Chapter Chapter X1 Resource Resource Masters Masters
Course 11 Course
Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide and Intervention Workbook Study Guide and Intervention Workbook (Spanish) Practice: Skills Workbook Practice: Skills Workbook (Spanish) Practice: Word Problems Workbook Practice: Word Problems Workbook (Spanish) Reading to Learn Mathematics Workbook
0-07-860085-5 0-07-860091-X 0-07-860086-3 0-07-860092-8 0-07-860087-1 0-07-860093-6 0-07-861057-5
Answers for Workbooks The answers for Chapter 1 of these workbooks can be found in the back of this Chapter Resource Masters booklet.
Spanish Assessment Masters Spanish versions of forms 2A and 2C of the Chapter 1 Test are available in the Glencoe Mathematics: Applications and Concepts Spanish Assessment Masters, Course 1 (0-07-860095-2).
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. 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, teacher, and families without charge; and be used solely in conjunction with Glencoe Mathematics: Applications and Concepts, Course 1. 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 Mathematics: Applications and Concepts, Course 1 Chapter 1 Resource Masters
ISBN: 0-07-846545-1 1 2 3 4 5 6 7 8 9 10
024
12 11 10 09 08 07 06 05 04 03
CONTENTS Vocabulary Builder .............................vii Family Letter ............................................ix Family Activity ........................................x Lesson 1-1 Study Guide and Intervention ............................1 Practice: Skills ....................................................2 Practice: Word Problems....................................3 Reading to Learn Mathematics..........................4 Enrichment .........................................................5
Lesson 1-2 Study Guide and Intervention ............................6 Practice: Skills ....................................................7 Practice: Word Problems....................................8 Reading to Learn Mathematics..........................9 Enrichment .......................................................10
Lesson 1-3 Study Guide and Intervention ..........................11 Practice: Skills ..................................................12 Practice: Word Problems..................................13 Reading to Learn Mathematics........................14 Enrichment .......................................................15
Lesson 1-6 Study Guide and Intervention ..........................26 Practice: Skills ..................................................27 Practice: Word Problems..................................28 Reading to Learn Mathematics........................29 Enrichment .......................................................30
Lesson 1-7 Study Guide and Intervention ..........................31 Practice: Skills ..................................................32 Practice: Word Problems..................................33 Reading to Learn Mathematics........................34 Enrichment .......................................................35
Lesson 1-8 Study Guide and Intervention ..........................36 Practice: Skills ..................................................37 Practice: Word Problems..................................38 Reading to Learn Mathematics........................39 Enrichment .......................................................40
Chapter 1 Assessment
Lesson 1-5
Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter
Study Guide and Intervention ..........................21 Practice: Skills ..................................................22 Practice: Word Problems..................................23 Reading to Learn Mathematics........................24 Enrichment .......................................................25
Standardized Test Practice Student Recording Sheet ..........................................A1 Standardized Test Practice Rubric...................A2 ANSWERS .............................................A3–A32
Lesson 1-4 Study Guide and Intervention ..........................16 Practice: Skills ..................................................17 Practice: Word Problems..................................18 Reading to Learn Mathematics........................19 Enrichment .......................................................20
iii
1 Test, Form 1 ..............................41–42 1 Test, Form 2A ............................43–44 1 Test, Form 2B ............................45–46 1 Test, Form 2C............................47–48 1 Test, Form 2D............................49–50 1 Test, Form 3 ..............................51–52 1 Extended Response Assessment ...53 1 Vocabulary Test/Review...................54 1 Quizzes 1 & 2..................................55 1 Quizzes 3 & 4..................................56 1 Mid-Chapter Test .............................57 1 Cumulative Review..........................58 1 Standardized Test Practice........59–60
Teacher’s Guide to Using the Chapter 1 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. 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 in the Glencoe Mathematics: Applications and Concepts, Course 1, TeacherWorks CD-ROM.
Vocabulary Builder Pages vii-viii include 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. When to Use Give these pages to students before beginning Lesson 1-1. Encourage them to add these pages to their mathematics study notebook. Remind them to add definitions and examples as they complete each lesson.
Family Letter and Family Activity Page ix is a letter to inform your students’ families of the requirements of the chapter. The family activity on page x helps them understand how the mathematics students are learning is applicable to real life. When to Use Give these pages to students to take home before beginning the chapter.
Study Guide and Intervention There is one Study Guide and Intervention master for each lesson in Chapter 1. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.
Practice: Skills
There is one master for each lesson. These provide practice that more closely follows the structure of the Practice and Applications section of the Student Edition exercises. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson.
Practice: Word Problems There is one master for each lesson. These provide practice in solving word problems that apply the concepts of the lesson. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson.
Reading to Learn Mathematics
One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques. When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students.
iv
There is one extension master for each lesson. These activities may extend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for use with all levels of students.
• A Vocabulary Test, suitable for all students, includes a list of the vocabulary words in the chapter and ten questions assessing students’ knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet.
When to Use These may be used as extra credit, short-term projects, or as activities for days when class periods are shortened.
• Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter.
Enrichment
Intermediate Assessment
• A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and freeresponse questions.
Assessment Options The assessment masters in the Chapter 1 Resources Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use.
Continuing Assessment • The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of Glencoe Mathematics: Applications and Concepts, Course 1. It can also be used as a test. This master includes free-response questions.
Chapter Assessment Chapter Tests • Form 1 contains multiple-choice questions and is intended for use with basic level students.
• The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which may appear on the standardized tests that they may encounter. This practice includes multiplechoice, short response, grid-in, and extended response questions. Bubble-in and grid-in answer sections are provided on the master.
• Forms 2A and 2B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. • Forms 2C and 2D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with axes are provided for questions assessing graphing skills.
Answers • Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 46-47. This improves students’ familiarity with the answer formats they may encounter in test taking.
• Form 3 is an advanced level test with free-response questions. Grids without axes are provided for questions assessing graphing skills. All of the above tests include a free-response Bonus question.
• Detailed rubrics for assessing the extended response questions on page 47 are provided on page A2.
• The Extended-Response Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment.
• The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. • Full-size answer keys are provided for the assessment masters in this booklet.
v
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics 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
algebra [AL-juh-bruh]
algebraic [AL-juh-BRAY-ihk] expression area
base
composite [com-PAH-zit] number cubed
divisible
equals sign
equation [ih-KWAY-zhuhn] evaluate
even
© Glencoe/McGraw-Hill
vii
Mathematics: Applications and Concepts, Course 1
Vocabulary Builder
Vocabulary Builder
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Vocabulary Builder Vocabulary Term
Found on Page
(continued) Definition/Description/Example
exponent [ex-SPOH-nuhnt] factor
formula [FOR-myuh-luh] numerical expression
odd
order of operations
power
prime factorization
prime number
solution
solve
squared
variable [VAIR-ee-uh-buhl]
© Glencoe/McGraw-Hill
viii
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Dear Parent or Guardian: classes because they do Students are often frustrated in math ial in the real world. In our not see how they can use the mater mathematics beyond the math class, however, we try to take realize and appreciate its classroom to a point where students importance in their daily lives. Algebra, your child will and ns ter Pat er mb Nu 1, er apt Ch In patterns, prime factors, the be learning about problem solving, ressions, and powers and order of operations, variables and exp equations and find the area ve sol o als l wil ld chi r You . nts one exp pter, your child will of rectangles. In the study of this cha assignments and activities complete a variety of daily classroom . and possibly produce a chapter 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 also relates the an activity you can do with your chi 1 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any other study help at www.msmath1.n contact me at school. questions or comments, feel free to Sincerely,
Signature of Parent or Guardian ______________________________________ Date ________
© Glencoe/McGraw-Hill
ix
Mathematics: Applications and Concepts, Course 1
Family Letter
Family Letter
NAME ________________________________________ DATE ______________ PERIOD _____
Family Activity Using Patterns Draw the next three figures in each pattern. You can take turns with a family member. 1.
2.
Find a pattern in your home or neighborhood. Sketch at least the first three figures in the pattern. Have a family member draw the next three figures in the pattern.
Have a family member find a pattern in your home or neighborhood. Have him or her sketch at least the first three figures. Draw the next three figures in the pattern.
2. Sample answer:
x
1. Sample answer:
© Glencoe/McGraw-Hill
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention A Plan for Problem Solving When solving problems, it is helpful to have an organized plan to solve the problem. The following four steps can be used to solve any math problem. 1 Explore – Read and get a general understanding of the problem. 2 Plan – Make a plan to solve the problem and estimate the solution. 3 Solve – Use your plan to solve the problem. 4 Examine – Check the reasonableness of your solution. SPORTS The table shows the number of field goals made by Henry
Name
3-Point Field Goals
Brad
216
Chris
201
Denny
195
Explore
You know the number of field goals made. You need to find how many more field goals Brad made than Denny.
Plan
Use only the needed information, the goals made by Brad and Denny. To find the difference, subtract 195 from 216.
Solve
216 195 21; Brad made 21 more field goals than Denny.
Examine Check the answer by adding. Since 195 21 216, the answer is correct.
1. During which step do you check your work to make sure your answer is correct?
2. Explain what you do during the first step of the problem-solving plan.
SPORTS For Exercises 3 and 4, use the field goal table above and the
four-step plan. 3. How many more field goals did Chris make than Denny?
4. How many field goals did the three boys make all together?
© Glencoe/McGraw-Hill
1
Mathematics: Applications and Concepts, Course 1
Lesson 1–1
High School’s top three basketball team members during last year’s season. How many more field goals did Brad make than Denny?
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills A Plan for Problem Solving Use the four-step plan to solve each problem. 1. GEOGRAPHY The president is going on a campaign trip to California, first flying about 2,840 miles from Washington D.C. to San Francisco and then another 390 to Los Angeles before returning the 2,650 miles back to the capital. How many miles will the president have flown?
2. POPULATION In 1990, the total population of Sacramento, CA was 369,365. In 2000, its population was 407,018. How much did the population increase? 3. MONEY The Palmer family wants to purchase a DVD player in four equal installments of $64. What is the cost of the DVD player?
4. COMMERCIALS The highest average cost of a 30-second commercial in October, 2002 is $455,700. How much is this commercial worth per second? 5. A tennis tournament starts with 16 people. The number in each round is shown in the table. How many players will be in the 4th round?
1st Round 2nd Round 3rd Round 4th Round
16 8 4 ?
Complete the pattern. 6. 2, 4, 8, 16, 32, …
7. 16, 19, 22, 25, 28, 31, …
8. 81, 72, 63, 54, …
9. 5, 15, 20, 30, 35, 45, 50, …
10. 50, 40, 45, 35, 40, 30, 35, ___, ___, ___, ___
11. 6, 12, 18, ___, ___, ___, ___
© Glencoe/McGraw-Hill
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Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems A Plan for Problem Solving Use the four-step plan to solve each problem.
