplication equation to find the number of payments. NAME ________________________________________ DATE ______________ PERIOD _____ 1-10 Word Problem Practice 6AF1.1 1. WAGES Felipe earns $9 per hour for helping his grandmother with her yard work. Write and solve a multiplication equation to find how many hours he must help his grandmother in order to earn $54. 2. SHOPPING Granola bars are on sale for $0.50 each. If Brad paid $5 for granola bars, write and solve a multiplication equation to find how many bars he bought. 3. EXERCISE Jasmine jogs 3 miles each day. Write and solve a multiplication equation to find how many days it will take her to jog 57 miles. 4. TRAVEL On a trip, the Rollins family drove at an average rate of 62 miles per hour. Write and solve a multiplication equation to find how long it took them to drive 558 miles. 5. ROBOTS The smallest robot can travel 20 inches per minute through a pipe. Write and solve a multiplication equation to find how long it will take this robot to travel through 10 feet of pipe. 6. BANKING Nate withdraws $40 from his checking account each day. Write and solve a multiplication equation to find how long it will take him to withdraw $680. 7. AGE The product of Bart’s age and 26 is 338. Write and solve a multiplication equation to find Bart’s age. 8. POPULATION The population of a small town is increasing at a rate of 325 people per year. Write and solve a multiplication equation to find how long it will take the population to increase by 6,825. Chapter 1 68 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Solving Multiplication and Division Equations NAME ________________________________________ DATE ______________ PERIOD _____ 1-10 Enrichment 7AF1.1 Consecutive Integers Equations can be used to solve problems that involve consecutive integers. In solving these problems, you will need to translate certain phrases into algebraic expressions. Here are some examples. Phrase A “five consecutive integers” Expression A n, n 1, n 2, n 3, n 4 Phrase B “five consecutive even integers” Expression B n, n 2, n 4, n 6, n 8 Phrase C “five consecutive odd integers” Expression C n, n 2, n 4, n 6, n 8 Use Expressions A, B, and C for these problems. 1. What five consecutive integers does Expression A produce when n 8? 3. What five consecutive odd integers does Expression C produce when n 9? Write an equation to solve each problem. 4. Find the three consecutive integers that have a sum of 12. 5. Find the four consecutive odd integers with a sum of 80. 6. The larger of two consecutive even integers is 6 less than 3 times the smaller. Find the integers. 7. Find four consecutive even integers such that the largest is twice the smallest. Chapter 1 69 Glencoe California Mathematics, Grade 7 Lesson Lesson 1-10 X–4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2. What five consecutive even integers does Expression B produce when n 0? NAME ________________________________________ DATE ______________ PERIOD _____ 1 Student Recording Sheet Use this recording sheet with pages 80-81 of the Student Edition. Read each question. Then fill in the correct answer. 1. A B C D 2. F G H J 3. A B C D 4. F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 10. F G H J 11. A B C D Pre-AP Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Assessment Record your answers for Question 12 on the back of this paper. Chapter 1 71 Glencoe California Mathematics, Grade 7 NAME ________________________________________ DATE ______________ PERIOD _____ 1 Rubric for Scoring Pre-AP (Use to score the Pre-AP question on page 81 of the Student Edition.) General Scoring Guidelines • If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended response questions require the student to show work. • A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response. • Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit. Exercise 12 Rubric Specific Criteria 4 The values n 1, r 0, and t 4 are correctly determined. Explanations are correct with properties correctly listed. 3 The values are correctly determined, but the explanations are not complete. 2 Two of the values and explanations are correct and the other value is not correct. OR The values and explanations are correct, but the properties are not named correctly. 1 Only one of the values and explanations is correct. OR The values are correct, but there are no explanations. 0 Response is completely incorrect. OR One or more of the values are correct, but the procedures are completely incorrect. Chapter 1 72 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Score NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Quiz 1 SCORE _____ (Lessons 1-1, 1-2, and 1-3) Use the four-step plan to solve the problem. 1. SCHOOL SUPPLIES At the school store, a pencil costs $0.24, and an eraser costs $0.18. What combination of pencils and erasers could you buy for exactly $0.66? 1. Evaluate each expression if x 4, y 2, and z 5. 2. 3x z 2. 3. 2(4 y) xz 3. 4. |6| |2| 4. 5. |15 6| 5. NAME ________________________________________ DATE ______________ PERIOD _____ 1 SCORE _____ Chapter 1 Quiz 2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. (Lessons 1-4 and 1-5) Add. 1. 10 6 1. 2. 32 (5) 2. 3. 17 (16) 3. 4. 9 (11) 2 4. Subtract. 5. 9 12 5. 6. 11 2 6. 7. 15 (7) 7. 8. 8 (4) 8. Evaluate each expression if a 6, b 15, and c 2. 9. |b| a 9. 10. a b c 10. Chapter 1 73 Glencoe California Mathematics, Grade 7 Assessment Evaluate each expression. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Quiz 3 SCORE _____ (Lessons 1-6 and 1-7) Multiply or divide. 1. 6(4) 1. 2. 5(7) 2. 3. 50 2 3. 4. 27 (3) 4. Evaluate each expression if x 7, y 1, and z 3. xz 5. 5. 6. 10 xy 6. 2 Write each verbal phrase as an algebraic expression. 7. the sum of a number and 5 7. 8. $3 more than the other CD cost 8. Write each verbal sentence as an algebraic equation. 9. 10. $15 less than the amount he spent is $12.50. 10. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Quiz 4 SCORE _____ (Lessons 1-8, 1-9, and 1-10) Solve each equation. Check your solution. 1. x 9 11 1. 2. m 6 15 2. 3. k 2 3. 4. 72 6w 4. 14 5. MONEY During the school week, Joshua spent $3 each day on lunch. On Tuesday, he bought a $5 ticket to the school play and on Friday he loaned $2 to his friend. When he checked his wallet at the end of the day Friday, he had $3 left. How much money did he start the week with? 5. Chapter 1 74 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 9. 9 more than a number is equal to 24. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Mid-Chapter Test SCORE _____ (Lessons 1-1 through 1-5) Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1. Evaluate 32 5 6 3. A. 22 B. 28 C. 16 D. 19 1. 2. Evaluate |x| y if x 3 and y 4. F. 7 G. 1 H. 1 J. 7 2. 3. Find 15 (12). A. 27 B. 27 C. 3 D. 3 3. 4. Find 9 (5). F. 4 H. 14 J. 4 4. 5. Name the property shown by the statement (x 9) 0 x 9. A. Commutative () C. Distributive B. Associative () D. Identity () 5. G. 14 6. Graph the set of integers {2, 2, 4, 0, 1} on a number line. 6. 7. Evaluate a b c if a 7, b 2, and c 6. 7. 8. GAMES During a card game, you give someone 5 cards, then someone else gives you 7 cards. Write an addition statement to describe this situation. Then find the sum. 8. 9. Draw the next two figures in the pattern below. 9. 10. FIELD TRIP Two classes are going on a field trip. The first class has 27 students and 9 adults. The second class has 33 students and 11 adults. If one bus holds 42 people, how many buses are needed for this field trip? Chapter 1 75 4 3 2 1 0 1 2 10. Glencoe California Mathematics, Grade 7 Assessment Write the letter for the correct answer in the blank at the right of each question. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Vocabulary Test absolute value additive inverse algebra algebraic expression conjecture coordinate counterexample defining a variable SCORE _____ equation evaluate inequality integer inverse operations negative number numerical expression opposites order of operations positive number property powers solution solve variable 1. Operations that "undo" each other are called __________. 1. 2. On a number line, the number that corresponds to a point is called the __________ of that point. 2. 3. The distance between a number and 0 on a number line is called the __________ of that number. 3. 4. A number less than 0 is a(n) __________. 4. 5. A statement that shows that a conjecture is false is a(n) __________. 5. 6. An integer and its opposite are __________. 6. 7. Expressions that represent repeated multiplication are called _________. 7. 8. The values of the variable that make an equation true are called the _________ of the equation. 8. 9. When you find the numerical value of an expression, you __________ the expression. 9. 10. A sentence containing the symbol is called a(n) __________. 10. Define each term in your own words. 11. conjecture 12. property Chapter 1 76 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Choose from the terms above to complete each sentence. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 1 SCORE _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1. EXERCISE Every 5 days Alma rides her skateboard in the park. Every 4 days she bikes to her best friend’s house. How often does Alma do both? A. every 10 days B. every 20 days C. every 4 days D. every 5 days 1. 2. Evaluate the expression 2(9) 6 3. F. 14 G. 2 H. 4 J. 16 2. 3. Evaluate the expression 2y x if x 4 and y 2. A. 10 B. 12 C. 8 D. 14 3. 4. Name the property shown by the statement (2 6) 19 2 (6 19). F. Commutative () H. Distributive G. Associative () J. Identity () 4. 5. Which of the following statements is true? A. 7 1 B. 5 2 C. 3 0 D. 6 4 5. 6. Evaluate the expression |10||3|. F. 7 G. 7 H. 13 J. 13 6. 7. Find 6 (21). A. 15 B. 27 C. 15 D. 27 7. 8. Find 9 (15). F. 6 G. 24 H. 24 J. 6 8. 9. BOOKS Marcos had 8 library books. Today he returned 3 books and checked out 5 more. How many library books does Marcos have now? A. 11 B. 7 C. 6 D. 10 9. 10. Find 8 12. F. 4 G. 20 H. 4 J. 20 10. 11. Find 4 (9). A. 5 B. 13 C. 13 D. 5 11. Chapter 1 77 Glencoe California Mathematics, Grade 7 Assessment Write the letter for the correct answer in the blank at the right of each question. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 1 (continued) 12. Evaluate b a if a 7 and b 15. F. 22 G. 8 H. 8 J. 22 12. 13. Find 2(7). A. 14 B. 14 C. 9 D. 9 13. 14. Find 24 4. F. 6 G. 6 H. 20 J. 20 14. 15. a number decreased by 9 A. 9 n B. 9 n C. 9n D. n 9 15. 16. the sum of a number and 6 F. 6n G. n H. n (6) J. n (6) 16. 6 17. SCHOOL DAY Winter Middle School must end at 3:00 P.M. for the buses. There needs to be 5 hours for classes, 45 minutes for lunch, 10 minutes for daily announcements, 25 total minutes for changing classes, and 1 2 hour for assemblies. What time does Winter Middle School need to start in the morning? A. 8:10 A.M. B. 8:00 A.M. C. 9:50 A.M. D. 8:50 A.M. 17. Solve each equation. Check your solution. 18. m 9 21 F. 12 G. 12 H. 30 J. 30 18. 19. 34 d 6 A. 28 B. 40 C. 28 D. 40 19. 20. 2r 46 F. 23 G. 23 H. 48 J. 46 20. Bonus Draw the next two figures in the pattern below. Chapter 1 78 B: Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Write each verbal phrase as an algebraic expression. NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 1 Test, Form 2A 1 SCORE _____ 1. ENROLLMENT Use the information in the table about enrollment at South Middle School. How many more 7th graders attended South Middle School during the 2001–2002 school year than during the 2005–2006 school year? A. 23 B. 48 2. Evaluate 32 16 4 2. F. 1 G. 7 School Year Number of 7th Graders 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006 164 189 195 155 141 C. 9 D. 57 1. H. 17 J. 4 2. 3. Name the property shown by the statement (7 9)3 7(3) 9(3). A. Commutative ( ) C. Distributive B. Associative ( ) D. Identity ( ) 3. 4. Graph the set of integers {5, 7, 2, 3} on a number line. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. F. G. 7 6 5 4 3 2 1 0 1 2 3 3 2 1 0 1 2 3 4 5 6 7 H. J. 7 6 5 4 3 2 1 0 1 2 3 3 2 1 0 1 2 3 4 5 6 7 4. 5. Evaluate |15||11|. A. 26 B. 26 C. 4 D. 4 5. 6. Find 9 (3) 7. F. 19 G. 13 H. 5 I. 1 6. 7. Find 15 (4). A. 19 C. 11 D. 11 7. 8. Evaluate a b if a 10 and b 6. F. 4 G. 16 H. 16 J. 4 8. 9. Find 3(2)(5). A. 25 B. 25 C. 30 D. 30 9. G. 5 H. 48 J. 48 B. 19 60 10. Find . 12 F. 5 Chapter 1 79 10. Glencoe California Mathematics, Grade 7 Assessment Write the letter for the correct answer in the blank at the right of each question. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 2A (continued) 11. Evaluate x 2y if x 3 and y 5. A. 1 B. 2 C. 13 D. 7 11. J. c 12. D. 16 n 2 13. 12. Write 15 more dogs than cats as an algebraic expression. F. c 15 G. c 15 H. 15c 15 Write each verbal sentence as an algebraic equation. 13. 16 is twice a number. A. 16 2 n B. 16 n 2 C. 16 2n 14. $20 less than the amount Josh earned is $6.50. F. a 20 6.50 H. 20a 6.50 G. 20 a 6.50 J. a 20 6.50 14. 15. p 13 8 A. 5 B. 21 C. 5 D. 21 15. 16. 42 m 10 F. 52 G. 32 H. 52 J. 32 16. 17. 39 3x A. 42 B. 36 C. 117 D. 13 17. G. 5 H. 50 J. 20 18. D. 30 19. 20. SHOPPING Jordan has $50 to spend on a new pair of jeans. He saves $10 with a coupon. After he pays $2 in sales tax, he receives $23 in change. What was the original price of the jeans? F. $27 G. $35 H. $38 J. $31 20. 18. c 10 5 F. 2 Write and solve an equation to find each number. 19. If you increase a number by 45, the result is 15. A. 3 B. 3 C. 30 Bonus Evaluate |x2 y2|3 if x 4 and y 6. Chapter 1 80 B: Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Solve each equation. Check your solution. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 2B SCORE _____ Write the letter for the correct answer in the blank at the right of each question. 1. READING Use the information in the table about the number of books Tyrone has read. How many more books did Tyrone read during the first year than during the last year? A. 10 books C. 1 books B. 36 books D. 5 books Number of Books 2002 2003 2004 2005 2006 15 21 18 25 10 1. H. 5 J. 4 3. Name the property shown by the statement 2 7 7 2. A. Commutative ( ) C. Distributive B. Associative ( ) D. Identity ( ) 2. 3. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4. Graph the set of integers {0, 2, 4, 1} on a number line. F. H. 5 4 3 2 1 0 1 2 3 4 5 G. 5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5 J. 5 4 3 2 1 0 1 2 3 4 5 4. 5. Evaluate |16| |5|. A. 21 B. 11 C. 21 D. 11 5. 6. Find 10 6 (3). F. 1 G. 7 H. 7 J. 1 6. 7. Find 12 (8). A. 20 C. 4 D. 20 7. 8. Evaluate c d if c 7 and d 3. F. 4 G. 10 H. 4 J. 10 8. 9. Find 5(4)(8). A. 8 9. B. 4 B. 160 C. 160 D. 8 G. 13 H. 56 J. 48 52 10. Find . 4 F. 13 Chapter 1 81 10. Glencoe California Mathematics, Grade 7 Assessment 2. Evaluate 42 (8 6) 9. F. 13 G. 17 Year NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 2B (continued) 11. Evaluate 3m n if m 2 and n 1. A. 2 B. 5 C. 5 D. 7 11. J. m 12. 12. Write half of Latisha’s markers as an algebraic expression. F. m 2 G. m 2 H. 2m 2 Write each verbal sentence as an algebraic equation. 13. 12 birds is 3 more birds than Rhonda saw yesterday. A. 12 3b C. 12 b 3 D. 12 b H. 92 4 n J. 92 n 14. B. 12 3 b 13. 3 14. 92 is the product of 4 and a number. F. 92 4 n G. 92 4n 4 15. r 15 7 A. 8 B. 22 C. 22 D. 8 15. 16. 25 n 10 F. 35 G. 35 H. 15 J. 15 16. 17. 3c 45 A. 48 B. 42 C. 15 D. 15 17. 18. 54 2m F. 27 G. 27 H. 56 J. 52 18. D. 2 19. Write and solve an equation to find each number. 