Visit Crater Lake National Park
GEOGRAPHY For Exercises 1 and 2, use the 90 miles of trails 26 miles of shoreline Boat tours available Open 24 hours
poster information about Crater Lake National Park in Oregon.
1. How many more miles of trails are there than miles of shoreline in Crater Lake National Park?
2. How many miles is it from Klamath Falls to Crater Lake National Park?
3. SPORTS Jasmine swims 12 laps every afternoon, Monday through Friday. How many laps does she swim in one week?
4. SPORTS Samantha can run one mile in 8 minutes. At this rate, how long will it take for her to run 5 miles?
5. SPORTS On a certain day, 525 people signed up to play softball. If 15 players are assigned to each team, how many teams can be formed?
6. PATTERNS Complete the pattern: 5, 7, 10, 14, ___, ___, ___
7. SHOPPING Josita received $50 as a gift. She plans to buy two cassette tapes that cost $9 each and a headphone set that costs $25. How much money will she have left?
8. BUS SCHEDULE A bus stops at the corner of Elm Street and Oak Street every half hour between 9 A.M. and 3 P.M. and every 15 minutes between 3 P.M. and 6 P.M. How many times will a bus stop at the corner between 9 A.M. and 6 P.M.?
© Glencoe/McGraw-Hill
3
Mathematics: Applications and Concepts, Course 1
Lesson 1–1
Directions from Klamath Falls: Take U.S. Highway 97 north 21 miles, then go west on S.R. 62 for 29 miles.
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics A Plan for Problem Solving Pre-Activity
Read the introduction at the top of page 6 in your textbook. Write your answers below.
1. How many pennies are in a row that is one mile long? (Hint: There are 5,280 feet in one mile.)
2. Explain how to find the value of the pennies in dollars. Then find the value.
3. Explain how you could use the answer to Exercise 1 to estimate the number of quarters in a row one mile long.
Reading the Lesson 4. Think of how you use the word explore. When was the last time you did some exploring of your own? Write a definition of the word explore that matches what you did during your exploration. Or maybe you would like to consider someone from history who was an explorer. Write a definition of the word explore that matches what that person did.
5. If you were doing an exploratory, when do you think this would happen? Before or after the thing you were exploring?
6. In the four-step plan for problem solving, think about the term examine. Does examine come before or after the solution? (Hint: What are you examining?)
Helping You Remember 7. Think about the four steps in the problem-solving plan: Explore, Plan, Solve, Examine. Write a sentence about something you like to help you remember the four words. For example, “I like to explore caves.”
© Glencoe/McGraw-Hill
4
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment Using a Reference Point There are many times when you need to make an estimate in relation to a reference point. For example, at the right there are prices listed for some school supplies. You might wonder if $5 is enough money to buy a small spiral notebook and a pen. This is how you might estimate, using $5 as the reference point. • The notebook costs $1.59 and the pen costs $3.69. • $1 $3 $4. I have $5 $4, or $1, left. • $0.59 and $0.69 are each more than $0.50, so $0.59 $0.69 is more than $1. So $5 will not be enough money.
Spira l No Large tebook Smal $2.29 l $1.5 9
Three -Ri Binde ng r $4.75
1. Jamaal has $5. Will that be enough money to buy a large spiral notebook and a pack of pencils?
2. Andreas wants to buy a three-ring binder and two packs of filler paper. Will $7 be enough money?
3. Rosita has $10. Can she buy a large spiral notebook and a pen and still have $5 left?
Filler P Pack aper of 10 $1.29 0
Ball-P oint Pen $3.69
4. Kevin has $10 and has to buy a pen and two small spiral notebooks. Will he have $2.50 left to buy lunch?
5. What is the greatest number of erasers you can buy with $2?
Penc Pack ils of 1 $2.39 0
6. What is the greatest amount of filler paper that you can buy with $5?
7. Lee bought three items and spent exactly $8.99. What were the items?
Erase r $0.55
8. Select five items whose total cost is as close as possible to $10, but not more than $10.
© Glencoe/McGraw-Hill
5
Mathematics: Applications and Concepts, Course 1
Lesson 1–1
Use the prices at the right to answer each question.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention Divisibility Patterns A whole number is divisible by another number if the remainder is 0 when the first is divided by the second. A whole number is even if it is divisible by 2. A whole number is odd if it is not divisible by 2. Rule
Examples
A whole number is divisible by: • 2 if the ones digit is divisible by 2. • 3 if the sum of the digits is divisible by 3. • 4 if the number formed by the last two digits is divisible by 4. • 5 if the ones digit is 0 or 5. • 6 if the number is divisible by both 2 and 3. • 9 if the sum of the digits is divisible by 9. • 10 if the ones digit is 0.
2, 4, 6, 8, 10, 12, 14, 16, … 3, 6, 9, 12, 15, 18, 21, 24, … 4, 8, 12, …, 104, 108, 112, … 5, 10, 15, 20, 25, 30, … 6, 12, 18, 24, 30, 36, … 9, 18, 27, 36, 45, … 10, 20, 30, 40, 50, …
Tell whether 112 is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd. 2: Yes; the ones digit is divisible by 2. 3: No; the sum of the digits, 4, is not divisible by 3. 4: Yes; the number formed by the last two digits, 12, is divisible by 4. 5: No; the ones digit is not a 0 or a 5. 6: No; the number is not divisible by 2 and 3. 9: No; the sum of the digits, 4, is not divisible by 9. 10: No; the ones digit, 2, is not 0. The number 112 is even because it is divisible by 2.
Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd. 1. 80
2. 93
3. 324
4. 81
5. 650
6. 23,512
7. 48
8. 268
9. 665
10. 3,579
11. 7,000
12. 24,681
Tell whether each sentence is sometimes, always, or never true. 13. A number that is divisible by both 2 and 3 is also divisible by 6.
14. Any number that is divisible by 10 is also divisible by 2 and 5.
© Glencoe/McGraw-Hill
6
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills Divisibility Patterns Tell whether the first number is divisible by the second number. 1. 527; 3
2. 1,048; 6
3. 693; 9
4. 1,974; 2
5. 305; 10
6. 860; 5
7. 4,672; 9
8. 2,310; 6
9. 816; 3
10. 13,509; 5
11. 2,847; 2
12. 192; 6
13. 24
14. 27
15. 90
16. 81
17. 104
18. 205
19. 1,000
20. 6,598
21. 399
22. 27,453
23. 33,324
24. 16,335
Use divisibility rules to find each missing digit. List all possible answers. 25. 1__2 is divisible by 9
26. 1,__24 is divisible by 4
27. 1,25__ is divisible by 3
28. 5,__32 is divisible by 6
29. 31,45__ is divisible by 5
30. 1,679,83__ is divisible by 2
© Glencoe/McGraw-Hill
7
Mathematics: Applications and Concepts, Course 1
Lesson 1–2
Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd.
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems Divisibility Patterns MONTHS OF THE YEAR For Exercises 1–3, use the table that shows how
many days are in each month, excluding leap years. (Every four years, the calendar is adjusted by adding one day to February.) JAN. FEB. MAR. APR. MAY JUN. JUL. AUG. SEP. OCT. NOV. DEC. 31
28
31
30
31
30
31
31
30
31
30
31
1. Which month has a number of days that is divisible by 4? During a leap year, is this still true?
2. Which months have a number of days that is divisible by both 5 and 10? During a leap year, is this still true?
3. The total number of months in a year are divisible by which numbers?
4. FOOD Jermaine and his father are in charge of grilling for a family reunion picnic. There will be 40 people attending. Ground beef patties come 5 to a package. How many packages of patties should they buy to provide 1 hamburger for each person? Will there by any patties left over? If so, how many?
5. RETAIL Li is stacking bottles of apple juice on the shelf at her parent’s grocery store. She has space to fit 4 bottles across and 6 bottles from front to back. She has 25 bottles to stack. Will all of the bottles fit on the shelf? Explain.
6. FARMING Sally is helping her mother put eggs into egg cartons to sell at the local farmer’s market. Their chickens have produced a total of 108 eggs for market. Can Sally package the eggs in groups of 12 so that each carton has the same number of eggs? Explain.
© Glencoe/McGraw-Hill
8
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Divisibility Patterns Pre-Activity
Complete the Mini Lab at the top of page 10 in your textbook. Write your answers below.
Describe a pattern in each group of numbers listed. 1. the numbers that can be evenly divided by 2 2. the numbers that can be evenly divided by 5 3. the numbers that can be evenly divided by 10 4. the numbers that can be evenly divided by 3 (Hint: Look at both digits.)
Reading the Lesson 5. Complete the following table. is divisible by
because
12
2
the ones digit is divisible by 2
12
3
the sum of the digits is divisible by 3
12
4
the number formed by the last two digits is divisible by 4
12
6
the number is divisible by both 2 and 3
20
5
the ones digit is 0 or 5
20
10
the ones digit is 0
6. The Pledge of Allegiance uses the term indivisible. How do the meanings of divisible and indivisible compare to each other?
Helping You Remember 7. Several commonplace items come in amounts that are divisible by smaller units. For example, a deck of playing cards has 4 suits of 13 cards, so 52 is divisible by 4 and 13. Name other everyday items that illustrate divisibility patterns. © Glencoe/McGraw-Hill
9
Mathematics: Applications and Concepts, Course 1
Lesson 1–2
The number
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment Leap Years You probably know that a leap year has 366 days, with the extra day being February 29. Did you know that divisibility can help you recognize a leap year? That is because the number of a leap year is always divisible by 4. A number is divisible by 4 if the number formed by its tens and ones digits is divisible by 4. 1936 is divisible by 4 because 36 is divisible by 4. 1938 is not divisible by 4 because 38 is not divisible by 4. So 1936 was a leap year, and 1938 was not. Be careful when you decide if a year is a leap year. A century year—like 1800, 1900, or 2000—is a leap year only if its number is divisible by 400. Decide whether each year is a leap year. Write yes or no. 1. 1928
2. 1930
3. 1960
4. 1902
5. 1492
6. 1776
7. 1812
8. 1900
9. 1994
10. 2000
11. 2001
12. 2100
13. How many leap years are there between 1901 and 2001? 14. How many leap years were there from the Declaration of Independence in 1776 to the bicentennial celebration in 1976? (Include 1776 and 1976 in your count.) 15. In 1896, the first modern Olympic games were held in Athens, Greece. After that, the officially recognized games were held every four years except for 1916, 1940, and 1944, when the world was at war. How many times were the games held from 1896 to 1992? 16. George Washington was first elected president in 1789. Since 1792, United States presidential elections have been held every four years. How many presidential elections will there have been up to and including the election in the year 2000? 17. CHALLENGE If a person lives to be exactly 100 years old, how many leap years or parts of leap years will that person see?
© Glencoe/McGraw-Hill
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Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention Prime Factors Factors are the numbers that are multiplied to get a product. A product is the answer to a multiplication problem. A prime number is a whole number that has only 2 factors, 1 and the number itself. A composite number is a number greater than 1 with more than two factors.
Tell whether each number is prime, composite, or neither. Number
Factors
Prime or Composite?
15
1 15 35
Composite
17
1 17
Prime
1
1
Neither
Find the prime factorization of 18. Write the number that is being factored at the top.
18 2
9
2 3 3
Choose any pair of whole number factors of 18. Except for the order, the prime factors are the same.
18 is divisible by 2, because the ones digit is divisible by 2. Circle the prime number, 2. 3 6 9 is divisible by 3, because the sum of the digits is divisible by 3. 3 2 3 Circle the prime numbers, 3 and 3. The prime factorization of 18 is 2 3 3. 18
1. 7
2. 12
3. 29
4. 81
5. 18
6. 23
7. 54
8. 28
9. 120
10. 243
11. 61
12. 114
Find the prime factorization of each number. 13. 125
14. 44
15. 11
16. 56
© Glencoe/McGraw-Hill
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Mathematics: Applications and Concepts, Course 1
Lesson 1–3
Tell whether each number is prime, composite, or neither.
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills Prime Factors Tell whether each number is prime, composite, or neither. 1. 0
2. 1
3. 2
4. 3
5. 4
6. 5
7. 6
8. 7
9. 8
10. 9
11. 10
12. 11
Find the prime factorization of each number. 13. 9
14. 25
15. 28
16. 54
17. 34
18. 72
19. 55
20. 63
SCHOOL For Exercises 21–24, use the table below.
Marisa’s History Test Scores Date
Test Score
January 28
67
February 15
81
March 5
97
March 29
100
21. Which test scores are prime numbers?
22. Which prime number is the least prime number?
23. Find the prime factorization of 100.
24. Find the prime factorization of 81.
© Glencoe/McGraw-Hill
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Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems Prime Factors ANIMALS For Exercises 1–3, use the table that shows the height and
weight of caribou. Height at the Shoulder
Weight
inches
centimeters
pounds
kilograms
Cows (females)
43
107
220
99
Bulls (males)
50
125
400
180
1. Which animal heights and weights are prime numbers?
2. Write the weight of caribou cows in kilograms as a prime factorization.
3. ANIMALS Caribou calves weigh about 13 pounds at birth. Tell whether this weight is a prime or a composite number.
4. SPEED A wildlife biologist once found a caribou traveling at 37 miles per hour. Tell whether this speed is a prime or composite number. Explain.
5. GEOMETRY To find the area of a floor, you can multiply its length times its width. The measure of the area of a floor is 49. Find the most likely length and width of the room.
6. GEOMETRY To find the volume of a box, you can multiply its height, width, and length. The measure of the volume of a box is 70. Find its possible dimensions.
© Glencoe/McGraw-Hill
13
Mathematics: Applications and Concepts, Course 1
Lesson 1–3
CARIBOU
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Prime Factors Pre-Activity
Complete the Mini Lab at the top of page 14 in your textbook. Write your answers below.
1. For what numbers can more than one rectangle be formed?
2. For what numbers can only one rectangle be formed?
3. For the numbers in which only one rectangle is formed, what do you notice about the dimensions of the rectangle?
Reading the Lesson 4. The word factorization is made up of factor a verb ending a noun ending. Write a definition for each of the following mathematical terms: a. factor
b. to factorize, or to factor
c. factorization
5. Is 9 a prime number or a composite number? Explain.
Helping You Remember 6. Pick a number that has two or three digits. Explain to someone else how to use a factor tree to find the prime factors of the number. In your explanation, show how the rules of divisibility help you to do the factoring.
© Glencoe/McGraw-Hill
14
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment Making Models for Numbers Have you wondered why we read the number 32 as three squared? The reason is that a common model for 32 is a square with sides of length 3 units. As you see, the figure that results is made up of 9 square units.
3 units
3 units
32 9 square units
Make a model for each expression. 1. 22
2. 42
3. 12
4. 52
Since we read the expression 23 as two cubed, you probably have guessed that there is also a model for this number. The model, shown at the right, is a cube with sides of length 2 units. The figure that results is made up of 8 cubic units.
2 units 2 units 2 units
23 8 cubic units
Exercises 5 and 6 refer to the figure at the right. 5. What expression is being modeled?
a. How many small cubes are there in all? b. How many small cubes have red paint on exactly three of their faces? c. How many small cubes have red paint on exactly two of their faces? d. How many small cubes have red paint on exactly one face? e. How many small cubes have no red paint at all? 7. CHALLENGE In the space at the right, draw a model for the expression 43. © Glencoe/McGraw-Hill
15
Mathematics: Applications and Concepts, Course 1
Lesson 1–3
6. Suppose that the entire cube is painted red. Then the cube is cut into small cubes along the lines shown.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention Powers and Exponents A product of prime factors can be written using exponents and a base. Numbers expressed using exponents are called powers. Powers 56
Words 4 to the second power or 4 squared 5 to the sixth power
44 5 5 5 5 5 5
74 93
7 to the fourth power 9 to the third power or 9 cubed
7777 999
42
Expression
Value 16 15,625 2,401 729
Write 6 · 6 · 6 using an exponent. Then find the value of the power. The base is 6. Since 6 is a factor 3 times, the exponent is 3. 6 · 6 · 6 63 or 216 Write 24 as a product. Then find the value of the product. The base is 2. The exponent is 4. So, 2 is a factor 4 times. 24 2 · 2 · 2 · 2 or 16 Write the prime factorization of 225 using exponents. The prime factorization of 225 can be written as 3 3 5 5, or 32 52.
Write each product using an exponent. Then find the value of the power. 1. 2 · 2 · 2 · 2 · 2
2. 9 · 9
3. 3 · 3 · 3
4. 5 · 5 · 5
5. 3 · 3 · 3 · 3 · 3
6. 10 · 10
Write each power as a product. Then find the value of the product. 7. 72
8. 43
9. 84
10. 55
11. 28
12. 73
Write the prime factorization of each number using exponents. 13. 40
14. 75
15. 100
16. 147
© Glencoe/McGraw-Hill
16
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills Powers and Exponents Write each expression in words. 1. 72 2. 83 3. 44 4. 56 Write each product using an exponent. Then find the value of the power. 5. 4 · 4 · 4 · 4
6. 3 · 3 · 3 · 3
7. 5 · 5 · 5 · 5
8. 7 · 7
9. 3 · 3 · 3 · 3 · 3 11. 6 · 6 · 6
10. 2 · 2 · 2 · 2 · 2 · 2 12. 6 · 6 · 6 · 6
Write each power as a product. Then find the value of the product. 13. 38
14. 25
15. 83
16. 105
17. 62
18. 74
19. 23
20. 35
21. 65
22. 27
23. 54
24. 36
25. 63
26. 245
© Glencoe/McGraw-Hill
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Mathematics: Applications and Concepts, Course 1
Lesson 1–4
Write the prime factorization of each number using exponents.
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems Powers and Exponents 1. SPACE The Sun is about 10 · 10 million miles away from Earth. Write 10 · 10 using an exponent. Then find the value of the power. How many miles away is the Sun?
2. WEIGHT A 100-pound person on Earth would weigh about 4 · 4 · 4 · 4 pounds on Jupiter. Write 4 · 4 · 4 · 4 using an exponent. Then find the value of the power. How much would a 100-pound person weigh on Jupiter?
3. ELECTIONS In the year 2000, the governor of Washington, Gary Locke, received about 106 votes to win the election. Write this as a product. How many votes did Gary Locke receive?
4. SPACE The diameter of Mars is about 94 kilometers. Write 94 as a product. Then find the value of the product.
5. SPACE The length of one day on Venus is 35 Earth days. Express this exponent as a product. Then find the value of the product:
6. GEOGRAPHY The area of San Bernardino County, California, the largest county in the U.S., is about 39 square miles. Write this as a product. What is the area of San Bernardino County?
7. GEOMETRY The volume of the block shown can be found by multiplying the width, length, and height. Write the volume using an exponent. Find the volume.
8. SPACE A day on Jupiter lasts about 10 hours. Write a product and an exponent to show how many hours are in 10 Jupiter days. Then find the value of the power.
© Glencoe/McGraw-Hill
2 in.
2 in.
2 in.
18
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Powers and Exponents Pre-Activity
Complete the Mini Lab at the top of page 18 in your textbook. Write your answers below.
1. What prime factors did you record?
2. How does the number of folds relate to the number of factors in the prime factorization of the number of holes?
3. Write the prime factorization of the number of holes made if you folded it eight times.
Reading the Lesson 4. Describe the expression 25. In your description, use the terms power, base, and exponent.
5. In the power 35, what does the exponent 5 indicate?
6. Complete the following table. Expression 72 96 8888 33333
4 7 9 8 3
to to to to to
the the the the the
third power or 4 cubed second power or 7 squared sixth power fourth power fifth power
Lesson 1–4
43
Words
Helping You Remember 7. Explain how to find the value of 54.
© Glencoe/McGraw-Hill
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Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment The Sieve of Erathosthenes Erathosthenes was a Greek mathematician who lived from about 276 B.C. to 194 B.C. He devised the Sieve of Erathosthenes as a method of identifying all the prime numbers up to a certain number. Using the chart below, you can use his method to find all the prime numbers up to 120. Just follow these numbered steps. 1. The number 1 is not prime. Cross it out. 2. The number 2 is prime. Circle it. Then cross out every second number—4, 6, 8, 10, and so on. 3. The number 3 is prime. Circle it. Then cross out every third number—6, 9, 12, and so on. 4. The number 4 is crossed out. Go to the next number that is not crossed out. 5. The number 5 is prime. Circle it. Then cross out every fifth number—10, 15, 20, 25, and so on. 6. Continue crossing out numbers as described in Steps 2–5. The numbers that remain at the end of this process are prime numbers. 7. CHALLENGE Look at the prime numbers that are circled in the chart. Do you see a pattern among the prime numbers that are greater than 3? What do you think the pattern is?
© Glencoe/McGraw-Hill
20
1
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3
4
5
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9
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17
18
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112
113
114
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117
118
119
120
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention Lesson 1–5
Order of Operations Order of Operations 1. Simplify the expressions inside grouping symbols, like parentheses. 2. Find the value of all powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.