19. The difference of a number and 9 is 18. A. 9 B. 9 C. 2 20. MONEY Phillip received money from his grandmother for his birthday. He put half in the bank for savings and bought two $15 CDs. Later that day, Phillip’s sister gave him $5 that she owed him. At the end of the day Phillip had $25 left. How much money did his grandmother give him for his birthday? F. $120 G. $90 H. $100 J. $50 Bonus Two more than the opposite of a number is 3. Use an equation to find the number. Chapter 1 82 20. B: Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Solve each equation. Check your solution. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 2C SCORE _____ 1. FISH When Maria filled her fish tank the water was 12 inches deep. One week later she noticed that the water was 10.5 inches deep, and after another week it was 9 inches deep. How deep will the water be after one more week? 1. 2. 42 5 4 2 2. 54 3. 3 3. 4. |18| 4. 5. |14 9| 5. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2 1 Evaluate each expression if a 5, b 2, c 4, and d 2. 6. 3b a 6. 7. b c d 7. 8. d c 8. 9. ab cd 9. 100 10. 10. 11. bcd 11. ac Add or subtract. 12. 19 9 12. 13. 5 (16) Chapter 1 13. 83 Glencoe California Mathematics, Grade 7 Assessment Evaluate each expression. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 2C (continued) 14. 7 7 14. 15. 12 (5) 15. For Questions 16-19, multiply or divide. 16. 4(7) 16. 17. 5(2)(4) 17. 18. 32 4 18. 54 19. 19. 20. Write the sum of a number and 16 as an algebraic expression. 20. 21. AGE Susan was 11 when her family moved into the house she still lives in. That was 82 years ago. If the year is now 2006, what year was Susan born? 21. Solve each equation. Check your solution. 22. g 7 9 22. 23. 12 z 16 23. 24. 8x 96 24. p 5 25. 10 25. Bonus Evaluate 5{32 4[8 (23 18 2 3)]}. Chapter 1 84 B: Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 9 NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 2D SCORE _____ 1. SHOPPING At the grocery store, a cucumber costs $0.33, and a green pepper costs $0.52. What combination of cucumbers and green peppers could you buy for exactly $5.00? 1. 2. 23 4 5 10 2. 69 3. 2 3. 4. |12| 4. 5. |6| |2| 5. 3 6 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Evaluate each expression if w 2, x 4, y 3, and z 5. 6. x 2y 6. 7. x y z 7. 8. z w 8. 9. 3w x 9. xyw 10. 12 10. 11. 4wz 11. Add or subtract. 12. 27 (9) 12. 13. 8 (10) 13. Chapter 1 85 Glencoe California Mathematics, Grade 7 Assessment Evaluate each expression. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 2D (continued) 14. 12 10 14. 15. 5 (11) 15. 16. 8(10) 16. 17. 4(7)(5) 17. 18. 48 (6) 18. 72 19. 19. 20. Write 14 less than a number as an algebraic expression. 20. 9 21. SUMMER JOB Jonah mows lawns in the summer. In the past three years he has averaged, 13, 6, and 12 lawns a week. What is the minimum number of lawns he must mow per week on average this summer in order to maintain an average of 10 lawns a week each summer? 21. Solve each equation. Check your solution. 22. m 12 10 22. 23. 2 x 9 23. 24. 7y 91 24. 25. a 36 25. 4 bh Bonus If A , write an expression for the value of h. 2 Chapter 1 86 B: Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. For Questions 16-19, multiply or divide. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 3 SCORE _____ Use the four-step plan to solve each problem. 1. MONEY Kenji earned $40 mowing lawns last week. He wants to use his money to buy 4 videos that cost $9.99, $12.95, $6.75, and $10.39. Does he have enough money to purchase the videos? 1. 2. (30 18)(24 6) 2. 3. 5[24 (9 3) 4] 3. For Questions 4-7, evaluate each expression if a 5, b 2, c 3, and d 4. a2 9 4. 2 4. 5. |c| d a 5. 6. 10 cd 6. 7. 5(7 2c)2 7. 8. Order the integers in the set {15, 2, 26, 25, 3} from least to greatest. 8. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. b Add or subtract. 9. 10 5 (12) 9. 10. 35 (57) 10. 11. 16 (13) 11. 12. 8 |19| 12. Chapter 1 87 Glencoe California Mathematics, Grade 7 Assessment Evaluate each expression. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Test, Form 3 (continued) For Questions 13–16, multiply or divide. 13. (3)4 13. 14. 5(2)3 14. 156 15. 15. 16. 78 (6) 16. 17. Find the mean of the set of integers {21, 17, 15, 25, 19}. 17. 13 18. 29 fewer points scored today than were scored yesterday 18. 19. the sum of a number and 12 19. Write each verbal sentence as an algebraic equation. 20. 4 less than the opposite of a number is 10. 20. 21. GRADES Elena has scored an 87, a 93, and an 86 on her last three math tests. What is the minimum score she must make on her fourth, and final test, in order to maintain a 90 average for her math tests? 21. Solve each equation. Check your solution. 22. 45 19 d 22. 23. x (3) 9 23. 24. t 15 24. 25. 17m 272 25. 7 h(a b) Bonus If A , write an expression for the value of a. 2 Chapter 1 88 B: Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Write each verbal phrase as an algebraic expression. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Chapter 1 Extended-Response Test SCORE _____ Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem. If necessary, record your answer on another piece of paper. 1. Theo has scores of 76, 87, 82, 91, and 79 on his first five math tests. a. Explain how to find the average of Theo’s test scores. Then find the average. b. Graph Theo’s five test scores and his average score on a number line. c. Find the difference between Theo’s first test score and his average test score. Find the difference between each of his other four scores and his average in the order that the scores are listed. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. e. Find the sum of the differences that you found in part c. 2. Tiffany has forgotten her score on the first test but remembers that her remaining scores are 85, 73, 87, and 84. Furthermore, Theo’s average score is three more than Tiffany’s average score. a. Write and solve an addition equation relating Theo’s average to Tiffany’s average. Use your result from Exercise 1a for Theo’s average. What does the solution represent? b. Let s represent the sum of Tiffany’s five test scores. The sum of Tiffany’s five scores divided by 5 is equal to her average score. Write and solve a division equation to find the value of s. c. Let m represent the missing score. Find the sum of Tiffany’s four known test scores. The sum of m and the number that you just found is equal to the value of s that you found in part b. Write and solve an addition equation to find the missing score. d. Subtract Tiffany’s average score from each of her five test scores. Start with the score you found in part b. List the five differences. Then find their sum. e. Compare the sums you found in part c with the sum you found in Exercise 1e. Then make a conjecture about the sum of the differences between a student’s actual test scores and average score. Chapter 1 89 Glencoe California Mathematics, Grade 7 Assessment d. Describe in at least two different ways the test scores for which the differences you found in part c are negative. NAME ________________________________________ DATE ______________ PERIOD _____ 1 Standardized Test Practice SCORE _____ (Chapter 1) Part 1: Multiple Choice Instructions: Fill in the appropriate circle for the best answer. 1. Evaluate 42 5 2 6 3. (Lesson 1-2) A 40 B 24 C 16 D 12 1. A B C D 2. F G H J D 15 3. A B C D 4. Which is in order from least to greatest? (Lesson 1-3) F 15, 11, 5, 1, 6 H 6, 1, 5, 11, 15 G 1, 6, 5, 11, 15 J 1, 5, 6, 11, 15 4. F G H J 5. Which is in order from least to greatest? (Lesson 1-3) A 15, 9, 1 C 5, 2, 1, 10 B 6, 4, 1 D 1, 0, 4, 6 5. A B C D 6. Find 16 (13). (Lesson 1-4) F 29 G 3 H 3 J 29 6. F G H J 7. Find 8 (19) (Lesson 1-4) A 27 B 11 C 11 D 27 7. A B C D 8. Find 6 (15) (Lesson 1-5) F 21 G 9 J 21 8. F G H J 9. A B C D 10. F G H J 11. A B C D 2. Which equation is an example of the Distributive Property? F 5(4 2) 5(4) 5(2) G 8 (9 7) (8 9) 7 H (21 9) 3 3 (21 9) J 1 2x 2x 3. Evaluate 52 3 · 4 (6 4) (Lesson 1-2) A 7 B 10 C 11 H 9 9. TEMPERATURE At 4:00 A.M. the temperature was 2°F. At 1:00 P.M. the temperature was 15°F. How much did the temperature change? (Lesson 1-5) A 17° B 13° C 13° D 17° 10. Find the mean of the set of integers {10, 6, 11, 8, 12, 7}. (Lesson 1-6) F 9 G 6 H 1 J 9 11. Sophia is 4 inches shorter than Maya. If Maya is x inches tall, which expression represents Sophia’s height? (Lesson 1-7) A 4x B 4x C. x 4 D x4 Chapter 1 90 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. (Lesson 1-2) NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. (continued) 12. Kevin has two dogs. Spot is 5 years older than Tucker. If S Spot’s age, which expression can be used to find Tucker’s age? (Lesson 1-7) F S5 H S5 G 5 S J 5 S 12. F G H J 13. The sum of a number and 17 is 32. Which equation can be used to to find the number. (Lesson 1-8) A n 17 32 C 17 32 n B n 17 32 D 32 17 n 13. A B C D 14. 45 is 16 more than a number. Which equation can be used to find the number? (Lesson 1-9) F y (45) 16 H y 45 16 G y 16 45 J 45y 16 14. F G H J 15. Solve t (7) 7 (Lesson 1-9) A 14 C 14 B 0 D 49 15. A B C D 16. Solve c 16. (Lesson 1-9) 4 F 64 G 20 H 12 J 4 16. F G H J 17. Solve 5n 85. (Lesson 1-9) A 90 C 17 B 80 D 425 17. A B C D H 3 J 11 18. F G H J C 1.5 D 54 19. A B C D 18. Evaluate |r s| if r 7 and s 4. F 11 G 3 19. Solve x 6 A 54 B 1.5 Chapter 1 9. 91 Glencoe California Mathematics, Grade 7 Assessment Standardized Test Practice 1 NAME ________________________________________ DATE ______________ PERIOD _____ 1 Standardized Test Practice (continued) Part 2: Short Response Instructions: Write your answers below or to the right of the questions. 20. Evaluate 52 3 2 (9 4) (Lesson 1-2) 20. 21. Order the integers in the set {14,3,10, 1,1} from least to greatest. (Lesson 1-3) 21. 4a 22. Evaluate if a 6 and b 2. (Lesson 1-6) b 23. AGE Maria is 4 years older than Samantha. Define a variable and write an expression for Maria’s age. (Lesson 1-7) 23. 24. The sum of a number and 12 is 6. Write and solve an equation to find the number. (Lesson 1-8) 24. Solve the following equation. r 25. 5 (Lesson 1-10) 3 25. 26. Consider the set of integers {3, 0, 1, 2}. (Lessons 1-3) a. Graph the set on a number line. 26a. b. Explain how you can use a number line to order the numbers from least to greatest. 26b. c. Order the numbers from least to greatest. Chapter 1 92 26c. Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 22. Chapter 1 Before you begin Chapter 1 Algebra: Integers Anticipation Guide A1 D A D A A D D A A D A 3. According to the Order of Operations, all operations within grouping symbols must be completed first. 4. According to the Order of Operations, all addition and subtraction should be done before multiplication and division. 5. The Commutative Property is true only for addition and multiplication. 6. Negative integers can be used to express values less than zero. 7. When comparing two negative integers, the greater integer is the one with the greater absolute value. 8. The sum of a positive integer and a negative integer is always negative. 9. When subtracting a negative integer, add its opposite. 10. The product of two negative integers is always positive. 11. The quotient of two negative integers is always negative. 12. Any letter can be used to represent an unknown in an expression or equation. After you complete Chapter 1 D 2. Algebraic expressions are any mathematical expressions that contain at least one operation symbol. Chapter 1 STEP 2 A or D 1. A conjecture is a statement proven to be true. Statement 7 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 • Reread each statement and complete the last column by entering an A or a D. • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a piece of paper to write an example of why you disagree. Step 2 STEP 1 A, D, or NS • Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). Step 1 1 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter Resources Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. A Plan for Problem Solving Lesson Reading Guide 7MR1.1, 6AF2.3 Chapter 1 9 Glencoe California Mathematics, Grade 7 7. Early problem solvers care is a mnemonic aid to remember the first letters of the steps in the problem-solving plan. Write a mnemonic aid of your own using the first letters of the steps. See students’ work. Remember What You Learned has the fastest top speed. 6. Look at the graph in Example 2 on page 26. Explain how the animals in the chart are listed. Why is the cheetah first? In order of speed; it The amount when two quantities are subtracted; since 1 minute 60 seconds, multiply the 1 second distance by 60. 5. Look at the Explore section in Example 2 on page 26. What does the word “difference” mean? Now read the Plan section. Explain how to find the distance traveled in 1 minute when you know the distance per second. first blue tile; 18 is the number of additional white tiles needed for 9 additional blue tiles. 4. Read the Check section in Example 1 at the bottom of page 25. In the equation 8 18 26, what does the 8 stand for? What does the 18 stand for? 8 is the number of white tiles needed to surround the Read the Lesson white tiles is two more than the last number of white tiles, so Garden 6 would need 8 5(2) or 18 tiles. 3. How many tiles will it take to border a garden that is 6 tiles long? Explain your reasoning. 18; Sample answer: The number of 2. Predict how many white tiles it will take to border the next-largest garden. Check your answer by modeling the garden. 14; Garden 1: 8; Garden 2: 10; Garden 3: 12 1. How many white tiles does it take to border each of these three gardens? Complete the Mini Lab at the top of page 24 in your textbook. Write your answers below. Get Ready for the Lesson 1-1 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Anticipation Guide and Lesson 1-1) Lesson 1–1 Chapter 1 A Plan for Problem Solving Study Guide and Intervention Solve the problem by carrying out your plan. Examine your answer to see if it seems reasonable. Solve Check 36 7 40 42 8 44 45 9 A2 Comparing each plant’s heights on consecutive days, we see that Plant A’s height increases by 3 millimeters each day, while Plant B’s height increases by 4 millimeters each day. To estimate Plant A’s height on day 12, assume that it will grow 3 millimeters each day past day 10, so it will be 51 3 3 or 57 millimeters. To estimate Plant B’s height on day 12, assume that it will grow 4 millimeters each day past day 10, so it will be 52 4 4 or 60 millimeters. Given what we know about each plant’s height and how plants grow in general, both estimates seem reasonable. Solve Check Chapter 1 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 52 51 10 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 10 2. FLOUR BEETLES The population of a flour beetle doubles in about a week. How long would it take for the population to grow to eight times its original size? 3 wk 1. MOVIES A movie ticket costs $3.50. A large popcorn costs $3.75 and a large soda costs $3.00. How much will it cost two friends to go to a movie if they share a popcorn and each has a large soda? $16.75 Use the four-step plan to solve each problem. Exercises Determine whether there is a pattern and extend that pattern to day 12. You know their heights for days 5 to 10. You need to determine their heights in two more days. 48 48 Plan Explore 32 Plant B 6 39 Estimate the height of each plant on day 12. 5 36 Day Plant A Plant A and Plant B are two new experimental apple trees being grown in a laboratory. The table displays their heights, in millimeters, when they are 5 to 10 days old. Select a strategy including a possible estimate. Plan Example 1 Determine what information is given in the problem and what you need to find. 7MR1.1, 6AF2.3 Explore You can always use the four-step plan to solve a problem. 1-1 NAME ________________________________________ DATE ______________ PERIOD _____ A Plan for Problem Solving Skills Practice 7MR1.1, 6AF2.3 Chapter 1 10. 9. 11 Glencoe California Mathematics, Grade 7 Draw the next two figures in each of the patterns below. 8. 1024, 256, 64, 16, 4 The numbers are divided by 4; 1. 7. 1860, 1890, 1920, 1950, 1980 The numbers increase by 30; 2010. Find a pattern in the list of numbers. Then find the next number in the list. 6. GUPPIES In January, Tate’s fish tank had 12 guppies. In February, it had 18, and in March it had 24. How many guppies do you expect to be in Tate’s fish tank in May? 36 guppies 23 pizzas 5. PIZZA The Chess Club sold 2,116 pizzas during a fundraiser that lasted for all of March, April, and May. How many pizzas did they sell per day? 4. PRODUCE At the local grocery store, lemons are 52 cents each and limes are 21 cents each. How many lemons and limes can you buy for exactly $3.75? 6 lemons and 3 limes 3. EXERCISE Trevor jogs every 3 days and swims every 4 days. How often does he jog and swim on the same day? every 12 days 2. FIELD TRIP A school policy requires that there be at least one chaperone for every 8 students on a field trip. How many chaperones are required for a field trip with 67 students? 9 chaperones 1. GAS MILEAGE Each day Ernesto drives 52 miles. If he can drive 26 miles on one gallon of gasoline, how many days can he drive on 14 gallons of gasoline? 7 days Use the four-step plan to solve each problem. 1-1 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-1) Lesson 1–1 Chapter 1 A Plan for Problem Solving Practice $13.79 $14.59 $15.39 2 3 4 A3 Chapter 1 12 6. GEOMETRY Draw the next two figures in the pattern. 3 paint brushes and 2 bottles of paint Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 5. ART SUPPLIES At the craft store, a paint brush costs $0.79, and a small bottle of paint costs $0.89. What combination of paint brushes and bottles of paint could you buy for exactly $4.15? 4. GEOGRAPHY The land area of Washington, D.C., is 61 square miles. In 2003, the population of Washington, D.C., was 563,384. If one square mile is equal to 640 acres, about how many people per acre were there in Washington, D.C., in 2003? About 14 people per acre 3. SPORTS The track coach must buy at least two bottles of water for each participant in a track meet. One team has 35 members, and the other team has 28 members. If each case of water contains 24 bottles, what is the fewest number of full cases that the coach can buy? 6 cases $28 Price $12.99 1 Toppings 7MR1.1, 6AF2.3 2. MOVIES Mr. Sedgwick paid $13 for one adult ticket and one child ticket for a movie. Mrs. Wong paid $18 for one adult ticket two child tickets to see the same movie, and Mr. Gomez paid $23 for one adult ticket and three child tickets. If the pattern continues, how much should Mrs. Beauregard expect to pay for one adult ticket and four child tickets? 1. FOOD The table shows a portion of the price list for a local pizzeria. Tony has $17 that he can spend to buy one large pizza. If the pattern in the prices continues, what is the greatest number of toppings that Tony can order on his pizza? What is the cost of that pizza? 6 toppings; $16.99 Use the four-step plan to solve each problem. 1-1 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. A Plan for Problem Solving Word Problem Practice Chapter 1 No; 9($1.69) 9($4.59) $50 5. OFFICE SUPPLIES At an office supply store, pens are $1.69 per dozen and note pads are $4.59 per dozen. Can Shirley buy 108 pens and 108 note pads for $50? Explain your reasoning. 3. HISTORY The area of Manhattan Island is 641,000,000 square feet. According to legend, the Native Americans sold it to the Dutch for $24. Estimate the area that was purchased for one cent. 267,000 ft 2 13 1. Estimate the total number of teenagers who voted. Sample answer: 55 Arto Saari Bam Margera Danny Way Bob Burnquist Skater 9 11 15 18 Votes 7MR1.1, 6AF2.3 Glencoe California Mathematics, Grade 7 6. SHOPPING Yoshi bought two pairs of shoes. The regular price of each pair was $108. With the purchase of one pair of shoes at regular price, the second pair was half price. How much did Yoshi pay altogether for the two pairs of shoes? $162 4. TRAVEL Britney’s flight to Rome leaves New York City at 5:15 P.M. on Wednesday. The flight time is 7.5 hours. If Rome is 6 hours ahead of New York City, use Rome time to determine when she is scheduled to arrive. 6:45 A.M. Thursday 2. How many more teenagers preferred Burnquist to Saari? 9 teenagers SKATEBOARDING For Exercises 1 and 2, use the table at the right. It shows the results of a recent survey in which teenagers were asked who the best professional skateboarder is. Use the four-step plan to solve each problem. 1-1 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-1) Lesson 1–1 Chapter 1 Enrichment 7MR2.3 N Y N N N N Y N Secretary Treasurer N N Y N N Y N N Keisha Sandra Jamal President Vice President Holly A4 Chapter 1 Track Discus 400-m 100-m Hurdles Kyle Rob Nick Cory Shot Put Mitch Glencoe California Mathematics, Grade 7 Y Y Y North Y Y Y South Y Y 14 Taft Y Discus Y 400-m Y 100-m Y Hurdles Glencoe California Mathematics, Grade 7 Cory, from Wilson, won the shot put. Kyle, from Vine, won the discus. Mitch, from South, won the 400-m. Nick, from Taft, won the 100-m. Rob, from North, won the hurdles. Y Shot Put Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Y Y Vine Two boys competed in the field events and three boys competed in the three track events. No boy participated in both track events and field events. The athlete from North Middle School, who is not Mitch, placed last in the 100-meter. The 100-meter winner lost to the South Middle School student in another event. The boy from Wilson Academy, who placed second in the discus throw, was not in any event with Mitch or Rob. The South Middle School boy and Kyle, who is not from Wilson, were not in any of the same events. The student from Taft Junior High did not participate in any field events. In one event Nick beat the student from North Middle School and the 400-meter winner. Field • • • • • • • • Five male athletes won events in the district track and field meet. Each boy won exactly one event. From the clues below, find each boy’s name, school name, and the event he won. Use the process of logical reasoning and the table below to answer the following question. Using the table, mark Y for relationships that are true, and N for relationships that are not true. For example, since you know that Sandra is the president, put a Y in that cell and put an N in each of the other cells of that column and in the president row. Fill in the remaining cells to show that Jamal must be the treasurer. Holly, Keisha, Sandra, and Jamal are Bexley Middle School’s student council officers. The offices they hold are president, vice-president, secretary, and treasurer. Sandra is the president, Holly is not the treasurer, and Keisha is the vice-president. What office does Jamal hold? When planning how to solve problems, it is helpful to be familiar with a number of problem-solving strategies. When a problem presents a large amount of information, one strategy that can be effective is logical reasoning combined with the use of a table to organize the information. Logical Reasoning 1-1 NAME ________________________________________ DATE ______________ PERIOD _____ 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties Lesson Reading Guide 4 1 8 2 3 4 5 6 12 16 20 24 2 ____ Division 1 ____ Multiplication 3 Chapter 1 15 Glencoe California Mathematics, Grade 7 is an example opposing or against a conjecture. 9. The word counter has several meanings in the English language. Use a dictionary to find the meaning of counter when it is used as a prefix in the word counterexample. Then write your own definition of counterexample. Sample answer: opposing; a counterexample Remember What You Learned orders; not equal 8. 10 2, 2 10 The numbers are being divided in opposite differently; equal; Assoc. () 7. 5 (4 7), (5 4) 7 The numbers being multiplied are grouped subtraction are different; equal; Dist. 6. 2(5 3), 2 5 2 3 The order of the multiplication and grouped differently; not equal 5. (6 4) 1, 6 (4 1) The numbers being subtracted are orders; equal; Comm. () 4. 2 5, 5 2 The numbers are being added in opposite For Exercises 4–8, describe how each pair of numerical expressions is different. Then determine whether the two expressions are equal to each other. If the expressions are equal, name the property that says they are equal. ____ Subtraction ____ Addition 4 3. Number the operations in the correct order for simplifying 2 4(9 6 3). Then simplify the expression. 30 Read the Lesson 2. What would be the perimeter of Figure 10? 40 units What is the relationship between the figure number and the perimeter of the figure? The perimeter is 4 times the figure number. Perimeter Figure Number 1. Complete the table below. Complete the Mini Lab at the top of page 29 in your textbook. Write your answers below. Get Ready for the Lesson 1-2 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lessons 1-1 and 1-2) Lesson 1–2 Chapter 1 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties Study Guide and Intervention A5 3x2 4y 3(3)2 4(2) 3(9) 4(2) 27 8 19 6. 2 32 8 5 3 8. 52 (8 6) 50 5. 2 3 10 14 14 7. (10 5) 3 5 12. 2 2 14 3 2 18 Chapter 1 16. (ab)2 225 13. a 3b 16 17. a(b c) 33 14. 4b 3c 2 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 18. 3(bc 8) a 22 15. 2a b 5c 31 10. 3 7(14 8 2) 73 Evaluate each expression if a 3, b 5, and c 6. 11. 5[24 (6 8)] 50 9. (17 5)(6 5) 132 2 4. 5 6 2 3 1 3. 14 2 3(5) 22 2 2. 16 12 4 13 1. 4 5 8 28 Replace x with 3 and y with 2. Evaluate the power first. Do all multiplications. Subtract. Evaluate the expression 3x2 4y if x 3 and y 2. Evaluate each expression. Exercises Example 2 Add inside the left parentheses. Add inside the remaining parentheses. Divide. Multiply. Subtract. Evaluate the expression (5 7) 2 3 (8 1). (5 7) 2 3 (8 1) 12 2 3 (8 1) 12 2 3 9 639 18 9 9 Example 1 Order of Operations 1. Perform all operations within grouping symbols first; start with the innermost grouping symbols. 2. Evaluate all powers before other operations. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. When finding the value of an expression with more than one operation, perform the operations in the order specified by the order of operations. 1-2 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties Skills Practice Chapter 1 17 Dist. Glencoe California Mathematics, Grade 7 34. 3(7 2) 3(7) 3(2) 33. 13 (5 10) (5 10) 13 Comm. () 32. (4 5) 0 4 5 Iden. () 30. (6 2) 5 6 (2 5) Assoc. () 28. 1 x2 x2 Iden. () 31. 2(bc) 2(cb) Comm. () 29. 2(bc) (2b)c Assoc. () 27. (4 5)3 4(3) 5(3) Dist. 3 26. 2t2 t 9 75 2 t 10 pn 24. Name the property shown by each statement. 25. n2 3n 8 12 1 22. 4(pt 3) n 15 p2 4 23. 3t 5 24 npt 21. 3 20. 6t2 t 210 19. p(n t) 30 18. 5(2t n) 40 17. np2 36 14. t 2p 16. (np)2 144 15 15. 3p n 4 9 13. 3n p 0 12. (15 9)2 (5 4) 4 10. 3[(8 2) 5] 7 10 8. 23 4 3 6 20 Evaluate each expression if n 4, p 3, and t 6. 28 7 11. 7 42 13 9. (4 4) 4 4 4 33 7. (27 24)(27 24) 153 6. 2(20 5) 35 34 14 4 4. 25 2 8 4 29 3. 24 12 4 21 5. 49 (32 8 3) 16 2. 4(9) 36 3 24 1. 10 2 8 13 Evaluate each expression. 1-2 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-2) Lesson 1–2 Chapter 1 7AF1.2, 7AF1.3, 7AF1.4 7. s(7 t) r 42 r2 1 6. 2 t 3 5. (st)2 100 Commutative Property of Addition 12. 5 (1 9) 5 (9 1) Identity Property of Multiplication 10. 1(2 3) 2 3 8. 2s2 8s 3 13 A6 5(3 + 4) 16. 5(3) 5(4), Distributive Property Chapter 1 68°F Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 18 18. TEMPERATURE When a temperature in degrees Celsius C is known, the expression 9C 160 can be used to find the temperature in degrees Fahrenheit. If a thermometer 5 shows that a temperature is 20C, what is the temperature in degrees Fahrenheit? 17. INTERNET A bookstore offers wireless Internet access to its customers for a charge. The m cost of using this service is given by the expression $1.50 , where m is the number 20 of minutes online. How much would it cost to be online 40 minutes? $3.50 x + (7 + 3) 15. (x 7) 3, Associative Property Rewrite each expression using the indicated property. 14. Multiplication of whole numbers is associative. true 13. The sum of an even number and an odd number is always even. false; 2 3 5 State whether each conjecture is true or false. If false, provide a counter example. Associative Property of Addition 11. (10 7) 4 10 (7 4) Distributive Property 9. 6(5 1) 6(5) 6(1) Name the property shown by each statement. 3. 8 6t r 17 2. 4s 5t 10 1. 3r s 14 4. rs2 75 Variables, Expressions, and Properties Practice Evaluate each expression if r = 3, s = 5, and t = 2. 1-2 NAME ________________________________________ DATE ______________ PERIOD _____ 7AF1.2, 7AF1.3, 7AF1.4 Variables, Expressions, and Properties Word Problem Practice 1 600 cm2 Chapter 1 $34 5. MOVIE RENTALS Mario intends to rent 10 movies for his birthday party. He can rent new releases for $4 each, while older ones are $2 each. If he rents n new releases, the total cost, in dollars, of the 10 movies is represented by the expression 4n 2(10 n). Evaluate the expression to find the total cost if he rents 7 new releases. 10 cm 19 3. GEOMETRY The expression 6s2 can be used to find the surface area of a cube, where s is the length of an edge of the cube. Find the surface area of a cube with an edge of length 10 centimeters. 1. Each team’s final score for a football game can be found using the expression 6t e 3f, where t is the number of touchdowns, e is the number of extra points, and f is the number of field goals. Find Pittsburgh’s final score in the 2006 Super Bowl. 21 3 Seattle 1 0 r Glencoe California Mathematics, Grade 7 24 expression to find the force when m 12, v 4, and r 8. expression . Evaluate the mv2 r 6. CIRCULAR MOTION Pelipa is able to spin her yo-yo along a circular path. The yo-yo is kept in this path by a force which can be described by the 4. VERTICAL MOTION The height of an object dropped from the top of a 300foot tall building can be described by the expression 300 16t2, where t is the time, in seconds, after the ball is dropped. Find the height of the object 3 seconds after it is dropped. 156 ft 2. Use the expression 6t e 3f to find Seattle’s final score in the 2006 Super Bowl. 10 1 3 Touchdowns Extra Points Field Goals Pittsburgh Team FOOTBALL For Exercises 1 and 2, use the table that shows statistics from the 2006 Super Bowl. 1-2 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-2) Lesson 1–2 Chapter 1 Enrichment 7AF1.3 0 y 0 0y0 A7 x0 6. 0 0 Chapter 1 x x0 3. 4x 0 x 7. 0 x 4. x 0 0 20 no solutions y x 0, y 0 x0 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 x 8. 