Find the value of 48 (3 3) 22. 48 (3 3) 22
48 6 22 48 6 4 84 4
Simplify the expression inside the parentheses. Find 22. Divide 48 by 6. Subtract 4 from 8.
Write and solve an expression to find the total cost of planting flowers in the garden. Item
Cost Per Item Number of Items Needed $4 $3 $4
pack of flowers bag of dirt bottle of fertilizer Words cost of 5 flower packs Expression 5 $4
plus
5 1 1 cost of dirt $3
plus
cost of fertilizer $4
5 $4 $3 $4 $20 $3 $4 $23 $4 $27 The total cost of planting flowers in the garden is $27.
Find the value of each expression. 1. 7 2 3
2. 12 3 5
3. 16 – (4 5)
4. 8 8 4
5. 10 14 2
6. 3 3 2 4
7. 80 – 8 32
8. 11 (9 – 22)
9. 25 5 6 (12 – 4)
10. GARDENING Refer to Example 2. Suppose that the gardener did not buy enough flowers and goes back to the store to purchase four more packs. She also purchases a hoe for $16. Write an expression that shows the total amount she spent to plant flowers in her garden.
© Glencoe/McGraw-Hill
21
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills Order of Operations Find the value of each expression. 1. 7 – 6 5
2. 31 19 – 8
3. 64 – 8 21
4. 17 34 – 2
5. 28 (89 – 67)
6. (8 1) 12 – 13
7. 63 9 8
8. 5 6 – (9 – 4)
9. 13 4 – 72 8
10. 16 2 8 3
11. 30 (21 – 6) 4
12. 6 7 (6 8)
13. 88 – 16 5 2 – 3
14. (2 6) 2 4 3
15. 43 – 24 8
16. 100 52 43
17. 48 23 25 (9 – 7)
18. 45 9 8 – 7 2 3
19. 18 72 (8 – 2) 3 8
20. (52 33) (81 9) 10
© Glencoe/McGraw-Hill
22
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems MONEY For Exercises 1–3, use the table that shows the price of admission to a movie theater.
Movie Theater Admission Adults: $8 Children (under 13): $5 Matinee (before 6 P.M.): $3 1. Janelle (age 12) and her cousin, Marquita (age 14), go to a 7:00 P.M. show. Write an expression for the total cost of admission. What is the total cost?
2. Jan takes her three children and two neighbor’s children to a matinee. All of the children are under age 13. Write an expression for the total cost of admission. How much in all did Jan pay for admission?
3. Connor (age 13), his sister (age 7), and Connor’s parents go to a movie on Saturday night. Write an expression for the total cost. What is the total cost?
4. SOCCER Eduardo is 16. Eduardo’s dad takes him and his younger sister to a soccer match. Tickets are $17 for adults and $13 for children (18 and under). Write an expression for the total cost of the tickets. What is the total cost of the tickets?
5. MONEY Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00. Write an expression to show how much he paid for lunch. Then find the value of the expression.
6. MONEY A store sells barrettes for $2 each and combs for $1. Shelby buys 3 barrettes and a comb. Kendra buys 2 barrettes and 4 combs. Write an expression for the amount the two girls spent all together. Find the total amount spent.
© Glencoe/McGraw-Hill
23
Mathematics: Applications and Concepts, Course 1
Lesson 1–5
Order of Operations
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Order of Operations Pre-Activity
Read the introduction at the top of page 24 in your textbook. Write your answers below.
1. How many Calories would you burn by walking for 2 hours?
2. Find the number of Calories a person would burn by walking for 2 hours and bike riding for 3 hours.
3. Explain how you found the total number of Calories.
Reading the Lesson 4. The steps for finding the value of a numerical expression are listed below. Number the steps in the correct order. _____ Find the value of all powers. _____ Add and subtract in order from left to right. _____ Simplify the expressions inside grouping symbols. _____ Multiply and divide in order from left to right. 5. Using the order of operations, explain how you would find the value of (7 5) 22 8.
6. How would the value of (7 5) 22 8 differ if you added the 8 before you divided by 4?
Helping You Remember 7. Using only operation symbols and grouping symbols, write the order of operations.
© Glencoe/McGraw-Hill
24
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment Lesson 1–5
Operations Puzzles Now that you have learned how to evaluate an expression using the order of operations, can you work backward? In this activity, the value of the expression will be given to you. It is your job to decide what the operations or the numbers must be in order to arrive at that value. with , , , or to make a true statement.
Fill in each 1. 48
3
3. 24
12
12 12
6
2. 30
15
36
34
4. 24
12
6
6. 45
3
8. 72
12
5. 4
16
2
8 24
7. 36
2
3
12
Fill in each
20
3 18
93
3
4
30
8
with one of the given numbers to make a true
statement. Each number may be used only once. 9. 6, 12, 24
10. 4, 9, 36
12
11. 6, 8, 12, 24
0
12. 2, 5, 10, 50
4
13. 2, 4, 6, 8, 10
50
14. 1, 3, 5, 7, 9
15. CHALLENGE Fill in each
0
1
with one of the digits from 1 through 9 to
make a true statement. Each digit may be used only once.
© Glencoe/McGraw-Hill
25
100
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention Algebra: Variables and Expressions • A variable is a symbol, usually a letter, used to represent a number. • Multiplication in algebra can be shown as 4n or 4 n. • Algebraic expressions are combinations of variables, numbers, and at least one operation.
Evaluate 35 x if x 6. 35 x 35 6 41
Replace x with 6. Add 35 and 6.
Evaluate y x if x 21 and y 35. y x 35 21 56
Replace x with 21 and y with 35. Add 35 and 21.
Evaluate 4n 3 if n 2. 4n 3 4 2 3 Replace n with 2. 83 Find the product of 4 and 2. 11 Add 8 and 3. Evaluate 4n 2 if n 5. 4n 2 4 5 2 Replace n with 5. 20 2 Find the product of 4 and 5. 18 Subtract 2 from 20.
Evaluate each expression if y 4. 1. 3 y
2. y 8
3. 4 y
4. 9y
5. 15y
6. 300y
7. y2
8. y2 18
9. y2 3 7
Evaluate each expression if m 3 and k 10. 10. 16 m
11. 4k
12. m k
13. m k
14. 7m k
15. 6k m
16. 3k – 4m
17. 2mk
18. 5k – 6m
19. 20m k
20. m3 2k2
21. k2 (2 m)
© Glencoe/McGraw-Hill
26
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills Algebra: Variables and Expressions Complete the table. Variables
Numbers
Operations
1. 5d 2c
? d, c
? 5, 2
? ,
2. 5w 4y 2s
? w, y, s
? 5, 4, 2
? , ,
3. xy 4 3m 6
? x, y, m
? 4, 3, 6
? , , ,
Evaluate each expression if a 3 and b 4. 4. 10 b
5. 2a 8
6. 4b – 5a
7. a b
8. 7a 9b
9. 8a – 9
10. b 22
11. a2 1
12. 18 2a
13. a2 b2
14. ab 3
15. 15a – 4b
16. ab 7 11
17. 36 6a
18. 7a 8b 2
Evaluate each expression if x 7, y 15, and z 8. 19. x y z
20. x 2z
21. xz 3y
22. 4x – 3z
23. z2 4
24. 6z – 5z
25. 9y (2x 1)
26. 15y x2
27. y2 4 6
28. y2 – 2x2
29. x2 30 – 18
30. 13y – zx 4
31. xz – 2y 8
32. z2 5y – 20
33. 3y 40x – 1,000
© Glencoe/McGraw-Hill
27
Mathematics: Applications and Concepts, Course 1
Lesson 1–6
Algebraic Expressions
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems Algebra: Variables and Expressions TRAVEL For Exercises 1 and 2, use the table that shows the distance between cities in Arizona.
Arizona Mileage Chart Flagstaff
Phoenix
Phoenix
136 miles
Tucson
253 miles
117 miles
Nogales
317 miles
181 miles
Tucson
Nogales
117 miles
181 miles 64 miles
64 miles
1. To find the speed of a car, use the expression d t where d represents the distance and t represents time. Find the speed of a car that travels from Phoenix to Flagstaff in 2 hours.
2. To find the time it will take for a bicyclist to travel from Nogales to Tucson, use the expression d/s where d represents distance and s represents speed. Find the time if the bicyclist travels at a speed of 16 miles per hour.
3. PERIMETER The perimeter of a rectangle can be w found using the formula 2 2w, where represents the length and w represents the width. Find the perimeter if 6 units and w 3 units.
4. PERIMETER Another formula for perimeter is 2( w). Find the perimeter of the rectangle in Exercise 3 using this formula. How do the answers compare? Explain how you used order of operations using this formula.
5. SHOPPING Write an expression using a variable that shows how much 3 pairs of jeans will cost if you do not know the price of the jeans. Assume each pair costs the same amount.
6. SHOPPING Write an expression using variables to show how much 3 plain T-shirts and 2 printed T-shirts will cost, assuming that the prices of plain and printed T-shirts are not the same.
© Glencoe/McGraw-Hill
28
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Algebra: Variables and Expressions Pre-Activity
Complete the Mini Lab at the top of page 28 in your textbook. Write your answers below.
2. Find the value of the expression if the unknown value is 4.
3. Write a sentence explaining how to evaluate an expression like the sum of some number and seven when the unknown value is given.
Reading the Lesson 4. Look up the word variable in a dictionary. What definition of the word matches its use in this lesson? If classmates use different dictionaries, compare the meanings among the dictionaries.
5. Exercise 4 of the Mini Lab uses the expression unknown value, which can also be read as "value of the unknown." In the expression value of the unknown, would the expression value of the variable mean the same thing?
Helping You Remember 6. Explain the difference between a numerical expression and an algebraic expression.
© Glencoe/McGraw-Hill
29
Mathematics: Applications and Concepts, Course 1
Lesson 1–6
1. Model the sum of five and some number.
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment What’s in a Word? Suppose you use the following code for the letters of the alphabet. A B C D E F G
1 2 3 4 5 6 7
H I J K L M N
8 9 10 11 12 13 14
O P Q R S T
U 21 V 22 W 23 X 24 Y 25 Z 26
15 16 17 18 19 20
To evaluate a word using this code, you replace each letter with its code number, then multiply. For instance, at the right you see how to find the value of the word MATH, which is 2,080. Use the code above to evaluate each word. 1. BOX
2. CUBE
3. TABLE
4. CATTLE
5. VARIABLE
6. ALGEBRA
13 (M) 1 (A) 13 20 (T) 260 8 (H) 2,080
Circle the word that has the greater value. (Hint: Do you have to evaluate the entire word, or is there a shortcut?) 7. PRINCIPAL or PRINCIPLE 9. THOUGHT or THROUGH
8. MARCH or CHARM 10. RIGHT or WRITE
Find a three-letter word that has a value as close as possible to the given number. 11. 1,000
12. 2,000
13. 3,000
14. 6,000
15. CHALLENGE What is the least possible value that you can find for a threeletter word? the greatest possible value?
© Glencoe/McGraw-Hill
30
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention Algebra: Solving Equations An equation is a sentence that contains an equals sign, =. Some equations contain variables. When you replace a variable with a value that results in a true sentence, you solve the equation. The value for the variable is the solution of the equation.
Solve m 12 15 mentally. m 12 15 Think: What number plus 12 equals 15? 3 12 15 You know that 12 3 15. m3 The solution is 3. Solve 14 – p 6 using guess and check.
Try 7. 14 – p 6 14 – 7 6 no
Try 6. 14 – p 6 14 – 6 8 no
Try 8. 14 – p 6 14 – 8 6 yes
The solution is 8 because replacing p with 8 results in a true sentence.
Identify the solution of each equation from the list given. 1. k – 4 13; 16, 17, 18
2. 31 x 42; 9, 10, 11
3. 45 24 k; 21, 22, 23
4. m – 12 15; 27, 28, 29
5. 88 41 s; 46, 47, 48
6. 34 – b 17; 16, 17, 18
7. 69 – j 44; 25, 26, 27
8. h 19 56; 36, 37, 38
Solve each equation mentally. 9. j 3 9
10. m – 5 11
11. 23 x 29
12. 31 – h 24
13. 18 5 d
14. 35 – a 25
15. y – 26 3
16. 14 n 19
17. 100 75 w
© Glencoe/McGraw-Hill
31
Mathematics: Applications and Concepts, Course 1
Lesson 1–7
Guess the value of p, then check it out.
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills Algebra: Solving Equations Solve each equation mentally. 1. 9 – m 8
2. 4 k 11
3. 23 – x 10
4. 31 – h 21
5. 18 20 – b
6. 16 z 25
7. y – 25 3
8. 7 f 15
9. 20 r 25
10. 18 – v 9
11. 26 – d 19
12. 49 – c 41
13. 45 r 59
14. 64 n 70
15. 175 w 75
True or False? 16. If 31 h 50, then h 29. 17. If 48 40 k, then k 8. 18. If 17 – x 9, then x 7. 19. If 98 – g 87, then g 11. 20. If p – 8 45, then p 51. Identify the solution of each equation from the list given. 21. s 12 17; 5, 6, 7
22. 59 – x 42; 15, 16, 17
23. 24 – k 3; 21, 22, 23
24. h – 15 31; 44, 45, 46
25. 69 50 s; 17, 18, 19
26. 34 – b 13; 20, 21, 22
27. 66 – d 44; 21, 22, 23
28. h 39 56; 15, 16, 17
29. 54 f 70; 16, 17, 18
30. 47 72 – b; 25, 26, 27
31. 28 v 92; 64, 65, 66
32. 56 c 109; 52, 53, 54
© Glencoe/McGraw-Hill
32
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems Algebra: Solving Equations INSECTS For Exercises 1–3, use the table that gives the average lengths of several unusual insects in centimeters.
Insect
Length (cm)
Insect
Length (cm)
Walking stick
15
Giant water bug
6
Goliath beetle
15
Katydid
5
Giant weta
10
Silkworm moth
4
Harlequin beetle
7
Flower mantis
3
2. The equation 7 y 13 gives the length of a Harlequin beetle and one other insect. If y is the other insect, which insect makes the equation a true sentence?
3. Bradley found a silkworm moth that was 2 centimeters longer than average. The equation m – 4 2 represents this situation. Find the length of the silkworm moth that Bradley found.
4. BUTTERFLIES A Monarch butterfly flies about 80 miles per day. So far it has flown 60 miles. In the equation 80 – m 60, m represents the number of miles it has yet to fly that day. Find the solution to the equation.
5. CICADAS The nymphs of some cicada can live among tree roots for 17 years before they develop into adults. One nymph developed into an adult after only 13 years. The equation 17 – x 13 describes the number of years less than 17 that it lived as a nymph. Find the value of x in the equation to tell how many years less than 17 years it lived as a nymph.
6. BEETLES A harlequin beetle lays eggs in trees. She can lay up to 20 eggs over 2 or 3 days. After the first day, the beetle has laid 9 eggs. If she lays 20 eggs in all, how many eggs will she lay during the second and third day?
Lesson 1–7
1. The equation 15 – x 12 gives the difference in length between a walking stick and one other insect. If x is the other insect, which insect is it?
© Glencoe/McGraw-Hill
33
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Algebra: Solving Equations Pre-Activity
Complete the Mini Lab at the top of page 34 in your textbook. Write your answers below.
1. Suppose the variable x represents the number of cubes in the cup. What equation represents this situation? 2. Replace the cup with centimeter cubes until the scale balances. How many centimeter cubes did you need to balance the scale? Let x represent the cup. Model each sentence on a scale. Find the number of centimeter cubes needed to balance the scale. 3. x 1 4 4. x 3 5 5. x 7 8 6. x 2 2
Reading the Lesson 7. In the Mini Lab, how did you make the scale balance?
8. In this lesson, what makes a mathematical sentence true?
9. How are the words solve and solution related?
10. Look up the word equate in a dictionary. How does it relate to the word equation?
Helping You Remember 11. Suppose you are buying a soda for $0.60 and you are going to pay with a dollar bill. Write an equation that represents this situation. What does your variable represent?
© Glencoe/McGraw-Hill
34
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment Equation Chains In an equation chain, you use the solution of one equation to help you find the solution of the next equation in the chain. The last equation in the chain is used to check that you have solved the entire chain correctly.
1. 5 a 12,
so a
.
ab 14,
so b
16 b c,
2. 9f 36,
so f
.
.
g 13 f, so g
.
so c
.
63 g h, so h
.
14 d c,
so d
.
h i 18, so i
.
e d 3,
so e
.
j i 9,
.
a e 25 → Check:
3. m 4 8,
so j
j f 5 → Check:
so m
.
m n 12,
so n
.
v w 3,
so w
.
np 100,
so p
.
80 wx,
so x
.
q 40 p,
so q
.
w x 2y, so y
.
p q 10 r, so r
4. 18 v 12,so v
xy z 40, so z
.
r m 8 → Check:
.
.
z v 2 → Check:
5. CHALLENGE Create your own equation chain using these numbers for the variables: a 10, b 6, c 18, and d 3.
© Glencoe/McGraw-Hill
35
Mathematics: Applications and Concepts, Course 1
Lesson 1–7
Complete each equation chain.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention Geometry: Area of Rectangles The area of a figure is the number of square units needed to cover a surface. You can use a formula to find the area of a rectangle. The formula for finding the area of a rectangle is A w. In this formula, A represents area, represents the length of the rectangle, and w represents the width of the rectangle.
Find the area of a rectangle with length 8 feet and width 7 feet. Aw Area of a rectangle A87 Replace with 8 and w with 7. A 56 The area is 56 square feet.
Find the area of a rectangle with width 5 inches and length 6 inches. Aw Area of a rectangle A65 Replace with 6 and w with 5. A 30 The area is 30 square inches.
Find the area of each rectangle. 1.
2.
3.
5 ft
7 cm
4. 3 cm
6 yd
5 yd 8 ft
5. What is the area of a rectangle with a length of 10 meters and a width of 7 meters?
6. What is the area of a rectangle with a length of 35 inches and a width of 15 inches?
© Glencoe/McGraw-Hill
36
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills Geometry: Area of Rectangles Complete each problem. 1. Give the formula for finding the area of a rectangle. 2. Draw and label a rectangle that has an area of 18 square units.
3. Give the dimensions of another rectangle that has the same area as the one in Exercise 2.
4. Find the area of a rectangle with a length of 3 miles and a width of 7 miles. 5. Find the area of a rectangle with a width of 54 centimeters and a length of 12 centimeters. Find the area of each rectangle. 9 in.
7.
6 in.
14 ft
8.
10 ft
9. 2 m
10.
16 cm
Lesson 1–8
6.
32 cm
7 yd
11.
9 in.
3 yd
11 m
8 in.
12.
5 ft
12 ft
© Glencoe/McGraw-Hill
13.
15 m
24 m
14.
7 cm
7 cm
37
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems Geometry: Area of Rectangles FLOOR PLANS For Exercises 1–6, use the diagram that shows the floor
plan for a house. 7 ft
Bath
2 ft
6 ft
10 ft
Closet
13 ft
2 ft Closet
9 ft
Bedroom 1
Bedroom 2
13 ft
Hall
14 ft
Kitchen
Living/Dining Room
12 ft
18 ft
14 ft
1. What is the area of the floor in the kitchen?
2. Find the area of the living/dining room.
3. What is the area of the bathroom?
4. Find the area of Bedroom 1.
5. Which two parts of the house have the same area?
6. How much larger is Bedroom 2 than Bedroom 1?
© Glencoe/McGraw-Hill
38
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics Geometry: Area of Rectangles Pre-Activity
Complete the activity at the top of page 39 in your textbook. Write your answers below.
1. Complete the table below. Object
Squares Along the Length
Squares Along the Width
Squares Needed to Cover the Surface
flag game board
2. What relationship exists between the length and the width, and the number of squares needed to cover the surface?
Reading the Lesson
4. In order to find the area of a surface, what two measurements do you need to know?
5. On page 39, the textbook says that the area of a figure is the number of square units needed to cover a surface. If the length and width are measured in inches, in what units will the area be expressed?
6. What unit of measure is indicated by m2? How large is one unit?
Helping You Remember 7. With a partner, measure a surface in your classroom. Explain how to find its area. Then find the area in the appropriate square units.
© Glencoe/McGraw-Hill
39
Mathematics: Applications and Concepts, Course 1
Lesson 1–8
3. Look up the word area in a dictionary. Write the meaning of the word as used in this lesson.
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment Tiling a Floor The figure at the right is the floor plan of a family room. The plan is drawn on grid paper, and each square of the grid represents one square foot. The floor is going to be covered completely with tiles. 1. What is the area of the floor?
2. Suppose each tile is a square with a side that measures one foot. How many tiles will be needed?
3. Suppose each tile is a square with a side that measures one inch. How many tiles will be needed?
4. Suppose each tile is a square with a side that measures six inches. How many tiles will be needed?
Use the given information to find the total cost of tiles for the floor. 5. tile: square, 1 foot by 1 foot cost of one tile: $3.50
6. tile: square, 6 inches by 6 inches cost of one tile: $0.95
7. tile: square, 4 inches by 4 inches cost of one tile: $0.50
8. tile: square, 2 feet by 2 feet cost of one tile: $12
9. tile: square, 1 foot by 1 foot cost of two tiles: $6.99
10. tile: rectangle, 1 foot by 2 feet cost of one tile: $7.99
11. Refer to your answers in Exercises 5-10. Which way of tiling the floor costs the least? the most?
© Glencoe/McGraw-Hill
40
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 1
SCORE _____
Write the letter for the correct answer in the blank at the right of each question. 1. ALLOWANCE Juyong saves $10 of her allowance each week. Use the fourstep plan to determine how many weeks she must save to buy a $40 radio. A. 45 weeks B. 4 weeks C. 40 weeks D. 10 weeks
1.