0 0 all numbers 5. x 0 x Describe the solution set for each equation. But, a b contradicts a b. Therefore, a b. 0 division by zero. Therefore, 0 a and 0 b. Step 3 Step 4 Step 3 involves Assume a b. 0 a 0 and 0 b 0 Step 2 2. Step 1 0 division by zero. Therefore, 1 2. Step 3 But, 1 2 is a contradiction. Step 2 involves 0 Therefore, 0 1 and 0 2. 0 0 1 0 and 0 2 0 Step 2 1. Step 1 Explain what is wrong with each of these “proofs.” Because division by zero leads to impossible situations, it is not a “legal” step in solving a problem. People say that division by zero is undefined, or not possible, or simply not allowed. There is no number that will make the left equation true. This equation has no solution. For the right equation, every number will make it true. The solution set for this equation is “all numbers.” 0x5 Because multiplication “undoes” division, you can write two equivalent equations for the ones above. 5 x 0 Some interesting things happen when you try to divide by zero. For example, look at these two equations. Division by Zero? 1-2 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Evaluating Expressions TI-73 Activity Evaluate 3(x 6) 2 (x2 15) for x 8 and for x 12. ) ( ENTER 6 ) 2nd [ENTRY] to redisplay the previous 2nd [ENTRY] to redisplay the line Press Press DEL [INS] 12 [ENTRY] to redisplay the expression. ENTER 2nd to reevaluate the expression. [ENTRY] 2. 2x2 10 28; 82; 460 Chapter 1 then Done.) 2nd 21 Glencoe California Mathematics, Grade 7 [TEXT] and using the cursor keys to select Y and See student’s work. (Hint: Enter Y by pressing 16x2 3. 48; 192; 1,200 4. x(20 x) 51; 84; 75 3 5. How would you evaluate xy2 for x 4 and y 7 on a TI-73 graphing calculator? 1. x2 9 0; 27; 216 Use a graphing calculator to evaluate each expression for x 3, x 6, and x 15. ENTER 2nd 2nd Use the cursor keys to move to the 8. Insert 12 in place of the 8. that stores the value for x. Press entries you made. Use You do not need to reenter the expression. Evaluate the same expression for x 12. 15 2 3 ( ENTER Evaluate the expression for x 8. 8 STO Exercises Step 2 Step 1 You could enter the expression, replacing the x with 8 and then enter it again, replacing x with 12. But it is easier to enter the expression just once and store the values for x. Example Graphing calculators follow the order of operations. So there is no need to perform each operation separately. To evaluate an expression, enter it just as it is written. If an expression contains parentheses, enter them in the calculator just as they are written. 1-2 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-2) Lesson 1–2 Chapter 1 Integers and Absolute Value Lesson Reading Guide 7NS2.5 A8 right; 72 0 left; 45 0 Chapter 1 Glencoe California Mathematics, Grade 7 22 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. |f s| 3 or |s f | 3 The Seahawks and the 49ers scored within 3 points of each other. 12. Write a mathematical expression that represents the following sentence. (Hint: Let f represent the 49ers’ score and s represent the Seahawks’ score.) Remember What You Learned 3 between two vertical bars; | 3| 11. Describe the symbol for the absolute value of 3. Then write the symbol. 10. 6 lies to the ________ of 7 on a number line. right; 6 7 9. 3 lies to the ________ of 95 on a number line. right; 3 95 8. 72 lies to the ________ of 0 on a number line. 7. 45 lies to the ________ of 0 on a number line. Complete each sentence with either left or right to make a true sentence. Then write a statement comparing the two numbers with either or . number line continues indefinitely in both directions. 6. Look at the number line on page 35 of your textbook. How are the ellipses (plural of ellipsis) in the set of integers {...,4, 3, 2, 1, 0, 1, 2, 3, 4,...} represented on the number line? The arrows indicate that the Sample answer: The rest of the list has been omitted. 5. How can you explain the usage of the ellipsis in the list in Exercise 3 in terms of the meaning for the ellipsis in the sentence in Exercise 4? or phrase has been omitted. 4. Use a dictionary to find the meaning of the ellipsis as it is used in the sentence The marathon began...downtown. Sample answer: A word 3. Look on page 35 in your textbook to find the meaning of the ellipsis as it is used in the list 1, 4, 7, 10,... . The list continues without end. The symbol ... is called an ellipsis. Read the Lesson 2. What does a temperature of 35º represent? 35 degrees below zero 86 meters below sea level 1. What does an elevation of 86 meters represent? Read the introduction at the top of page 35 in your textbook. Write your answers below. Get Ready for the Lesson 1-3 NAME ________________________________________ DATE ______________ PERIOD _____ Integers and Absolute Value Study Guide and Intervention 7NS2.5 Order the set of integers {10, 3, 9, 4, 0} from least to greatest. 0 2 4 6 8 10 12. |4| |4| 0 9. |13| |15| 28 6. |21| 21 23 Glencoe California Mathematics, Grade 7 19. |2b c| 13 18. 2|a| c 17 17. |3b| 12 Chapter 1 16. b |c| 9 15. |c b| 1 38 3 14. |a| 14 20 13. |23 15| 10. |21 18| 7. |3| |5| 8 {34, 9, 0, 7, 31} 4. {31, 0,34,9, 7} {8, 6, 4, 1, 3} 2. {6,8, 3,1,4} Evaluate each expression if a 6, b 4, and c 5. 11. |11| |5| 6 8. |9| |8| 17 5. |13| 13 Evaluate each expression. {21, 11, 2, 5, 13} 3. {2, 13,11,21, 5} {5, 0, 1, 3, 4} 1. {3, 0,5, 1, 4} Order each set of integers in each set from least to greatest. Exercises The absolute value of 220 is 20. The absolute value of 10 is 10. Simplify. Evaluate the expression |20| |10|. |20| |10| 20 |10| 20 10 30 Example 2 The absolute value of a number is the distance of that number from 0 on a number line. The numbers from left to right are {9, 3, 0, 4, 10}. 10 8 6 4 2 Graph each integer on a number line. Example 1 A number line can help you order a set of integers. When graphed on a number line, the smaller of two integers is always to the left of the greater integer. 1-3 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-3) Lesson 1–3 Chapter 1 Integers and Absolute Value Skills Practice 2 1 75 A9 19. |6| |6| 18. 3 13 20. |4| |5| 17. 10 8 30. |28| |26| 54 29. |28| |26| 2 24 36. |3b| 24 35. a |a| 6 Chapter 1 33. |b| 2 6 32. |a| 5 8 Evaluate each expression if a 3, b 8, and c 5. 27. |3| |19| 22 26. |256| 256 31 24. |31| Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 37. |a 16| 19 34. 2|c| b 18 31. |24| |15| 9 28. |12| |13| 25 25. |1| 1 {3, 2, 1, 1, 2, 3} 23. |8| 8 Evaluate each expression. {6, 4, 0, 2, 7} 22. {1, 2, 3, 3, 2, 1} Order each set of integers in each set from least to greatest. 16. 4 5 15. 12 4 21. {0, 6, 7, 2, 4} 15 14. 20 fathoms below the surface 20 12. a $75 deposit 10. a loss of 15 pounds 8. a gain of 6 hours 6 6. 7 inches below normal 7 Replace each with , , or to make a true sentence. 13. 1 mile above sea level 11. a $35 withdrawal 35 9. 2° above zero 7. $5 off the original price 5 12 4. an 8-yard gain 8 3. a 6-yard loss 6 5. 12 centimeters longer 2. 10 strokes above par 10 7NS2.5 1. 3 strokes below par 3 Write an integer for each situation. 1-3 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Integers and Absolute Value Practice 5. 12 10 8. 0 8 4. 4 4 7. 6 7 18. |19||8| 27 15. |15| 19. |12||4| 8 16. |0| 0 39 24. |n| 4 3 21. n |p| 2 25. 9|m| 14 4 22. k |p| 9 Chapter 1 ⫺5 5 0 5 5 5 10 5 15 5 20 25 Glencoe California Mathematics, Grade 7 26. On which day was it the coldest at noon? Tuesday 27. On which day was it the warmest at noon? Friday 28. The temperature at noon on Saturday was 25 warmer than the temperature on Tuesday. What was the temperature on Saturday? Justify your answer using a number line. 20 During a five-day cold spell, Jose recorded the temperature each day at noon. The temperature was 3F on Monday, 5F on Tuesday, 4F on Wednesday, 1F on Thursday, and 0F on Friday. TEMPERATURE For Exercises 26 and 28, use the following information. 23. 5|n| k 20. |m| 6 8 Evaluate each expression if k 4, m 2, n 7, and p 5. 17. |1||3| 4 14. |19| 19 Evaluate each expression. {9, 7, 3, 1, 0, 1} 13. {0, 9, 3, 7, 1, 1} 12. {2, 4, 6, 8, 10, 12} {12, 10, 6, 4, 2} 11. {1, 2, 3, 4} {3, 1, 2, 4} 9. 10 10 6. 5 6 3. 1 7 7NS2.5 10. {5, 7, 0, 5, 7} {7, 5, 0, 5, 7} 15 Order each set of integers from least to greatest. 2. 5 3 1. 0 8 Replace each with , , or to make a true sentence. 1-3 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-3) Lesson 1–3 Chapter 1 Integers and Absolute Value Word Problem Practice Pressel, Morgan Ochoa, Lorena 5 1 Kane, Lorie Kerr, Cristie A10 Chapter 1 Glencoe California Mathematics, Grade 7 0 6 1 1 Glencoe California Mathematics, Grade 7 Mariana Trench 6. OCEAN TRENCHES The elevation of the Puerto Rican Trench in the Atlantic Ocean is 8,605 meters, the elevation of the Mariana Trench in the Pacific Ocean is 10,924 meters, and the elevation of the Java Trench in the Indian Ocean is 7,125 meters. Which trench has the the lowest elevation? Tuesday: 23; Wednesday: 67 4. STOCK MARKET Your stock loses 53 points on Monday and 23 points on Tuesday, but gains 67 points on Wednesday. Write an integer for each day's change. Monday: 53; Birdie Kim Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 5. SOLAR SYSTEM The average temperature of Saturn is 218°F, while the average temperature of Jupiter is 162°F. Which planet has the lower average temperature? Saturn New York: 74; Tokyo: 140 3. LONGITUDE London, England, is located at 0° longitude. Write integers for the locations of New York City whose longitude is 74° west and Tokyo whose longitude is 140° east. Assume that east is the positive direction. 2, 1, 1, 0, 0, 1, 1, 1, 5, 6 26 Lang, Brittany 1 Jo, Young 2 Score 7NS2.5 2. Who had the lowest score? Kung, Candie 1 Icher, Karine 1. Order the scores in the table from least to greatest. Kim, Birdie Player 0 Score Gulbis, Natalie Player their scores in Round 3 of the 2005 60th U.S. Women’s Open. GOLF For Exercises 1 and 2, use the table that lists ten players and 1-3 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment 7AF1.3 or or no bicycles no parking 11. 8. no U turn no smoking 12. 9. no littering no left turn Chapter 1 27 Glencoe California Mathematics, Grade 7 13. Create three different “no” signs of your own. Signs will vary. 10. 7. What does each of these signs mean? 6. ____ means the same as . 4. For any nonzero integer n, n ____ n. 2. |4| ____ |4| 5. A number x is either greater than 0 or less than 0. So, x ____ 0. 3. For any number x, |x| ____ x. 1. 2 ____ 0 Which of the symbols, , , and will make the statement true? Some problems have more than one correct answer. Many symbols and signs use a slash mark such as /, \, or | to mean is not or no. For example, the symbol means is not equal to. When You Want to Be Negative 1-3 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-3) Lesson 1–3 Chapter 1 Absolute Value TI-83/84 Plus Activity A11 (–) 1 (–) ) 1 (–) So, |5| |14| 9. MATH 5. ⏐7⏐ 4. ⏐10⏐ MATH Chapter 1 3 28 17. ⏐11⏐ ⏐8⏐ 12 9 16. ⏐3⏐ ⏐9⏐ 8 14. ⏐14⏐ ⏐5⏐ 2 11. ⏐7 9⏐ 7 8. ⏐15 8⏐ 17 ENTER 13. ⏐7⏐ ⏐15⏐ 5 10. ⏐1 4⏐ 10 7. ⏐6 4⏐ 7 8 4 10 2. ⏐8⏐ ) 1. ⏐4⏐ 5 ) ENTER — 3 + 8 17 Simplify |5| |14|. Enter: Exercises Simplify. MATH So, |3 8| 5. Example 3 1 Simplify |3 8|. Enter: Example 2 So, |17| 17. MATH Simplify |17|. Enter: Example 1 1 14 5 9 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 1 18. ⏐6⏐ ⏐7⏐ 20 15. ⏐8⏐ ⏐12⏐ 7 11 9. ⏐3 14⏐ 25 6. ⏐25⏐ 12 3. ⏐12⏐ ENTER 12. ⏐2 (5)⏐ ) A graphing calculator can be used to evaluate problems containing absolute value. The absolute value function on the TI-83/84 Plus is found in the MATH (NUM) menu. 1-3 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Adding Integers Lesson Reading Guide 7. 23, 16 23 5. 3, 5 5 add; same sign 11. 23 (16) subtract; different signs 9. 3 5 85 68 26. 97 (165) 39 22. 43 4 10 18. 6 (4) 19 124 27. 49 (75) 23. 11 (30) 15 19. 7 8 15. 23 (16) negative; 39 13. 3 5 positive; 2 Chapter 1 long a tape has been rewound. 29 Glencoe California Mathematics, Grade 7 28. You have seen what a negative number means in terms of weather or money. Describe what a negative number means on a video cassette recorder. Sample answer: A negative number shows for how Remember What You Learned 144 51 25. 39 124 24. 81 (63) 8 21. 34 (17) 1 17. 3 4 20. 25 (17) 1 16. 3 (4) Add. 14. 9 (12) negative; 3 12. 4 8 positive; 12 Determine whether the sum is positive or negative. Then find the sum. subtract; different signs 10. 9 (12) add; same sign 8. 4 8 Determine whether you add or subtract the absolute values of the numbers to find the sum. Give a reason for your answer. 6. 9, 12 12 4. 4, 8 8 Identify the number with the greater absolute value. addend; 2,600: addend; 13,200: sum 7NS1.2, 7AF1.3 3. Look at your answer for Exercise 2. Identify each number in the addition sentence as either an addend or a sum. 3,200: addend; 7,400: Read the Lesson 3,200 (7,400) (2,600) 13,200 2. Write an addition sentence that describes this situation. 13,200 1. Write an integer that describes the game show host’s statement. Read the introduction at the top of page 41 in your textbook. Write your answers below. Get Ready for the Lesson 1-4 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lessons 1-3 and 1-4) Lesson 1–4 Chapter 1 Adding Integers Study Guide and Intervention 7NS1.2, 7AF1.3 A12 1 Chapter 1 18. |x y| 1 8 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 20. x |y| 7 17. y 2 1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 30 19. |x| y 1 16. x (6) 2 Evaluate each expression if x 4 and y 3. 15. 11 y 33 12. 13 (8) (12) 14. 17 31 (14) 26 26 11. 3 10 (6) 13. 3 (10) (16) 11 12 9 10. 5 (4) 8 9. 74 36 38 8. 61 (39) 100 7. 55 81 26 1 6. 39 (38) 5. 45 35 10 4. 23 (15) 38 8 2. 10 (10) 20 3. 18 (26) Subtract |12| from |16|. The sum is negative because |16| |12|. Find 16 12. 1. 9 16 25 Add. Exercises 16 12 4 Example 2 To add integers with different signs, subtract their absolute values. The sum has the same sign as the integer with the greater absolute value. Add |3| |4|. Both numbers are negative, so the sum is negative. Find 3 (4). 3 (4) 7 Example 1 To add integers with the same sign, add their absolute values. The sum has the same sign as the integers. 1-4 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 1 22. |a| b 3 31 23. |a| |c| 17 20. b 8 4 Glencoe California Mathematics, Grade 7 24. |b c| 4 21. 6 c 2 18. 23 (18) 41 (17) 17 16. 35 (31) (39) 105 Evaluate each expression if a 9, b 12, and c 8. 19. 3 a 6 66 24 12. 86 77 9 9. 15 (51) 6. 11 (13) 3. 8 9 1 7NS1.2, 7AF1.3 14. 16 (5) 12 9 11. 53 (28) 25 8. 44 (26) 18 5. 27 18 9 17. 8 (12) 15 (13) 2 15. 2 17 (12) 3 13. 10 (4) 6 12 10. (17) (13) 30 7. 44 26 18 4. 12 (3) 9 2. 4 7 11 Adding Integers Skills Practice 1. 2 (3) 5 Add. 1-4 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-4) Lesson 1–4 Chapter 1 Adding Integers Practice 16 9 44 335 220 Pittsburgh, Pennsylvania Rochester, New York A13 8 18 67 30 Change as of 2005 (thousands) Overall, you moved 6 spaces forward. Chapter 1 32 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 30 80; 50; Mrs. Brown's office is 50 feet above street level. 21. ELEVATOR Mrs. Brown parked in the parking garage 30 feet below street level. She then got in an elevator and went up 80 feet to her office. temperature is 8F below zero. 20. WEATHER Before you went to sleep last night, the temperature was 3F. During the night the temperature dropped by 5. 3 (5); 8; The campsite is 156 feet below sea level. 19. CAMPING While hiking down into a canyon, Manuel passed a sign stating that the elevation was 100 feet below sea level. He descended another 56 feet before reaching his campsite. 