2. LAWN CARE Luis mows lawns. The first week of spring he mowed 2 lawns. The second week he mowed 4 lawns. The third week he mowed 6 lawns. If this pattern continues, how many lawns did Luis mow the fourth week? F. 8 G. 12 H. 5 I. 10
2.
3. Find the area of the rectangle. A. 15 m2 B. 2 m2 C. 30 m2 D. 50 m2
3.
10 m 5m
4. Find the next three numbers in the pattern 2, 4, 6, 8, F. 16, 32, 64 G. 10, 12, 14 H. 8, 10, 12
,
, . I. 9, 10, 11
4.
For Questions 5–7, tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. B. 2, 3, 5
C. 3, 5
6. 55 F. 5, 11
G. 5, 10
H. 2, 5, 10
7. 800 A. 2, 4, 5, 10
B. 2, 400
C. 2, 4, 5
8. Write 3 · 3 using an exponent. F. 2 · 3 G. 32
H. 3 · 2
9. Evaluate 23. A. 8
C. 9
B. 6
D. 5
5.
I. 5
6.
D. 2, 4, 10
7.
I. 9
8.
D. 5
9.
10. Write 54 as a product. F. 5 · 4 G. 4 · 4 · 4 · 4 · 4
H. 5 · 5 · 5 · 5
11. Evaluate 2 42 3. A. 26 B. 29
C. 61
D. 13
11.
12. Find the value of 5 7 4. F. 48 G. 33
H. 574
I. 39
12.
© Glencoe/McGraw-Hill
41
I. 625
10.
Mathematics: Applications and Concepts, Course 1
Assessment
5. 15 A. 3
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 1 13. Find the value of 21 4 5 2. A. 81 B. 40
C. 74
14. Find the value of 58 2 3 1. F. 50 G. 53
H. 169
15. Find the value of 4 3 9 8. A. 84 B. 168
C. 384
16. Evaluate cd if c 9 and d 8. F. 98 G. 17 17. Evaluate 2 3n if n 5. A. 37 B. 10
(continued)
D. 15
I. 224
13.
14.
D. 59
15.
H. 72
I. 89
16.
C. 25
D. 17
17.
I. 18
18.
18. Evaluate s t u if s 12, t 8, and u 20. F. 10 G. 0 H. 15
For Questions 19–21, find the prime factorization of each number. 19. 14 A. 2 7
B. 1 14
C. 2 2 3
20. 26 F. 1 13
G. 1 26
H. 2 13
21. 200 A. 2 2 5 5 C. 2 100
D. 2 2 7
19.
I. 2 2 7
20.
B. 2 2 2 5 5 D. 4 25
21.
22. Which number is the solution of x 4 3? F. 12 G. 1 H. 7
I. 6
22.
23. Which number is the solution of 14 y 4? A. 12 B. 20 C. 18
D. 10
23.
I. 55
24.
D. 150
25.
24. Solve n 27 29 mentally. F. 2 G. 56
H. 3
25. Solve 30 f 5 mentally. A. 25 B. 35
C. 45
Bonus Find the greatest prime number that is less than 29.
© Glencoe/McGraw-Hill
42
B:
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2A
SCORE _____
Write the letter for the correct answer in the blank at the right of each question. 1. TRAVEL A train is traveling at an average speed of 55 miles per hour. Use the four-step plan to find how far it will travel in 5 hours. A. 60 miles B. 275 miles C. 11 miles D. 50 miles
1.
2. MONEY Amad went to the fair four days in a row. The first day he spent $2. The second day he spent $4. The third day he spent $8. If this pattern continues, how much did Amad spend on his fourth day? F. $16 G. $10 H. $12 I. $14
2.
3. Find the area of the rectangle. A. 10 cm2 B. 20 cm2 C. 21 cm2 D. 58 cm2
3.
3 cm
7 cm
4. Find the next three numbers in the pattern 17, 26, 35, ? , ? , ? . F. 44, 53, 62 G. 54, 63, 72 H. 42, 55, 68 I. 52, 78, 87
4.
For Questions 5–7, tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. B. 5
C. 2, 5
6. 63 F. 3
G. 3, 3, 7
H. 3, 9
7. 234 A. 2, 3, 4, 6, 9
B. 2, 3, 6, 9
C. 2, 3
8. Write 9 · 9 · 9 using an exponent. F. 39 G. 3 · 9
H. 93
9. Evaluate 53. A. 125
C. 243
B. 15
10. Write 85 as a product. F. 8 · 8 · 8 · 8 · 8 · 8 H. 8 · 8 · 8 · 8 · 8
G. 8 · 5 I. 5 · 8
11. Evaluate 4 · 23 5. A. 24 B. 3
C. 19
© Glencoe/McGraw-Hill
43
D. 2, 5, 10
I. 7, 9
5.
6.
D. 2, 3, 6
7.
I. 9 · 3
8.
D. 25
9.
10.
D. 27
11.
Mathematics: Applications and Concepts, Course 1
Assessment
5. 10 A. 2
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2A
(continued)
12. Find the value of 18 2 3. F. 39 G. 60
H. 23
I. 24
12.
13. Find the value of 16 3 2 5. A. 130 B. 23
C. 55
D. 75
13.
14. Find the value of 11 12 24 ÷ 3. F. 140 G. 52
H. 220
15. Find the value of 28 13 2 1. A. 11 B. 31
C. 45
16. Evaluate ab if a 91 and b 8. F. 918 G. 99
H. 728
17. Evaluate 42 5r if r 4. A. 148 B. 41
C. 33
D. 22
17.
18. Evaluate x ÷ y z if x 32, y 4, and z 2. F. 6 G. 16 H. 10
I. 34
18.
I. 139
D. 3
I. 891
14.
15.
16.
For Questions 19–21, find the prime factorization of each number. 19. 50 A. 2 25
B. 2 5 5
C. 1 50
20. 37 F. 9 4
G. 2 2 3 3
H. 3 3 4
21. 104 A. 4 26
B. 2 4 13
D. 5 10
19.
I. 1 37
20.
C. 2 2 2 13 D. 8 13
21.
22. Which number is the solution of x 6 24? F. 4 G. 18 H. 20
I. 30
22.
23. Which number is the solution of 23 18 n? A. 5 B. 6 C. 41
D. 15
23.
24. Solve n 8 16 mentally. F. 8 G. 128
H. 2
I. 24
24.
25. Solve 28 x 4 mentally. A. 32 B. 24
C. 7
D. 112
25.
Bonus Find the value of the expression 8 32 (9 5) 2 10. B:
© Glencoe/McGraw-Hill
44
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2B
SCORE _____
Write the letter for the correct answer in the blank at the right of each question. 1. SHOPPING A television sells for $495 plus tax. The tax is $24. Use the fourstep plan to find the total cost of the television. A. $471 B. $419 C. $529 D. $519
1.
2. JOGGING Wendie decided to start training for track. The first day, she jogged 6 laps. The second day, she jogged 12 laps. The third day, she jogged 18 laps. If this pattern continues, how many laps did she jog on the fourth day? F. 22 G. 24 H. 36 I. 30
2.
3. Find the area of the rectangle. A. 26 mm2 B. 13 mm2 C. 30 mm2 D. 109 mm2
3.
10 mm 3 mm
4. Find the next three numbers in the pattern 1, 5, 9, 13, ? , ? , ? . F. 3, 7, 9 G. 15, 17, 19 H. 17, 21, 25 I. 19, 25, 31
4.
For Questions 5–7, tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. B. 2, 4, 6
C. 2, 8
6. 170 F. 2
G. 5
H. 2, 5
7. 780 A. 2, 3, 5, 6
B. 2, 3, 4, 5
C. 2, 3, 4, 5, 6, 10
D. 4
8. Write 5 · 5 · 5 · 5 using an exponent. F. 45 G. 54
H. 5 · 4
9. Evaluate 105. A. 10,000
C. 1,000,000
B. 50
5.
I. 2, 5, 10
6.
D. 2, 3, 4, 6
7.
I. 4 · 5
D. 100,000
8.
9.
10. Write 43 as a product. F. 4 · 3 G. 3 · 3 · 3 · 3
H. 4 · 4 · 4
11. Evaluate 52 3 2. A. 73 B. 28
C. 25
D. 60
11.
12. Find the value of 20 8 ÷ 4. F. 48 G. 3
H. 22
I. 18
12.
© Glencoe/McGraw-Hill
45
I. 4 · 4 · 4 · 4
10.
Mathematics: Applications and Concepts, Course 1
Assessment
5. 16 A. 2, 4
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2B 13. Find the value of 28 6 4 2. A. 134 B. 50
C. 68
14. Find the value of 51 2 13 14. F. 1,323 G. 3
H. 39
15. Find the value of 42 3 10 ÷ 5. A. 23 B. 7
C. 124
16. Evaluate mn if m 23 and n 5. F. 115 G. 235
H. 28
17. Evaluate 3 2m if m 6. A. 30 B. 15
C. 29
(continued)
D. 40
I. 651
D. 84
I. 523
18. Evaluate a b c if a 20, b 10, and c 5. F. 5 G. 35 H. 25
13.
14.
15.
16.
D. 11
17.
I. 22
18.
For Questions 19–21, find the prime factorization of each number. 19. 30 A. 2 3 5
B. 5 6
C. 3 10
20. 47 F. 2 2 2 2 3 H. 4 12
G. 2 23 I. 1 47
21. 68 A. 4 17
C. 1 2 17
B. 2 2 17
D. 2 15
19.
20.
D. 2 34
21.
22. Which number is the solution of x 7 42? F. 29 G. 35 H. 49
I. 52
22.
23. Which number is the solution of 24 14 m? A. 10 B. 38 C. 28
D. 18
23.
24. Solve 5 n 14 mentally. F. 10 G. 19
H. 8
I. 9
24.
25. Solve 36 r 9 mentally. A. 4 B. 27
C. 5
D. 45
25.
Bonus Find the value of the expression 4 23 (8 5) 2 7. © Glencoe/McGraw-Hill
46
B:
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2C
SCORE _____
1. SWIMMING On Saturday, 221 adults were at the swim club. On Sunday, there were 198 adults. How many more adults were at the swim club on Saturday than on Sunday?