100 (56); 156; The 18. GAMES On one turn, you move 10 spaces forward around the game board. On the next turn, you move 4 spaces backward. 10 (4); 6; Write an addition expression to describe each situation. Then find each sum and explain its meaning. 17. What was the total population change for these four cities? 11 Las Vegas: 545; Pittsburgh: 317; Rochester: 212 16. What is the population of each of these cities as of 2005? Boston: 559; Source: U.S. Census Bureau 478 2000 Population (thousands) 589 Las Vegas, Nevada Boston, Massachusetts City POPULATION For Exercises 16 and 17, use the table below that shows the change in population for four cities between 2000 and 2005. 4 22 14. 8 (7) (8) (9) 15. 15 10 (16) 12 8 12. 13 (13) (18) 9. 29 (25) 54 13. 5 8 (1) (6) 8. 33 55 22 7. 46 27 19 6. 5 (26) 31 11. 15 (17) 10 5. 12 10 2 4. 14 (14) 28 3. 19 (7) 12 7NS1.2, 7AF1.3 10. 6 14 (12) 2. 13 15 28 1. 1 (8) 9 Find each sum. 1-4 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 1 1,500 525 (350); 1,325 5. OCEANOGRAPHY A research team aboard an underwater research vessel descends 1,500 feet beneath the surface of the water. They then rise 525 feet and descend again 350 feet. Write an addition expression to represent this situation. Then find the sum. 12 3. GOLF In 2005, Tiger Woods won the Masters Tournament. His scores were 2, 6, 7, and 1 for four rounds. Write an addition expression that represents his final score. Then find the sum. 2 (6) (7) (1); 5 (8); 13 Adding Integers 33 Glencoe California Mathematics, Grade 7 156 (4) 2 (5) (3); 146 6. SPORTS Peter weighs 156 pounds, but he would like to wrestle in a lower weight class. He loses 4 pounds one week, gains back 2 pounds the next week, loses 5 pounds the third week, and loses 3 pounds the fourth week. Write an addition expression to represent this situation. Then find the sum. 30 (6) (3) 24 (8); 37 4. INVENTORY A local bookstore has 30 copies of a bestseller when it opens Monday morning. On Monday, it sells 6 copies of the book. On Tuesday, it sells 3 copies. On Wednesday, it receives a shipment containing 24 copies of the book and also sells 8 copies. Write an addition expression that represents the number of copies of the book that store has at the end of the day on Wednesday. Then find the sum. 3 12; 9 7NS1.2, 7AF1.3 2. ELEVATOR You park in a garage 3 floors below ground level. Then you get in the elevator and go up 12 floors. Write an addition expression to represent this situation. Then find the sum. Word Problem Practice 1. FOOTBALL A football team loses 5 yards on one play and then loses 8 yards on the next play. Write an addition expression that represents the change in position of the team for the two plays. Then find the sum. 1-4 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-4) Lesson 1–4 Chapter 1 Enrichment 7NS1.2 30 125 1 62 130 82 25 40 5 6 7 8 A14 Chapter 1 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 34 Micah: 425; Juanita: 276; Taylor: 350 6. What was each player’s final score at the end of the game? 5. Who won the game? Micah; 425 4. Who was in second place after round 7? How many points did this player have? Taylor; 362 Micah: 410; Juanita: 146; Taylor: 315 3. What was each player’s score after round 6? 2. Who had the lowest score after round 5? What was his or her score at this point in the game? Juanita; 161 1. Who had the highest total score after round 3? How many points did this player have? Micah; 182 Refer to the table above to answer the following questions. 12 47 110 37 15 146 4 0 20 5 0 3 0 95 54 105 72 15 2 68 Micah Juanita Taylor Hand Listed below are the scores for a game of cards in which the highest score wins. The three players recorded their scores for each hand, but did not total the scores until they were done playing. Adding Integers 1-4 NAME ________________________________________ DATE ______________ PERIOD _____ Subtracting Integers Lesson Reading Guide 7NS1.2 7 b. 6 4; 6 (4) 10; 10 273 21. 139 134 362 22. 97 (265) 45 18. 41 4 18 23. 59 (77) 57 19. 31 (26) 14. 7 (3) 4 15. 6 8 2 11. 5 (16) 5 16; 11 9. 3 8 3 (8); 11 Chapter 1 35 Glencoe California Mathematics, Grade 7 addend may be undone by subtracting the second addend from the sum. 25. Subtraction and addition are often referred to as opposite operations. Explain in your own words the relationship between addition and subtraction. Sample answer: The addition of a second addend to a first Remember What You Learned subtraction sign to an addition sign, change the number to the right of the subtraction sign to its opposite, and then add. 24. Describe the method for subtracting integers. Sample answer: Change the 48 20. 81 (33) 12 17. 24 (12) 16. 23 (17) 40 13. 3 5 8 12. 3 (5) 8 Subtract. 10. 10 (12) 10 12; 22 8. 2 9 2 (9); 7 Rewrite each difference as a sum. Then find the sum. 7. How is the opposite of a number different from the additive inverse of the number? There is no difference. 6. Find the additive inverse of 7. 7 5. Find the opposite of 7. Read the Lesson a. 1 5; 1 (5) 4; 4 4. Use algebra tiles to find each difference and sum. Compare the results in each group. The results are the same in each group. 3. How does this result compare to 4 (2)? The results are both 6. 2. Use algebra tiles to find 4 2. 6 The results are both 2. 1. How does this result compare with the result of 3 (5)? Complete the Mini Lab at the top of page 46 in your textbook. Write your answers below. Get Ready for the Lesson 1-5 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lessons 1-4 and 1-5) Lesson 1–5 Chapter 1 Subtracting Integers Study Guide and Intervention A15 8. 21 16 37 7. 9 16 7 36 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 18. c b a 15 17. b a c 1 16. c b 8 Chapter 1 15. a c 12 10 14. 20 b 23 12. 19 |29| 9. 28 37 9 6. 16 9 7 3. 10 8 18 7NS1.2 13. a 8 15 Evaluate each expression if a 7, b 3, and c 5. 11. 65 (6) 71 5. 23 (28) 5 4. 15 (12) 3 10. 34 (46) 12 2. 5 (2) 7 1. 3 4 7 Subtract. Exercises To subtract 22, add 22. Add. Find 13 (22). 13 (22) 13 22 35 Example 2 To subtract 15, add 15. Add. Find 8 15. 8 15 8 (15) 7 Example 1 To subtract an integer, add its opposite or additive inverse. 1-5 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 17. |10| |7| 3 14. 33 (68) 35 11. 38 (39) 77 8. 21 (23) 44 5. 13 (25) 12 11 Chapter 1 25. m k 15 22. k m 15 19. k 19 37 26. k m 16 31 23. p m 3 20. 19 m 26 9. 34 (11) 18. |52| 49 3 15. 76 18 58 23 6. 14 (19) 33 3. 9 9 18 7NS1.2 12. 72 27 45 25 Glencoe California Mathematics, Grade 7 27. k m p 24. m 3 10 21. p 11 21 Evaluate each expression if k 8, m 7, and p 10. 16. 4 |6| 2 13. 36 47 83 10. 56 94 38 7. 25 15 40 4. 17 18 35 2. 12 8 4 Subtracting Integers Skills Practice 1. 6 7 1 Subtract. 1-5 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-5) Lesson 1–5 Chapter 1 A16 12. 10 (5) 5 6,960 Chapter 1 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 3 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 38 27. [15 (7)] (8 11) 25. [22 (18)] (5 11) 34 24. 25 [16 (9)] 18 26. (5 9) (20 12) 23. 10 [8 (16)] 2 Source: www.worldoffacts.com 6,194 42 28 Europe 86 5,642 12 Australia South America 2,228 400 Asia North America 8,850 156 Africa 22. 29 (4) (15) 48 36 21. Find the difference between the lowest point in South America and the lowest point in Africa. 114 m 20. How far below the highest point in North America is the lowest point in Asia? 6,594 m 19. How far below the highest point in Australia is the lowest point in Australia? 2,240 m Highest Point (m) 5,895 Lowest Point (m) Continent 18. g d f 22 17. d f g 8 16. d f 3 GEOGRAPHY For Exercises 1921, use the table that shows the elevations above sea level of the lowest and highest points on six continents. 15. d g 15 14. g 15 4 13. d 10 14 Evaluate each expression if d 4, f 7, and g 11. 11. 12 19 7 9. 8 (22) 30 8. 19 (13) 6 7. 14 (18) 4 10. 1 15 16 6. 8 (9) 1 5. 18 (7) 25 3. 8 9 17 4. 4 (12) 16 Subtracting Integers 2. 3 12 9 Simplify. 1-5 Subtracting Integers Chapter 1 5. WATER The boiling point of water is 212°F, while 460°F is its absolute lowest temperature. Find the difference between these two temperatures. 672°F 3. TEMPERATURE The highest recorded temperature on Earth was recorded in Africa at 136°F, while the lowest was 129°F in Antarctica. What is the range of temperatures recorded on Earth? 265°F 1. Find the difference in elevation between the top of Mt. McKinley and and the top of Mt. Everest. 8,715 ft Death Valley 39 29,035 $5 Glencoe California Mathematics, Grade 7 6. STOCK MARKET During the course of one day, the price of a stock fluctuated between a high of $3 above the previous day’s closing price and a low of $2 below the previous day’s closing price. What was the difference between the high and low prices for that day? 4. WEATHER If the overnight temperature at the Arctic Circle was 14°F, but the temperature rose to 8°F during the day, what was the difference between these high and low temperatures? 22°F 2. Find the difference in elevation between Death Valley and the Dead Sea. 1,066 ft 282 1,348 28,232 Mt. Everest Dead Sea 20,320 Puerto Rican Trench Elevation (feet) Mt. McKinley Place elevations of several places on Earth. GEOGRAPHY For Exercises 1 and 2, use the table. The table shows the 7NS1.2 Word Problem Practice 7NS1.2 Practice 1. 15 7 8 Subtract. 1-5 NAME ________________________________________ DATE ______________ PERIOD _____ NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-5) Lesson 1–5 Chapter 1 7 6 5 4 A17 X 7 6 5 4 7 6 5 4 2 1 0 2 Y 1 3 2 1 |5 (5)| 10 3 0 0 |(7) (1)| 6 3 |(4) 2| 6 1 1 1 2 2 2 G 3 3 3 4 4 4 5 A 5 5 6 6 6 7 6 5 4 3 2 1 0 1 2 3 M 4 5 7 Chapter 1 8 6 5 4 3 2 1 y1 40 0 1 2 8 4 5 6 6 7 7 7 7 8 8 8 8 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 3 y2 5. Graph the two solutions to the equation |y 2| 3. Call the points y1 and y2. 8 N 4. Graph two points, M and N, that are each 5 units from 2. Make M N. Use the number lines to solve the problems. 8 B 3. A at 5 and B at 5 8 2. X at 7 and Y at 1 8 H 1. H at 4 and G at 2 Graph each pair of points on the number line. Then write an expression using absolute value to find the distance between the points. 7 Multiplying and Dividing Integers Lesson Reading Guide 7NS1.2, 7AF1.3 negative 7. The quotient of two integers with different signs is __________ . negative; 8 Chapter 1 41 Glencoe California Mathematics, Grade 7 divide by the number of numbers in the set; average. 17. Explain how to find the mean of a set of numbers. What is another name for the mean? Sample answer: Find the sum of the numbers and then Remember What You Learned 8 64 16. 21 15. positive; 7 14. 35 (7) positive; 5 13. 12 (4) negative; 3 3 12. 6(7) positive; 42 10. 3 5 negative; 15 11. 9(2) negative; 18 9. 4 8 positive; 32 Determine whether each product or quotient is positive or negative. Then evaluate the expression. positive positive 6. The product of two integers with the same signs is __________ . 8. The quotient of two integers with the same signs is __________ . negative 5. The product of two integers with different signs is __________ . Complete each sentence with either positive or negative. 4. Identify each number in the multiplication sentence 3(120) 360 as either a factor or a product. 3: factor; 120: factor; 360: product Read the Lesson 10(120); 1,200 3. Write a multiplication sentence that could be used to find the submersible’s depth after 10 minutes. Then find the product. three times. 2. Write a multiplication sentence that could be used to find this same depth. Explain your reasoning. 3(120); you are adding 120 answers: 240 (120) or 120 (120) (120); 360 1. Write two different addition sentences that could be used to find the submersible’s depth after 3 minutes. Then find their sums. Sample Read the introduction at the top of page 51 in your textbook. Write your answers below. 1-6 Get Ready for the Lesson 7NS2.5 The absolute value of the difference between two integers can be interpreted as the distance between two points on a number line. That is, if point A has a as a coordinate and point B has b as a coordinate, then |a b| is the distance between points A and B. Enrichment NAME ________________________________________ DATE ______________ PERIOD _____ Distance on the Number Line 1-5 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Answers (Lessons 1-5 and 1-6) Lesson 1–6 Chapter 1 Multiplying and Dividing Integers Study Guide and Intervention 7NS1.2, 7AF1.3 A18 15 75 10. 5 6. 25 5 5 11. 6(3)(5) 90 7. 48 4 12 3. 9(4) 36 Chapter 1 13. 3c b 17 Glencoe California Mathematics, Grade 7 42 96 1 11 Glencoe California Mathematics, Grade 7 a6 16. c 13 143 12. 8. 63 (7) 9 4. 12(8) Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 14. a(b c) 3 15. c2 5b 29 Evaluate each expression if a 1, b 4, and c 7. 9. (4)2 16 5. 33 (3) 11 1. 8(8) 64 2. 3(7) 21 The dividend and divisor have the same sign. The quotient is positive. Find 54 (6). The dividend and divisor have different signs. The quotient is negative. Find 15 (3). The factors have the same sign. The product is positive. Find 5(6). The factors have different signs. The product is negative. Find 7(4). Multiply or divide. Exercises 54 (6) 9 Example 4 15 (3) 5 Example 3 5(6) 30 Example 2 7(4) 28 Example 1 Use the following rules to determine whether the product or quotient of two integers is positive or negative. • The product of two integers with different signs is negative. • The product of two integers with the same sign is positive. • The quotient of two integers with different signs is negative. • The quotient of two integers with the same sign is positive. 1-6 NAME ________________________________________ DATE ______________ PERIOD _____ 3 16 48 22. 8 18. 40 (5) 12 14. 1(3)(4) 100 10. (10)2 3 19 57 23. 9 19. 63 (7) 1,000 15. (10)3 144 11. 6(8)(3) 45 7. 15(3) 8 3. 4(2) Chapter 1 ab 29. c 2 25. abc 60 b 2a c 30. 2 26. 2b c 4 43 31. b2 5a a 2b c 27. 5 32. (c)2 36 28. ab c 4 15 75 24. 19 20. 76 4 84 16. 3(4)(7) 64 12. (4)3 91 8. 7(13) 35 4. 5 7 7NS1.2, 7AF1.3 Glencoe California Mathematics, Grade 7 35 8 Evaluate each expression if a 2, b 5, and c 6. 14 4 56 21. 5 17. 15 3 Divide. 81 13. (9)2 70 9. 5(2)(7) 72 132 6. 11 12 5. 9(8) 6 2. 3(3) 9 Multiplying and Dividing Integers Skills Practice 1. 2 3 Multiply. 1-6 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-6) Lesson 1–6 Chapter 1 56 11. 8 7 A19 17. r2 16 32 42 16. 14 rt 122 12 27. 12 24. 3(5)2 75 4 12 28. 6 8 Chapter 1 44 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 30. WEATHER During a six hour period, the temperature dropped 18F. Find the average hourly change in the temperature. 3F 29. MONEY If you have $216 and you spend $12 each day, how long would it be until you had no money left? 18 days 10(15) 26. 25 6 23. (3)2 (4)2 144 25. 5(2)(4)(3) 120 22. 22, 19, 14, 17, 18 18 21. 5, 4, 8, 12, 10 1 Find each product or quotient. 20. 11, 15, 16, 17, 20, 18, 22 9 18. (2t 4)2 4 25 5s 15. 5 t4 80 12. 16 5 9. 48 (6) 8 6. 2(5)(3) 30 3. 8(9) 72 7NS1.2, 7AF1.3 19. 8, 5, 3, 9, 5, 2 2 Find the mean of each set of integers. 14. 10 rt 18 13. s + 5t 24 Evaluate each expression if r 4, s 11, and t 7. 66 10. 11 6 7. 14 2 7 8. 35 (7) 5 5. (7)2 49 4. 4(12) 48 Divide. 2. 3 12 36 Multiplying and Dividing Integers Practice 1. 5(7) 35 Multiply. 1-6 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 14 F Chapter 1 6 yr 45 7. DEPRECIATION The value of a piece of office equipment is changing at a rate of $175 per year. How long will it take for the change in value to be $1,050? 7h 5. WEATHER On a certain day, the temperature changed at a rate of 2ºF per hour. How long did it take for the change in temperature to be 14ºF? G 10 20 30 40 50 40 30 20 10 G 3. FOOTBALL A football team lost 9 yards on each of three consecutive plays. What was the team’s total change in position for the three plays? 27 yd Glencoe California Mathematics, Grade 7 8. POPULATION The population of a small town is changing at a rate of 255 people per year. How long will it take for the change in population to be 2,040 people? 8 yr 6. GEOLOGY The length of an island is changing at the rate of 17 inches per year. How long will it take for the change in the length of the island to be 255 inches? 15 years 2,400 ft 4. HIKING A group of hikers is descending a mountain at a rate of 400 feet per hour. What is the change in the elevation of the hikers after 6 hours? 15 in. 7NS1.2, 7AF1.3 2. EVAPORATION The height of the water in a tank decreases 3 inches each week due to evaporation. What is the change in the height of the water over a fiveweek period due to evaporation? Multiplying and Dividing Integers Word Problem Practice 1. STOCK MARKET The price of a stock decreased $2 per day for four consecutive days. What was the total change in value of the stock over the four-day period? $8 1-6 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-6) Lesson 1–6 Chapter 1 Enrichment 7NS1.2, 7AF1.3 2 6. 609 1,218 5. 57 114 A20 18. 364 182 17. 116 58 16. 54 27 30. 57 40 57 2 2 10 32. 93 125 93 1,000 2 2 2 46 29. 472 50 472 100 2 31. 138 25 138 100 2 2 Chapter 1 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Glencoe California Mathematics, Grade 7 28. 613 5 613 10 2 27. 256 20 256 10 2 Transform each product into an expression that uses doubling or halving. Change only the second factor. 26. 20 317 6,340 25. 20 361 7,220 24. 20 93 1,860 4,360 23. 5 (872) 22. 5 234 1,170 21. 5 126 630 Compute mentally. 15. 38 19 14. 56 28 13. 72 36 12. 1,484 742 8. 6,523 13,046 4. 2,512 5,024 19. 5,296 2,648 20. 7,436 3,718 11. 690 345 7. 383 766 3. 48 96 10. 468 234 9. 64 32 Halve each number. Use mental math. 2. 214 428 1. 13 26 Double each number. Use mental math. 2 10 1 5 ; 5 10 ; 87 5 87 10 2 870 2 435 Most numbers are easy to double or halve mentally. And, many types of multiplication problems can be done mentally by using doubling and halving. In working problems of this type, it is helpful to remember that 5 equals 10 divided by 2. And, dividing by 2 is the same as multiplying by one-half. So, multiplying by 5 is the same as first multiplying by 10 and then halving. Doubles and Halves 1-6 NAME ________________________________________ DATE ______________ PERIOD _____ Calculating with Integers TI-83/84 Plus Activity (–) 10 (–) 24 (–) ENTER 4 8 (–) 4 — (–) 1 ENTER 3 So, g t 3 when g 4 and t 1. Enter: 16 8. 36 (11) 47 5. 48 (3) 2. 4 (11) 7 0 Chapter 1 19. x (z) 4 16. x y 1 13. 0 y 10. 15 x 11 47 20. x y (2) 10 17. y z 5 14. z (6) 7 11. y (4) 1 Evaluate each expression if x 4, y 5, and z 1. 7. 12 (11) 132 4. 6 12 6 1. 8 16 8 3 ENTER Evaluate g t if g 4 and t 1. So, 24 (3) 8. Enter: Find 24 (3). So, 6 (10) 5 (4). Enter: 6 + Find 6 (10). Perform the indicated operation. Exercises Example 3 Example 2 Example 1 28 Glencoe California Mathematics, Grade 7 21. x y z 20 18. x y z 9 15. 14 (z) 14 12. 10 z 10 9. 84 (3) 6. 3 (9) 6 3. 5 17 85 You can solve problems involving integers on a graphing calculator. When a number is positive, you do not need to enter a sign. But when a number is negative, use the (–) key before you enter the number. 1-6 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-6) 1–6 Lesson X–6 Chapter 1 Writing Equations Lesson Reading Guide 7AF1.1, 7AF1.4 A21 Writing Equations Study Guide and Intervention 4n a number divided by 3 the quotient of z and 3 the ratio of z and 3 Chapter 1 48 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 sentence is translated as an equation with the verb representing . 12. Devise your own way to determine how a verbal description should be translated as an algebraic equation. Sample answer: A complete Remember What You Learned division 11. Find the ratio of the amount of gasoline used and the distance traveled. 10. Find the high temperature on Wednesday if this temperature is 3º less than the high temperature on Tuesday. subtraction 9. Find the product of the price of a calculator and the number of students in the class. multiplication addition 8. Find the flight time after the time has been increased by 15 minutes. 6. the difference of 32 and x Chapter 1 49 12. 5 shirts at $d each is $105.65. 5d 105.65 32 x Glencoe California Mathematics, Grade 7 11. The original price decreased by $5 is $34. p 5 34 x 7 10. The quotient of x and 7 is equal to 13. 13 9. The sum of r and 45 is 79. r 45 79 8. The product of 7 and b is equal to 63. 7b 63 7. 5 more than a number is 6. n 5 6 Write each verbal sentence as an algebraic equation. 5. 14 less than f f 14 4. p increased by 10 p 10 3. the product of 5 and b 5b addition 7. Find how much an executive spent on breakfast, lunch, and dinner. g 15 2. the quotient of g and 15 n 9 45 Equation 1. the sum of 8 and t 8 t Write each verbal phrase as an algebraic expression. Exercises Sentences 9 less than a number is equal to 45. The difference of a number and 9 is 45. A number decreased by 9 is 45. 45 is equal to a number minus 9. z 3 Expression r6 Phrases Expression Phrases the difference of r and 6 6 subtracted from a number 6 less than a number r minus 6 7AF1.1, 7AF1.4 The table shows several verbal sentences that represent the same equation. 4 multiplied by n 4 times a number the product of 4 and n Expression x8 Phrases Expression Phrases 8 more than a number the sum of 8 and a number x plus 8 x increased by 8 The table shows several verbal phrases for each algebraic expression. 1-7 NAME ________________________________________ DATE ______________ PERIOD _____ 6. Find the price of an airline ticket after the price has been decreased by $50. subtraction 5. Find the cost per person when the price of a pizza is split among several people. division 4. Find the difference between the cost of a gallon of premium gasoline and the cost of a gallon of regular gasoline. subtraction Look at the steps for writing an algebraic equation on page 57. Then determine whether each situation requires addition, subtraction, multiplication, or division. Read the Lesson number of guest times $8 per guest is a party cost of $120. 3. What does the equation g 8 120 represent in this situation? The 8 g or 8g 2. Write an expression representing the cost of a party with g guests. 1. What is the relationship between the number of guests and the cost of the party? The cost is equal to 8 times the number of guests. Read the introduction at the top of page 57 in your textbook. Write your answers below. Get Ready for the Lesson 1-7 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Answers (Lesson 1-7) Lesson 1-7 Chapter 1 Writing Equations Skills Practice 4. the difference of t and 1 t 1 3. the product of 10 and c 10c 25s 12. 25 times the number of students s 75 A22 Chapter 1 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 50 24. Carla’s height plus 4 inches is 68 inches. h 4 68 23. The cost of 10 books at $d each is $159.50. 10d 159.50 22. The total area decreased by 75 square feet is 250 square feet. a 75 250 21. 65 is 5 times a number. 65 5n 20. The total of Joshua’s savings and $350 is $925. s 350 925 19. The number of members divided by 6 is 15. 15 m 6 18. 17 more than some number is equal to 85. n 17 85 17. $12 less than the original price is $48. p 12 48 16. The quotient of z and 10 is equal to 32. 32 z 10 15. The difference of 100 and x is 57. 100 x 57 14. The product of 6 and m is 216. 6m 216 13. The sum of a number and 16 is equal to 45. n 16 45 Write each verbal sentence as an algebraic equation. e2 11. 2 hours more than the estimate p 500 10. the total of Ben’s score and 75 8. the height decreased by 2 inches h 2 7. the cost of 7 CDs at $d each 7d 9. $500 less than the sticker price 6. the cost split among 4 people 5. the score increased by 8 points p 8 c 4 2. the sum of d and 7 d7 7AF1.1, 7AF1.4 1. a number divided by 5 n 5 Write each verbal phrase as an algebraic expression. 1-7 NAME ________________________________________ DATE ______________ PERIOD _____ Writing Equations Practice 7AF1.1, 7AF1.4 n 4 3 15 5 p 2,000 3,000 4,000 2 3 4 g 1,000k g 1,000 1 k Grams, g Kilograms, k 9. Chapter 1 a 3h 51 10. MONEY Carlotta earns $3 for every hour that she baby sits. Complete the table of values showing the amount she earns for baby sitting 1, 2, 3, 4, and h hours. Given h, a number of hours, write an equation to find a, the amount that Carlotta earns. 8. 3 4 9 12 3 6 9 12 3h Amount, a Glencoe California Mathematics, Grade 7 1 2 3 4 h Hours, h f y 3 2 6 y 1 3 f Yards, y Feet, f Write an equation to model the relationship between the quantities in each table. p 15 p number of plays; 5 or 7. FOOTBALL A team had a total gain of 15 yards over several plays with an average gain of 5 yards per play. How many plays are represented? 6. GEOMETRY A rectangle's width is one-third its length. If the width is 8 1 inches, what is the length of the rectangle? length; 8 score; m 6 88 5. GRADES Kelly’s test score was 6 points higher than Michelle’s. If Kelly’s test score was 88, what was Michelle’s test score? m Michelle’s test Define a variable. Then write an equation that could be used to solve each problem. b 6 4. When the bananas were divided evenly among the 6 monkeys, each monkey received 4 bananas. b the total number of bananas; 3. A class of 30 students separated into equal sized teams results in 5 30 students per team. n the number of teams; 5 m Michael’s age, m 3 14 Latisha had before her birthday; m 25 115 2. At 14 years old, Adam is 3 years younger than his brother Michael. 1. After receiving $25 for her birthday, Latisha had $115. m = the money Define a variable. Then write an equation to model each situation. 1-7 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-7) Lesson 1-7 Chapter 1 A23 Chapter 1 p population of Oakland; p 9,477 390,007 52 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 h height of Kings Peak; h 8,667 4,861 8. GEOGRAPHY Kings Peak in Utah is 8,667 feet taller than Spruce Knob in West Virginia. Spruce Knob is 4,861 feet tall. Define a variable and write an equation to find the height of Kings Peak. d distance of Mars from the Sun; 6d 1,429,400,000 7. POPULATION The population of Oakland, California, is 9,477 more than the population of Omaha, Nebraska. Omaha has a population of 390,007. Define a variable and write an equation to find the population of Oakland. b number of San Diego branches; 79 b 44 6. ASTRONOMY Saturn is 6 times farther from the Sun than Mars. Define a variable and write an equation to find the distance of Mars from the Sun if Saturn is about 1,429,400,000 km from the sun. 2 5. LIBRARIES The San Diego Public Library has 44 fewer branches than the Chicago Public Library. Define a variable and write an equation for the number of branches in the San Diego Public Library if Chicago has 79 branches. e the amount of energy Brazil used; 4e 12,000 number of curium; 48 1c 4. CHEMISTRY The atomic number of cadmium is half the atomic number of curium. The atomic number for cadmium is 48. Define a variable and write an equation to find the atomic number of curium. c atomic a Julia’s age; 13 j 3 3. ENERGY One year, China consumed 4 times as much energy as Brazil. Define a variable and write an equation to find the amount of energy Brazil used that year if China used 12,000 kilowatt-hours. v Tennessee’s votes; 23 v 34 7AF1.1, 7AF1.4 2. CIVICS In the 2004 presidential election, Texas had 23 more electoral votes than Tennessee. Define a variable and write an equation to find the number of Tennessee’s electoral votes if Texas had 34 votes. Writing Equations Word Problem Practice 1. AGE Julia is 3 years younger than Kevin. Kevin is 13. Define a variable and write an equation to find Julia’s age. 1-7 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Enrichment 7AF1.1 1 4 2 8 3 12 4 16 5 20 7 28 6 24 8 32 Multiply the previous term by three; 729, 2187, 6561 D. 3, 9, 27, 81, 243, ___, ___, ___ Subtract three from the previous term; 21, 24, 27 B. 3, 6, 9,12, 15, 18, ___, ___, ___ Add to the previous term two more than was added one term before; 49, 64, 81 t 62300 0.1n 5. Sequence E 2. Sequence B t 3n 6. Sequence F t n Chapter 1 t n 10; 110 11. 11, 12, 13, 14, 15, … t 2n 2; 198 9. 0, 2, 4, 6, 8, … t 3n 1; 301 7. 4, 7, 10, 13, 16, … t 0.75n; 75 Glencoe California Mathematics, Grade 7 See students’ work. 12. Write your own sequence rule and find the first 5 terms. 10. 0.75, 1.5, 2.25, 3, 3.75, … t n2 1; 10,001 8. 2, 5, 10, 17, 26, … 53 2 3. Sequence C t 2n 1 Write an equation rule for each of the sequences below. Then use the equation to find the 100th term. 4. Sequence D t 3 n 1. Sequence A t 2n Write an equation rule for each of the sequences in exercises 1–6. Be careful that your rule gives the correct first term. Look again at the beginning example. The rule is multiply the position number by four. If we call the position numbers n, the algebraic expression for the rule is 4n. For each term t 4n. The rule of a sequence can be generalized into an equation so that it is possible to find the 10th term, 100th term, or nth term without writing out of the terms in between. The rule of the sequence shows the relationship between a term and its position number. Divide the previous term by ten; 0.0623, 0.00623, 0.000623 E. 6,230, 623, 62.3, 6.23, 0.623, ___, ___, ___ F. 1, 4, 9, 16, 25, 36, ___, ___, ___ Add two to the previous term; 15, 17, 19 C. 3, 5, 7, 9, 11, 13, ___, ___, ___ Add two to the previous term; 14, 16, 18 A. 2, 4, 6, 8, 10, 12, ___, ___, ___ Pattern 4 4 4 4 Describe the pattern in words and write the next three terms in each of the following sequences. Position Term A sequence can be extended by finding the pattern, describing it, and then applying the description to produce successive terms. To describe the pattern in words, we could write, “Add four to the previous term to find the next term.” Determine the pattern rule for the sequence below. What are the next three terms? Writing Equations to Describe Sequences 1-7 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-7) Lesson 1-7 Chapter 1 7MR1.1, 7NS1.2 Problem-Solving Investigation: Work Backward Study Guide and Intervention • Select a strategy including a possible estimate. • Solve the problem by carrying out your plan. • Examine your answer to see if it seems reasonable. Plan Solve Check A24 Start with $110 for the first week and work forward. On the second week she deposited twice as much money in the bank than on the first week, which is $220. On the third week, she deposited $40 less than the second week, which is $180. On the fourth week she deposited $20 more than on the third week, or $200. This is what you know she deposited on the fourth week. Chapter 1 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 54 Xing is 18 years old; Eliot is 9 years old; Sam is 13 years old. 2. AGE Sam is 4 years older than Eliot. Eliot is 9 years younger than Xing. Xing is 3 years older than Damien. If Damien is 15 years old, how old are each of the other boys? 1. SHOPPING Jack spent a total of $87.58 when he went shopping for camping supplies. He spent $36.89 on food, $23.24 on a sleeping bag, and bought lunch. When he got home, he had $15.70. How much did he spend on lunch? $11.75 Use the work backward strategy to solve each problem. Exercises Check 2 Work backward. Divide by 2. First Week $110 Start with the $200 Mari put in the bank on the fourth week. Solve Third Week Second Week $20 $180 $40 $220 Work This is $40 less Work This is twice as backward. than the second backward. much as the Subtract week. Add $40. first week. $20. Start with the amount she put in the bank on the last week and work backward. Plan Fourth Week $200 This is $20 more than the third week. You know that Mari put $200 in the bank on the fourth week. You need to know how much money she put in the bank on the first week. Explore Mari put money in her savings account each week. She put a certain amount of money in the bank on the first week. On the second week she put twice as much money in the bank as the first week. On the third week, she put $40 less in the bank than on the second week. On the fourth week, she put $20 more in the bank than on the third week. Mari put $200 in the bank on the fourth week. How much money did Mari put in the bank on the first week? Example 1 • Determine what information is given in the problem and what you need to find. Explore You may need to work backward to solve a problems. 