1.
2. Complete the pattern: 7, 10, 13, 16,
2.
,
,
3. Find the area of the rectangle.
. 16 yd
3.
2 yd
Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify each number as even or odd. 4. 20
4.
5. 81
5.
6. 1,300
6.
7. 4,896
7.
8. 11 · 11
8.
9. 5 · 5 · 5
9.
10. 10 · 10 · 10 · 10
10.
11. 8 · 8 · 8
11.
Write each power as a product. Then find the value of the product. 12. 32
12.
13. 43
13.
14. 105
14.
15. five squared
15.
© Glencoe/McGraw-Hill
47
Mathematics: Applications and Concepts, Course 1
Assessment
Write each product using an exponent. Then find the value of the power.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2C
(continued)
Find the prime factorization of each number. 16. 21
16.
17. 31
17.
18. 88
18.
19. 100
19.
Find the value of each expression. 20. 5 20 7
20.
21. 8 (29 11)
21.
22. 3 4 2 2
22.
23. 55 ÷ 5 23
23.
Evaluate each expression if a 3, b 10, and c 6. 24. 12 b
24.
25. 2a 5
25.
26. 2c 3a
26.
27. c2 3a b
27.
Identify the solution of each equation from the list given. 28. 14 d 20; 6, 7, 8
28.
29. p 11 17; 26, 27, 28
29.
Solve each equation mentally. 30. j 3 13
30.
31. m 5 10
31.
32. 14 h 12
32.
33. 20 k 25
33.
Bonus Find the value of the expression 36 32 (15 3) 8 1. B: © Glencoe/McGraw-Hill
48
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2D
SCORE _____
1. TENNIS On Saturday, 138 adults were at the tennis club. On Sunday, there were 187 adults. How many more adults were at the tennis club on Sunday than on Saturday?
1.
2. Complete the pattern: 3, 7, 11, 15,
2.
,
,
.
3. Find the area of the rectangle.
12 m
3.
8m
Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify each number as even or odd. 4. 24
4.
5. 65
5.
6. 1,100
6.
7. 2,925
7.
8. 12 · 12
8.
9. 3 · 3 · 3
9.
10. 10 · 10 · 10
10.
11. 4 · 4 · 4 · 4 · 4
11.
Write each power as a product. Then find the value of the product. 12. 112
12.
13. 33
13.
14. 106
14.
15. nine squared
15.
© Glencoe/McGraw-Hill
49
Mathematics: Applications and Concepts, Course 1
Assessment
Write each product using an exponent. Then find the value of the power.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 2D
(continued)
Find the prime factorization of each number. 16. 15
16.
17. 29
17.
18. 99
18.
19. 78
19.
Find the value of each expression. 20. 8 12 3
20.
21. 7 (31 10)
21.
22. 4 5 3 2
22.
23. 9 42 ÷ 8
23.
Evaluate each expression if x 2, y 12, and z 5. 24. 15 y
24.
25. 3z 4
25.
26. 5x 2z
26.
27. x2 2y z
27.
Identify the solution of each equation from the list given. 28. 12 m 30; 17, 18, 19
28.
29. k 9 31; 40, 41, 42
29.
Solve each equation mentally. 30. d 4 14
30.
31. p 7 9
31.
32. 20 j 17
32.
33. 30 h 37
33.
Bonus Find the value of the expression 32 22 (20 5) 10 2. © Glencoe/McGraw-Hill
B:
50
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 3
SCORE _____
1. PIZZA A pizza parlor sold 78 pizzas on Monday, 54 pizzas on Tuesday, and 89 pizzas on Wednesday. How many more pizzas were sold on Wednesday than on Tuesday?
1.
2. MONEY The McWilliams family wants to buy a home theater that costs $580. They plan to pay in four equal payments. What will be the amount of each payment?
2.
3. Find the area of the rectangle.
3.
18 ft 9 ft
4. TECHNOLOGY A computer screen measures 12 inches by 14 inches. What is the area of the viewing screen?
4.
For Questions 5–7, tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify each number as even or odd. 5. 70
5.
6. 2,925
6.
7. 103,428
7.
8. 12 · 12
8.
9. 3 · 3 · 3 · 3 · 3
9.
For Questions 10 and 11, write each power as a product. Then find the value of the product. 10. 103
10.
11. 26
11.
12. List the factors of 56.
12.
13. Tell whether 37 is prime, composite, or neither.
13.
© Glencoe/McGraw-Hill
51
Mathematics: Applications and Concepts, Course 1
Assessment
For Questions 8 and 9, write each product using an exponent. Then find the value of the power.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Test, Form 3
(continued)
Find the prime factorization of each number. 14. 124
14.
15. 48
15.
Find the value of each expression. 16. 22 (10 2) 1
16.
17. 15 5 (32 5)
17.
Evaluate each expression if e 4, f 9, and g 5. 18. 3e g
18.
19. 4g f 2e
19.
For Questions 20–22, solve each equation mentally. 20. 17 h 25
20.
21. 16 29 y
21.
22. 45 m 12
22.
23. What is the value of 50 divided by 10 times 6 minus 15?
23.
24. CARS To find the speed of a car, use the expression d t where d represents the distance and t represents time. Find the speed of a car that travels 448 miles in 8 hours.
24.
25. Which of the numbers 4, 5, or 6 is a solution of x 5 10?
25.
Bonus Derick bought party prizes that each cost the same. He spent a total of $35. Find three possible costs per prize and the number of prizes that he could have purchased.
B:
© Glencoe/McGraw-Hill
52
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Extended Response Assessment
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. Name in order the four steps of the problem-solving plan. Tell what you do at each step.
2. Write the order of operations in your own words.
3. Mr. Berkowitz is planning the half-time show for the first football game of the season. He expects 120 band members this year and needs to determine possible marching formations.
a. Tell how to find the prime factorization of a number.
b. Find the prime factorization of 120. Show your work.
c. Give all possible rectangular formations the band can make.
a. They can borrow only one kind of tent from a selection of tents that hold 2, 3, 4, or 5 people. Explain how to use divisibility rules to find out which sizes of tents could be used to house 300 people.
b. The club is planning a night of stargazing. To spark interest, the president says that the Milky Way galaxy is about 105 light years wide. Explain how to write this number as a product. Then find the value of the product.
© Glencoe/McGraw-Hill
53
Mathematics: Applications and Concepts, Course 1
Assessment
4. The camping club is planning a trip for 300 people.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Vocabulary Test/Review algebra (p. 28) algebraic expression (p. 28) area (p. 39) base (p. 18) composite number (p. 14) cubed (p. 18) divisible (p. 10) equals sign (p. 34)
equation (p. 34) evaluate (p. 29) even (p. 10) exponent (p. 18) factor (p. 14) formula (p. 39) numerical expression (p. 24) odd (p. 10)
SCORE _____
order of operations (p. 24) power (p. 18) prime factorization (p. 15) prime number (p. 14) solution (p. 34) solve (p. 34) squared (p. 18) variable (p. 28)
Choose from the terms above to complete each sentence. 1. The _______________ is the small raised number in a power that tells how many times the base is multiplied by itself.
1.
2. When two or more numbers are multiplied, each number is called a(n) _______________ of the product.
2.
3. The value for a variable that results in a true sentence is called a(n) _______________.
3.
4. A(n) _______________ is an equation that shows a relationship 4. among certain quantities. 5. In mathematics, a(n) _______________ is a sentence that contains an equals sign.
5.
6. The _______________ is the number of square units needed to cover a surface.
6.
7. A(n) _______________ is a whole number that has exactly two factors, 1 and the number itself.
7.
8. The word _______________ means "to the third power."
8.
9. A(n) _______________ is a symbol, usually a letter, used to represent a number.
9.
10. Numbers expressed using exponents are called _______________.
10.
In your own words, define each term. 11. prime factorization
12. divisible
© Glencoe/McGraw-Hill
54
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Quiz
SCORE _____
(Lessons 1-1 and 1-2) For Questions 1 and 2, use the four-step plan to solve each problem. 1. TRAVEL On a trip to Florida, the Rodriguez family bought 4 adult plane tickets costing a total of $1,500. What was the cost of each ticket?
1.
2. MONEY Mika saved $8 each week for 20 weeks. How much did she save in all?
2.
3. Complete the pattern: 8, 13, 18, 23,
3.
,
,
.
For Questions 4 and 5, tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify each number as even or odd. 4. 60
4.
5. 855
5.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Quiz
SCORE _____
(Lessons 1-3 and 1-4) 1. List the factors of 18.
1.
2. Is 87 prime, composite, or neither?
2.
3. 13
4. 84
4.
5. 66
5.
For Questions 6 and 7, write each product using an exponent. Then find the value of the power. 6. 8 · 8
3.
7. 5 · 5 · 5 · 5
6. 7.
For Questions 8–10, write each power as a product. Then find the value of the product. 8. 23
8.
9. 104
9.
10. seven squared © Glencoe/McGraw-Hill
10.
55
Mathematics: Applications and Concepts, Course 1
Assessment
For Questions 3–5, find the prime factorization of each number.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Quiz
SCORE _____
(Lessons 1-5 and 1-6) Find the value of each expression. 1. 3 12 9
1.
2. (7 4) 3 2
2.
3. 24 6 2
3.
4. 5 4 (2 7)
4.
For Questions 5–9, evaluate each expression if m 3 and n 7. 5. n 9
5.
6. 4m 5
6.
7. n2 2m
7.
8. 3mn
8.
9. 20 8m 2
9.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Quiz
SCORE _____
(Lessons 1-7 and 1-8) Identify the solution of each equation from the list given. 1. a 12 25; 12, 13, 14
1.
2. 19 28 z; 9, 10, 11
2.
3. 3 h 20; 16, 17, 18
3.
Find the area of each rectangle. 4.
9 ft
5.
10 in.
3 ft
4. 5.
11 in.
© Glencoe/McGraw-Hill
56
Mathematics: Applications and Concepts, Course 1
Assessment
10. MULTIPLE-CHOICE TEST ITEM Find the value of 43 2b2 3 10. if b 3. A. 42 B. 37 C. 34 D. 40
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Mid-Chapter Test
SCORE _____
(Lessons 1-1 through 1-4)
Write the letter for the correct answer in the blank at the right of each question. 1. LIBRARY At the library, 2,312 books were checked out on Friday, and 3,234 books were checked out on Saturday. Late charges of $74 and $87 were collected on Friday and Saturday, respectively. Find the total amount of late charges collected. A. $13 B. 5,546 C. 922 D. $161 1. For Questions 2 and 3, tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. 2. 30 F. 2, 3, 5
G. 2, 3, 5, 6, 10
H. 2, 3, 6, 9, 10
3. 306 A. 2, 3, 6, 9
B. 2, 3, 6
C. 2, 3, 9
I. 2, 3, 5, 10
D. 17, 18
2.