1-8 NAME ________________________________________ DATE ______________ PERIOD _____ 7MR1.1, 7NS1.2 Problem-Solving Investigation: Work Backward Skills Practice Arrival Time 10:37 A.M. 1:45 P.M. 3:30 P.M. Chapter 1 55 Glencoe California Mathematics, Grade 7 6. Mrs. Gonzales left her office at 7:25 a.m. She planned that it would take her 30 minutes to get to the airport, but the traffic was so heavy it took an additional 20 minutes. It takes 30 minutes to check her baggage and walk to the boarding gate. What is the first flight she can take to Dallas? Flight 142 5. Charles needs to take Flight 295. He needs 45 minutes to eat breakfast and pack. It takes 25 minutes to get to the airport. To be at the airport 90 minutes early, what is the latest time he can start eating breakfast? 9:20 A.M. Flight Number 253 142 295 Airline Schedule Minneapolis, MN to Dallas, TX Departure Time 8:20 A.M. 11:52 A.M. 12:00 P.M. Use the table to solve each problem. 4. JOGGING Edmund is training for a marathon. He ran a certain number of miles on Monday. On Wednesday, he ran 2 more miles than on Monday. On Saturday, he ran twice as far as on Wednesday. On Sunday, he ran 6 miles less than on Saturday. He ran 8 miles on Sunday. How many miles did Edmund run on Monday? 5 miles 3. NUMBERS Jana is thinking of a number. If she divides her number by 12 and then multiplies the quotient by 8, the result is 520. What number is Jana thinking of? 780 2. SHIPPING An overseas cargo ship was being loaded. At the end of each day, a scale showed the total weight of the ship’s cargo. On Monday, 48 tons of cargo were loaded onto the ship. On Tuesday, three times as much cargo was loaded on to the ship as on Monday. On Wednesday, 68 tons of cargo were loaded onto the ship. On Thursday, 0.75 as much cargo was loaded onto the ship as on Wednesday. On Friday, 120 tons of cargo were loaded onto the ship. At the end of the day on Friday, the scale showed that the ship was carrying 690 tons of cargo. How much cargo was the ship carrying when it first came into port on Monday? 259 tons 1. SKATEBOARDS On Monday, David’s skateboard shop received its first shipment of skateboards. David sold 12 skateboards that day. On Thursday, he sold 9 skateboards. On Friday, he received a shipment of 30 more skateboards and sold 10 skateboards. He then had a total of 32 skateboards in his shop. How many skateboards were delivered on Monday? 33 Use the work backward strategy to solve each problem. 1-8 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-8) Lesson 1-8 Chapter 1 A25 3. BAKING Isabel doubled her recipe for chocolate chip cookies. After her brothers ate 8 cookies, she set aside half of the remaining cookies for a school party. Isabel then gave 2 dozen cookies to her neighbor. She had 12 cookies left over. How many cookies does one recipe make? 40 cookies • Use the four-step plan. • Work backward. Problem-Solving Strategies Use any strategy to solve Exercises 3 and 4. Some strategies are shown below. 2. GRADES Kumiko had an average of 92 on her first three math tests. Her scores on the second and third tests were 97 and 89. What was her score on the first test? 90 1. TRAVEL Rajiv and his family left home on a trip and drove for 2 hours before they stopped to eat. After 1.5 hours, they were back on the road. They arrived at their destination 3 hours later at 5:00 P.M. What time did they leave home? 10:30 A.M. Use the work backward strategy to solve Exercises 1 and 2. Chapter 1 7MR1.1, 7NS1.2 33 min 72 min 255 min 213 min 56 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 Subtract; 1972 1944 28; 88 28 60; 60 years old 6. U.S. PRESIDENTS Harry S Truman was elected president in 1944. He died in 1972 at the age of 88. How old was he at the time he was elected? Subtraction; division; addition; 775 97 678; 678 2 339; 339 97 436; $436 million 5. MOVIES The two animated films with the highest box office receipts brought in a total of $775 million. If one film brought in $97 million more than the other, how much did the film with the highest receipts bring in? For Exercises 5 and 6, select an appropriate operation to solve the problem. Justify your solution and solve the problem. Select the Operation How many more minutes per week do boys spend using the Internet for purposes other than school work than girls? 81 min Boys Girls Gender Time Used for Total Time School Work per Week 4. ANALYZE TABLES The table below gives the results from a poll taken at school about the times in minutes that boys and girls spend using the Internet for school work and the total time spent using the Internet each week. Problem-Solving Investigation: Work Backward Practice Mixed Problem Solving 1-8 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 7MR1.1, 7NS1.2 Problem-Solving Investigation: Work Backward Word Problem Practice Tuesday 20 minutes more than Monday Chapter 1 2 hours and 20 minutes 5. WEATHER On Monday, Eliza read her book. On Tuesday, she read three times as long as she read on Monday. On Wednesday she read 20 minutes less than Tuesday. On Thursday she read for 20 minutes, which was half as long as she read on Wednesday How many minutes did Eliza read over the 4-day period? 17 minutes 3. HOCKEY During a hockey game, Brandon played 7 less minutes than Nick. Zach played 12 minutes more than Brandon. Hunter played twice as long as Zach. Hunter played for 44 minutes. How many minutes did Nick play in the hockey game? 30 minutes 57 Saturday Twice as long as Thursday Sunday 15 minutes less than Saturday– 45 minutes Glencoe California Mathematics, Grade 7 30 stamps 6. STAMPS Zoe added 23 stamps to her collection. Three months later her collection had tripled in number to a total of 159 stamps. How many stamp did Zoe have to start her collection? 4. PACKAGES In the morning, a delivery truck delivers 24 of it packages to a factory. It then goes to a distribution lot, where the remaining packages are separated into 4 equal groups and put on other trucks. There were 18 packages in each of the groups. How many packages were on the delivery truck to begin with? 96 packages 20 minutes 2. How many minutes did Elena practice on Monday? Thursday 10 minutes less than Tuesday 1. How many minutes did Elena practice the clarinet on Thursday? Monday ? record of the amount of time Elena practiced her clarinet in a week. CLARINET PRACTICE For Exercises 1 and 2, use the table at the right. It is a Use the work backward strategy to solve each problem. 1-8 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-8) Lesson 1-8 Chapter 1 ⫽ ⫽ 1 x 1 1. x 1 4 3 4 1 1 1 1 x 3 x 1 ⫽ ⫽ 1 1 1 7 1 1 1 1 ⫺1 ⫺1 x (4) x ⫺1 ⫺1 c. Add 3 to each side. d. Add 5 to each side. _____ d _____ c s 5 14 4 3 p 11 m 33 _____ a A26 Add 7 to each side. 13 Chapter 1 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 58 Chapter 1 13. 62 b 45 17 7. 17 c 41 24 4. x 5 8 1. s 4 12 16 59 14. x 39 65 11. 13 t 29 26 42 8. v 36 25 61 5. b 10 34 24 2. d 2 21 19 9. y 29 51 6. f 22 6 22 16 3. h 6 15 9 Glencoe California Mathematics, Grade 7 15. 56 47 n 9 12. 55 39 k 16 51 25 51 (25) or 76 Replace h with 51. Is this sentence true? Write the original equation. 25 25 0 and 76 25 51. h is by itself. Add 25 to each side. Write the equation. Solve each equation. Check your solution. 10. 19 z 32 51 11. 9 g 14 5 h 25¬ 76 51 25¬ 76 76¬ 76 ✓ Exercises Check 26 19 45 Replace w with 26. Is this sentence true? Write the original equation. Solve h 25 76. Check your solution. w 19¬ 45 26 19¬ 45 45¬ 45 ✓ h 25¬ 76 h 25 25¬ 76 25 h¬ 51 Example 2 Check 19 19 0 and 45 19 26. w is by itself. Subtract 19 from each side. Write the equation. Solve w 19 45. Check your solution. w 19 45 w 19 19 45 19 w 26 Example 1 12. Write two addition and two subtraction equations of your own. Trade your equations with a partner and solve. Explain to each other the method you used to solve the equations. See students’ work. 10. 3 7 r 10 5 ⫺1 ⫺1 ⫺1 6AF1.1 Solving Addition and Subtraction Equations Study Guide and Intervention You can use the following properties to solve addition and subtraction equations. • Addition Property of Equality — If you add the same number to each side of an equation, the two sides remain equal. • Subtraction Property of Equality — If you subtract the same number from each side of an equation, the two sides remain equal. 1-9 NAME ________________________________________ DATE ______________ PERIOD _____ Remember What You Learned 9. z 8 2 6 Solve each equation. Subtract 11 from each side. _________________________ Subtract 3 from each side. 8. 17 11 k _________________________ 7. c 3 9 6. w 7 2 _________________________ For Exercises 6–8, explain how to solve each equation. b. Subtract 6 from each side. _____ b x69 a. Subtract 11 from each side. 5. Match the method of solving with the appropriate equation. Read the Lesson ⫽ ⫽ ⫺1 ⫺1 3. x (4) 5 1 4. Explain how you would find a value of x that makes x (3) 8 true without using models. Subtract 3 from each side. 1 1 2. x 3 7 4 Solve each equation using algebra tiles. Complete the Mini Lab at the top of page 65 in your textbook. Write your answers below. x 6AF1.1 Solving Addition and Subtraction Equations Lesson Reading Guide Get Ready for the Lesson 1-9 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-9) Lesson 1-9 Chapter 1 A27 60 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 24. 27 z 47 74 23. 54 32 w 22 22. 111 x 68 43 Chapter 1 21. g 35 62 27 18. m 65 11 54 15. f 25 35 60 20. n 75 42 117 36 19. r 53 19 72 14. 17 19 x 12. 22 y 29 7 17. s 46 72 26 8 11. 19 z 21 2 16. y 37 59 22 13. 16 24 p 10. 17 b 8 25 8. 8 d 14 7. u 4 1 3 9. 19 x 7 12 6. h 3 6 5. a 4 3 7 4. z 5 1 6 6 3. t 2 2 4 2. y 6 5 1 1. x 3 4 1 3 6AF1.1 Solving Addition and Subtraction Equations Skills Practice Solve each equation. Check your solution. 1-9 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 6AF1.1 8. 15 n 10 5 7. 14 2 d 16 140 R S 12. 12 c 16 4 9. 8 r 6 2 6. y 10 3 7 Chapter 1 31 p 14; 45 points 61 16. ANALYZE TABLES The total points scored by both teams in the 2006 Super Bowl was 14 less than the total points for 2005. Write and solve an equation to find the total points for 2005. p 31 2005 2006 Glencoe California Mathematics, Grade 7 Source: www.superbowl.com Points Year Total Points Scored by Both Teams in Super Bowl 45; Add the numbers on the left and then subtract the total from each side, or subtract each number on the left from each side one at a time; 14 boxes. 15. FUND RAISING During a five-day fund raiser, Shantell sold 8 boxes of greeting cards the first day, 6 boxes the second day, 10 boxes the third day, and 7 boxes the fourth day. If she sold a total of 45 boxes of greeting cards during the five days, write an equation that can be used to find the number of boxes Shantell sold the fifth day. Explain two methods of solving this equation. Then solve the equation. 8 6 10 7 f 14. ARCHITECTURE The Sears Tower in Chicago was the tallest building in the world when it was completed. Twenty-three years later, a taller building was completed in 1996 on Taiwan. Write and solve an equation to find the year that the Sears Tower was completed. y 23 1996; 1973 13. GEOMETRY Two angles are supplementary if the sum of their measures is 180. The two angles shown are supplementary. Write and solve an equation to find the measure of angle R. m 140 180; 40 11. 9 g 9 18 5. m 9 7 16 4. k 4 14 10 10. 11 w 5 16 2. h 3 8 11 1. t 7 12 5 3. 8 b 9 17 Solving Addition and Subtraction Equations Practice Solve each equation. Check your solution. 1-9 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-9) Lesson 1-9 Chapter 1 6AF1.1 A28 62 a 67 80; 13 Chapter 1 Glencoe California Mathematics, Grade 7 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. h 543 8; 535 ft p 832,598 6,823,568; p 7,656,166 8. POPULATION In 2005, the population of Honduras is the population of Haiti decreased by 832,598. The population of Honduras is 6,823,568. Write and solve a subtraction equation to find the population of Haiti. t 12 7; 5°F 7. ELEVATION The lowest point in Louisiana is 543 feet lower than the highest point in Louisiana. The elevation of the lowest point is 8 feet. Write and solve a subtraction equation to find the elevation of the highest point in Louisiana. mA ⫽ 78˚ 6. CHEMISTRY The atomic number of mercury is the sum of the atomic number of aluminum and 67. The atomic number of mercury is 80. Write and solve an addition equation to find the atomic number of aluminum. B A 5. WEATHER After the temperature had risen 12°F, the temperature was 7°F. Write and solve an addition equation to find the 7 F starting temperature. 180˚ m 78° 180°; 102° b 40 287; $327 4. BANKING After you withdraw $40 from your checking account, the balance is $287. Write and solve a subtraction equation to find your balance before this withdrawal. r 24 29; 53 representatives 3. GEOMETRY Two angles are supplementary if the sum of their measures is 180°. Angles A and B are supplementary. If the measure of angle A is 78°, write and solve an addition equation to find the measure of angle B. a 2 79; 77 years old 2. CIVICS New York has 24 fewer members in the House of Representatives than California. New York has 29 representatives. Write and solve a subtraction equation to find the number of California representatives. Solving Addition and Subtraction Equations Word Problem Practice 1. AGE Walter lived 2 years longer than his brother Martin. Walter was 79 at the time of his death. Write and solve an addition equation to find Martin’s age at the time of his death. 1-9 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Chapter 1 D. A. 45˚ 2(45°) x° 180° 63 Glencoe California Mathematics, Grade 7 45° 90° D 360° x° 150° 90° F 120° B x° 72° 180° 30° x° 15° 90° 75° 108° E A 90° x° 15° 125° 30˚ Angle Measurement (x) 15˚ x˚ 15˚ C x˚ F. Letter of Figure 45˚ E. 35˚ x˚ Equation x˚ 150˚ x˚ 90˚ C. 35° 20° x° 180° 72˚ x˚ B. Match each equation in the chart at the bottom of the page with a figure that could be used to solve for the missing angle measurement. Then solve for that measurement. Angles are complementary if their measures add to 90°. If their measures add to 180°, they are supplementary. The total number of degrees in the measures of the central angles of a circle is 360°. The sum of the measures of the angles in a triangle is 180°. A straight angle measures 180°. 20˚ 7AF1.1 Equations are often used to solve geometric problems. To work the problems on this page, you will need to use the following facts. Geometric Equations 1-9 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-9) Lesson 1-9 Chapter 1 6AF1.1 Solving Multiplication and Division Equations Lesson Reading Guide multiply divide A29 135 15 9 64 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 3 14 Chapter 1 9. 29t 145 5 132 7. 17c 68 4 Chapter 1 10. 125 5z 25 65 11. 13t 182 Glencoe California Mathematics, Grade 7 12. 117 39k 10 8. h 12 11 8 6. x 7 70 3. 7h 21 3 5. f 6 48 5 2. 2d 12 6 Solve each equation. Check your solution. Exercises 9¬ 9 ✓ Replace d with 135. Write the original equation. d 135 Multiply each side of the equation by 15. 4. 8x 40 5 11. 9 9g 1 Check d ¬ 9 15 135 ¬ 9 15 d (15) 9(15) 15 d 9 15 15 This sentence is true. Replace w with 6. Solve d 9. Check your solution. 114¬ 114 ✓ Write the original equation. Identity Property; 1w w 1. r 6 30 21 19w¬ 114 w6 19 19 1 and 114 19 6. Divide each side of the equation by 19. 19w 114 19 19 1w 6 Write the equation. 19w 114 Solve 19w 104. Check your solution. 19(6)¬ 114 Example 2 Check Example 1 • Multiplication Property of Equality — If you multiply each side of an equation by the same number, the two sides remain equal. • Division Property of Equality — If you divide each side of an equation by the same nonzero number, the two sides remain equal. 12. Write two multiplication and two division equations of your own. Trade your equations with a partner and solve. Explain to each other the method you used to solve the equations. See students’ work. 10. 3 x 7 Divide each side by 16. 6AF1.1 Solving Multiplication and Division Equations Study Guide and Intervention You can use the following properties to solve multiplication and division equations. 1-10 NAME ________________________________________ DATE ______________ PERIOD _____ Remember What You Learned 9. 8r 32 4 Solve each equation. 8. 64 16k _________________________ _________________________ Divide each side by 2. 7. 2c 14 6 _________________________ Multiply each side by 6. multiply 6. u 13 Explain how to solve each equation. 5. To solve 7 d, __________ each side by 6. 6 4. To solve 65 5t, __________ each side by 5. divide 3. To solve b 4, __________ each side by 2. 2 2. To solve 3x 51, __________ each side by 3. Complete each sentence. Read the Lesson 1. If d represents the number of days the bamboo has been growing, write a multiplication equation you could use to find how long it would take for the bamboo to reach a height of 210 inches. 35d 210 Read the introduction at the top of page 70 in your textbook. Write your answers below. Get Ready for the Lesson 1-10 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Answers (Lesson 1-10) Lesson 1-10 Chapter 1 A30 Chapter 1 22. 23 506 g 22 31 Glencoe California Mathematics, Grade 7 4 210 Glencoe California Mathematics, Grade 7 24. 47k 517 11 14 21. 15 z 19 18. s 9 171 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 66 23. 16 400 y 25 20. 16q 272 17 19. m 7 217 98 17. 21a 126 6 153 y 14. 14 7 16. 17c 136 8 13. w 17 9 11. 11d 143 8 99 15. 112 8v 14 12. 116 29k 13 10. 135 9z 15 9. 18y 144 7. 14g 56 4 12 8. t 11 132 4. 7z 49 7 21 6. a 11 9 5. n 7 3 3 3. 5x 15 21 2. 3c 12 4 1. u 3 7 6AF1.1 Solving Multiplication and Division Equations Skills Practice Solve each equation. Check your solution. 1-10 NAME ________________________________________ DATE ______________ PERIOD _____ n 11. 9 72 8 a 12. 3 75 25 c 9. 43 86 2 6. 56 7d 8 3. 36 9b 4 Chapter 1 Solve each equation. 84 17. 3 28 g 8g 104; 13 gallons 67 4 18. 8 0.5 x 16. the number of gallons in 104 pints 2q 24; 12 quarts Glencoe California Mathematics, Grade 7 144 19. 16 9 r 1 gallon 8 pints 1 gallon 4 quarts 1 quart 4 cups 1 quart 2 pints 1 pint 2 cups MEASUREMENT For Exercises 15 and 16, refer to the table. Write and solve an equation to find each quantity. Customary System 15. the number of quarts in 24 pints Conversions (capacity) 14. POPULATION The population of South Africa is four times the population of Greece. If the population of South Africa is 44 million, write and solve a multiplication equation to find the population of Greece. 44 4g; 11 million 13. CARS Mrs. Alvarez bought a new car. Her monthly payments are $525. If she will pay a total of $25,200 in payments, write and solve a multiplication equation to find the number of payments. 525n 25,200; 48 payments y 10. 16 48 3 v 8. 20 80 4 5. 12m 72 6 4. 3p 24 8 55 2. 8h 64 8 1. 5s 45 9 x 7. 11 5 6AF1.1 Solving Multiplication and Division Equations Practice Solve each equation. Check your solution. 1-10 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-10) Lesson Lesson 1-10 X–4 Chapter 1 A31 26a 338; 13 yr 7. AGE The product of Bart’s age and 26 is 338. Write and solve a multiplication equation to find Bart’s age. 20m 120; 6 min 5. ROBOTS The smallest robot can travel 20 inches per minute through a pipe. Write and solve a multiplication equation to find how long it will take this robot to travel through 10 feet of pipe. 3d 57; 19 days 3. EXERCISE Jasmine jogs 3 miles each day. Write and solve a multiplication equation to find how many days it will take her to jog 57 miles. 9h 54; 6 h Chapter 1 6AF1.1 68 Glencoe California Mathematics, Grade 7 Answers Glencoe California Mathematics, Grade 7 325p 6,825; 21 yr 8. POPULATION The population of a small town is increasing at a rate of 325 people per year. Write and solve a multiplication equation to find how long it will take the population to increase by 6,825. 40w 680; 17 days 6. BANKING Nate withdraws $40 from his checking account each day. Write and solve a multiplication equation to find how long it will take him to withdraw $680. 62h 558; 9 h 4. TRAVEL On a trip, the Rollins family drove at an average rate of 62 miles per hour. Write and solve a multiplication equation to find how long it took them to drive 558 miles. 0.50b 5; 10 bars 2. SHOPPING Granola bars are on sale for $0.50 each. If Brad paid $5 for granola bars, write and solve a multiplication equation to find how many bars he bought. Solving Multiplication and Division Equations Word Problem Practice 1. WAGES Felipe earns $9 per hour for helping his grandmother with her yard work. Write and solve a multiplication equation to find how many hours he must help his grandmother in order to earn $54. 1-10 NAME ________________________________________ DATE ______________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Enrichment 7AF1.1 Chapter 1 69 n 6 2n; n 6; integers are 6, 8, 10, 12 Glencoe California Mathematics, Grade 7 7. Find four consecutive even integers such that the largest is twice the smallest. n 2 3n 6; n 4; integers are 4 and 6 6. The larger of two consecutive even integers is 6 less than 3 times the smaller. Find the integers. n (n 2) (n 4) (n 6) 80; n 23; integers are 23, 21, 19, 17 5. Find the four consecutive odd integers with a sum of 80. n (n 1) (n 2) 12; n 5; integers are 5, 4, 3 4. Find the three consecutive integers that have a sum of 12. Write an equation to solve each problem. 9, 11, 13, 15, 17 3. What five consecutive odd integers does Expression C produce when n 9? 0, 2, 4, 6, 8 2. What five consecutive even integers does Expression B produce when n 0? 8, 9, 10, 11, 12 1. What five consecutive integers does Expression A produce when n 8? Use Expressions A, B, and C for these problems. Phrase C “five consecutive odd integers” Expression C n, n 2, n 4, n 6, n 8 Phrase B “five consecutive even integers” Expression B n, n 2, n 4, n 6, n 8 Phrase A “five consecutive integers” Expression A n, n 1, n 2, n 3, n 4 Equations can be used to solve problems that involve consecutive integers. In solving these problems, you will need to translate certain phrases into algebraic expressions. Here are some examples. Consecutive Integers 1-10 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 1-10) Lesson Lesson 1-10 X–4 Chapter 1 Assessment Answer Key 2 pencils and 1 eraser 1. 2. 7 3. 32 4. 8 5. 9 Quiz 2 (Lesson 1-4 and 1-5) Page 73 1. 4 2. 27 3. 33 4. 18 5. 3 6. 13 7. 22 8. 4 9. 9 10. 19 Quiz 3 (Lesson 1-6 through 1-8) Page 74 1. 24 2. 35 3. 25 4. 9 5. 2 6. 17 7. n (5) 8. c3 9. n 9 24 10. Mid-Chapter Test Page 75 1. D 2. H 3. A 4. F 5. D 6. 4 3 2 1 0 1 2 a 15 12.50 Quiz 4 (Lesson 1-9 and 1-10) Page 74 1. 2 2. 21 3. 28 4. 12 5. $25 7. 3 8. 5 7; 2 cards 9. 10. 2 buses (continued on the next page) Chapter 1 A32 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Quiz 1 (Lesson 1-1 through 1-3) Page 73 Chapter 1 Assessment Answer Key Vocabulary Test Page 76 1. inverse operations 2. coordinate 3. absolute value 4. negative number Form 1 Page 77 Page 78 1. B 12. J 2. J 13. A 3. C 14. G 4. G 15. D 5. A 16. J 6. H 7. D 17. A 8. F 18. H 19. A 20. G 5. counterexample 7. powers 8. solutions 9. evaluate 10. inequality an educated guess used in some problem-solving strategies where, for example, you guess that the numbers in the problem follow 11. some pattern an open sentence that is true for any numbers, such as a b b a, the Commutative Property of Addition 12. Chapter 1 9. D 10. F 11. C B: A33 Glencoe California Mathematics, Grade 7 Answers Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 6. additive inverses Chapter 1 Assessment Answer Key 1. A 2. F 3. C 4. 5. F Page 80 11. D 12. F 13. C 14. J A 15. 6. D 2. G 3. A 18. 12. J 13. C 14. G D B 16. F 5. 17. C 18. F 19. B 20. H G A D 8. H C H 9. D 9. 10. F 10. Chapter 1 B 15. 7. G 11. H G C Page 82 4. 6. 17. 8. 1. A G 16. 7. Form 2B Page 81 19. D 20. G B: 8,000 F B: A34 5 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Form 2A Page 79 Chapter 1 Assessment Answer Key Form 2C Page 83 2. 3. 4. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 5. 7.5 in. 14 15. 17 16. 28 17. 40 18. 8 19. 6 20. n (16) 21. 1913 22. 16 23. 4 24. 12 25. 50 B: 265 26 6 18 5 6. 11 7. 4 8. 2 9. 2 10. 5 11. 16 12. 10 13. 21 Chapter 1 14. A35 Glencoe California Mathematics, Grade 7 Answers 1. Page 84 Chapter 1 Assessment Answer Key Form 2D Page 85 Page 86 1. 12 cucumbers & 2 green peppers 3. 4. 5. 16. 80 17. 140 18. 8 19. 8 20. n 14 21. 9 lawns 22. 22 23. 7 24. 13 25. 144 B: 2A b 12 4 7. 4 8. 3 9. 2 2 40 12. 18 13. 18 Chapter 1 16 23 10 11. 15. 6 6. 10. 22 A36 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 2. 14. Chapter 1 Assessment Answer Key Form 3 Page 87 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. No; 9.99 12.95 1. 6.75 10.39 40 2. 360 3. 105 13. 81 14. 40 15. 12 16. 13 17. 1 4. 4 5. 6 18. p 29 6. 2 19. n (12) 7. 5 20. n 4 10 21. 94 8. {25, 15, 3, 2, 26} 9. 17 10. 22 22. 64 11. 29 23. 12 12. 11 24. 105 25. 16 B: 2A b h Chapter 1 A37 Glencoe California Mathematics, Grade 7 Answers Page 88 Chapter 1 Assessment Answer Key Extended-Response Test, Page 89 Scoring Rubric Specific Criteria 4 The student demonstrates a thorough understanding of the mathematics concepts and/or procedures embodied in the task. The student has responded correctly to the task, used mathematically sound procedures, and provided clear and complete explanations and interpretations. The response may contain minor flaws that do not detract from the demonstration of a thorough understanding. 3 The student demonstrates an understanding of the mathematics concepts and/or procedures embodied in the task. The student’s response to the task is essentially correct with the mathematical procedures used and the explanations and interpretations provided demonstrating an essential but less than thorough understanding. The response may contain minor errors that reflect inattentive execution of the mathematical procedures or indications of some misunderstanding of the underlying mathematics concepts and/or procedures. 2 The student has demonstrated only a partial understanding of the mathematics concepts and/or procedures embodied in the task. Although the student may have used the correct approach to obtaining a solution or may have provided a correct solution, the student’s work lacks an essential understanding of the underlying mathematical concepts. The response contains errors related to misunderstanding important aspects of the task, misuse of mathematical procedures, or faulty interpretations of results. 1 The student has demonstrated a very limited understanding of the mathematics concepts and/or procedures embodied in the task. The student’s response to the task is incomplete and exhibits many flaws. Although the student has addressed some of the conditions of the task, the student reached an inadequate conclusion and/or provided reasoning that was faulty or incomplete. The response exhibits many errors or may be incomplete. 0 The student has provided a completely incorrect solution or uninterpretable response, or no response at all. Chapter 1 A38 Glencoe California Mathematics, Grade 7 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Level Chapter 1 Assessment Answer Key Extended-Response Test, Page 89 Sample Answers In addition to the scoring rubric found on page A38, the following sample answers may be used as guidance in evaluating open-ended assessment items. b. The equation is s 80. 1. a. To find the average of Theo’s test scores, add the five scores and then divide the sum by 5, the number of scores. 5 s ¬ 80 5 s (5)¬ 80(5) 5 415 76 87 82 91 79 5 5 s¬ 400 83 The sum of Tiffany’s scores is 400. Theo’s average is 83. c. 85 73 87 84 329 The sum of Tiffany’s scores is 400. The equation is m 329 400. b. 72 74 76 78 80 82 84 86 88 90 92 94 83 83 83 83 83 7 4 1 8 4 The missing score is 71. d. 71 85 73 87 84 d. Sample answer: The negative differences correspond to the scores that are less than the average score. The negative differences correspond to the scores that are to the left of the average score on the number line. 80 80 80 80 80 9 5 7 7 4 e. The sums are both 0. The sum of the differences between a student’s actual test scores and average score is always 0. e. 7 4 (1) 8 (4) 0 2. a. Theo’s average is three more than Tiffany’s average. Let t represent Tiffany’s average. Then the equation is 83 t 3. 83 t 3 83 3 t 3 3 80 t Tiffany’s average score is 80. Chapter 1 A39 Glencoe California Mathematics, Grade 7 Answers Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. c. 76 87 82 91 79 m 329 400 m 329 329 400 329 m 71 Chapter 1 Assessment Answer Key Standardized Test Practice Page 90 Page 91 1. A B C D 12. F G H J 2. F G H J 13. A B C D 3. A B C D 14. F G H J 15. A B C D 16. F G H J 17. A B C D 18. F G H J 19. A B C D F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 10. F G H J 11. A B C D Chapter 1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4. A40 Glencoe California Mathematics, Grade 7 Chapter 1 Assessment Answer Key Standardized Test Page 92 24 20. 21. {10, 3, 1, 1, 14} 22. 12 S Samantha’s age; s 4 23. 24. n 12 6; n 18 25. r = 15 26a. When the numbers are graphed on a number line, the numbers appear in order from least to greatest from left to right. 26b. 26c. Chapter 1 Answers Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. ⫺2 ⫺1 0 1 2 3 2, 0, 1, 3 A41 Glencoe California Mathematics, Grade 7