3.
4. Write two to the fifth power using an exponent. Then find the value of the power. F. 52; 25 G. 2 · 5; 10 H. 25; 32 I. 25; 10 4. For Questions 5 and 6, find the prime factorization of each number. B. 3 7
C. 2 10 1
6. 60 F. 3 20
G. 2 3 5
H. 3 4 5
D. 2 3 7
I. 2 2 3 5 6.
7. TIME A train departed at 10:15 A.M. It traveled 210 miles at 70 miles per hour. How many hours did it take for the train to reach its destination?
7.
8. Complete the pattern: 11, 13, 15, 17,
8.
,
,
.
9. Is 825 even or odd?
9.
Write each product using an exponent. Then find the value of the power.
10.
10. 10 · 10
11.
11. 3 · 3 · 3 · 3
Tell whether each number is prime, composite, or neither.
12.
12. 0
13.
13. 51
14. 71
14.
15. WALKING Lucas can walk one mile in 12 minutes. At this rate, how long will it take him to walk 4 miles?
15.
© Glencoe/McGraw-Hill
5.
57
Mathematics: Applications and Concepts, Course 1
Assessment
5. 21 A. 1 21
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 1 Cumulative Review 1. Order the numbers from least to greatest: 18, 80, 12, 21
SCORE _____
1.
(Prerequisite Skill)
2. Round 2,536 to the nearest ten. (Prerequisite Skill)
2.
Add. (Prerequisite Skill) 3. 19 21
3. 4. 128 293
4.
Subtract. (Prerequisite Skill) 5. 49 32
5. 6. 501 293
6.
Multiply. (Prerequisite Skill) 7. 14 3
7. 8. 626 4
8.
Divide. (Prerequisite Skill) 9. 60 6
9. 10. 84 7
10.
For Questions 11 and 12, tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify each number as even or odd. (Lesson 1-2) 11. 54
11.
12. 69
12.
13. List the factors of 10. Then tell whether 10 is prime, composite, or neither. (Lesson 1-3)
13.
14. Write 43 as a product. Then find the value of the product.
14.
(Lesson 1-4)
15. Find the value of 3 10 (2 5). (Lesson 1-5)
15.
16. Evaluate 32s, if s 7. (Lesson 1-6)
16.
17. Evaluate 2c a b if a 7, b 1, and c 4. (Lesson 1-6)
17.
18. Find the area of the rectangle. (Lesson 1-8)
18.
5 ft 3 ft
Solve each equation mentally. (Lesson 1-7) 19. 20 n 15
19.
20. x 9 17
20.
© Glencoe/McGraw-Hill
58
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice
SCORE _____
(Chapter 1)
Part 1: Multiple Choice Instructions: Fill in the appropriate oval for the best answer.
1. On a map of Illinois, each inch represents approximately 21 miles. Helena is planning to travel from Springfield to Chicago. If the distance on the map from Springfield to Chicago is about 10 inches, about how far will she travel? (Lesson 1-1) A. 21 miles B. 10 miles C. 210 miles D. 21 inches
1.
A
B
C
D
2.
F
G
H
I
3. Which of these numbers is 210 divisible by? (Lesson 1-2) A. 2, 3, 5, 10 B. 2, 3, 5, 6, 10 C. 2, 5, 6, 10 D. 2, 5, 10
3.
A
B
C
D
4. Which number is prime? (Lesson 1-3) F. 12 G. 4 H. 15
4.
F
G
H
I
5. Find the prime factorization of 20. (Lesson 1-3) A. 4 5 B. 2 2 5 C. 2 10 D. 1 20
5.
A
B
C
D
6. Write 34 as a product. (Lesson 1-4) F. 81 G. 3 3 3 H. 3 3 3 3
6.
F
G
H
I
7. Find the value of 22 24 4 2 7. (Lesson 1-5) A. 9 B. 7 C. 6 D. 28
7.
A
B
C
D
8. Evaluate a bc if a 2, b 1, and c 4. (Lesson 1-6) F. 8 G. 7 H. 6 I. 12
8.
F
G
H
I
9. Which number is the solution of x 12 19? (Lesson 1-7) A. 7 B. 6 C. 8 D. 9
9.
A
B
C
D
10.
F
G
H
I
11.
A
B
C
D
,
I. 19
I. 3 3 3 3 3
10. Solve 32 40 m using mental math. (Lesson 1-7) F. 72 G. 7 H. 8 I. 12 11. What is the area of the rectangle? (Lesson 1-8) A. 34 mm2 B. 17 mm2 C. 145 mm2 D. 72 mm2
© Glencoe/McGraw-Hill
59
9 mm 8 mm
Mathematics: Applications and Concepts, Course 1
Assessment
2. Find the next three numbers in the pattern 250, 275, 300, , . (Lesson 1-1) F. 325, 350, 375 G. 275, 250, 225 H. 350, 400, 450 I. 305, 310, 315
NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice
(continued)
Part 2: Short Response/Grid In Instructions: Enter your grid in answers by writing each digit of the answer in a column box and then shading in the appropriate circle that corresponds to that entry. Write answers to short answer questions in the space provided.
12. Jan and 3 friends went to the skating rink. Each person rented skates for $8 and bought a snack for $3 and a soda for $2. Find the total dollars spent.
12.
0 1 2 3 4 5 6 7 8 9
(Lessons 1-1, 1-5)
13. Find the prime factorization of 81. (Lesson 1-3)
14. Evaluate 2 52 32. (Lesson 1-5)
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
13.
14.
15. Write 2 2 2 2 2 using exponents. Then find the value of the power.
15. 0 1 2 3 4 5 6 7 8 9
(Lesson 1-4)
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Part 3: Extended Response Instructions: Write your answers below or to the right of the questions.
16. MUSIC A store sells DVDs for $18 each and CDs for $14 each. (Lessons 1-2, 1-5)
a. Write an expression for the total cost of 3 DVDs and 2 CDs.
b. What is the total cost of the items?
© Glencoe/McGraw-Hill
60
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice
SCORE _____
Student Recording Sheet (Use with pages 46-47 of the Student Edition.) Multiple Choice
Part 1:
Select the best answer from the choices given and fill in the corresponding oval. 1.
A
B
C
D
4.
F
G
H
I
7.
A
B
C
D
10.
F
G
H
I
2.
F
G
H
I
5.
A
B
C
D
8.
F
G
H
I
11.
A
B
C
D
3.
A
B
C
D
6.
F
G
H
I
9.
A
B
C
D
12.
F
G
H
I
Part 2:
Short Response/Grid in
Solve the problem and write your answer in the blank. For grid in questions, also enter your answer by writing each number or symbol in a box. Then fill in the corresponding circle for that number of symbol. 13.
16.
19.
20.
14. 0 1 2 3 4 5 6 7 8 9
16.
(grid in)
17. 18. 19.
(grid in)
20.
(grid in)
21.
(grid in)
22.
(grid in)
23. 24.
Part 3:
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
21.
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
22.
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
Extended Response
Record your answers for Questions 25 and 26 on the back of this paper.
© Glencoe/McGraw-Hill
A1
Mathematics: Applications and Concepts, Course 1
Answers
15.
Standardized Test Practice Rubrics (Use to score the Extended Response questions on page 47 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 25 Rubric
Score
Specific Criteria
4
The next value in the pattern is determined to be $17. A complete and accurate explanation of the pattern is given.
3
The next value in the pattern is determined to be $17. However, the explanation is correct but not complete.
2
A complete and accurate explanation of the pattern is given, but a computational error is made in determining the next value in the pattern.
1
The next value in the pattern is given, but the explanation is incorrect or not given.
0
Response is completely incorrect.
Exercise 26 Rubric
Score
Specific Criteria
4
A complete and accurate explanation for how to find all of the prime numbers between 1 and 100 is given. The prime numbers between 1 and 100 are found to be 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Three prime numbers between 200 and 250 are given.
3
All the prime numbers between 1 and 100 are given, and three prime numbers between 200 and 250 are given. However, the explanation is correct but not complete. OR The explanation is correct and complete, but one error is made in the list of prime numbers between 1 and 100. Three prime numbers between 200 and 250 are given. OR The explanation and the list of prime numbers between 1 and 100 is correct, but one of the prime numbers between 200 and 250 is incorrect.
2
The explanation and the list of prime numbers between 1 and 100 is correct, but the prime numbers between 200 and 250 are incorrect. OR The explanation and prime numbers between 200 and 250 are correct, but there are several errors in the list of prime numbers between 1 and 100. OR The prime numbers are all correct, but the explanation is incorrect or not given.
1
Only one of the parts (explanation, list of prime numbers between 1 and 100, and three prime numbers between 200 and 250) are correct.
0
Response is completely incorrect.
© Glencoe/McGraw-Hill
A2
Mathematics: Applications and Concepts, Course 1
© Glencoe/McGraw-Hill
A3
Use only the needed information, the goals made by Brad and Denny. To find the difference, subtract 195 from 216.
216 195 21; Brad made 21 more field goals than Denny.
Plan
Solve
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
612 three-point field goals
1
Mathematics: Applications and Concepts, Course 1
4. How many field goals did the three boys make all together?
6 more field goals
3. How many more field goals did Chris make than Denny?
four-step plan.
SPORTS For Exercises 3 and 4, use the field goal table above and the
read and get a general understanding of the problem
2. Explain what you do during the first step of the problem-solving plan.
1. During which step do you check your work to make sure your answer is correct? Examine
Examine Check the answer by adding. Since 195 21 216, the answer is correct.
You know the number of field goals made. You need to find how many more field goals Brad made than Denny.
195
Explore
201
Chris
216
Brad
Denny
3-Point Field Goals
Name
High School’s top three basketball team members during last year’s season. How many more field goals did Brad make than Denny?
SPORTS The table shows the number of field goals made by Henry
4 Examine – Check the reasonableness of your solution.
3 Solve – Use your plan to solve the problem.
2 Plan – Make a plan to solve the problem and estimate the solution.
1 Explore – Read and get a general understanding of the problem.
When solving problems, it is helpful to have an organized plan to solve the problem. The following four steps can be used to solve any math problem.
A Plan for Problem Solving
Study Guide and Intervention
NAME ________________________________________ DATE ______________ PERIOD _____
64
© Glencoe/McGraw-Hill
2
11. 6, 12, 18, ___, ___, ___, ___ 24, 30, 36, 42
10. 50, 40, 45, 35, 40, 30, 35, ___, ___, ___, ___
9. 5, 15, 20, 30, 35, 45, 50, … 60
8. 81, 72, 63, 54, … 45
7. 16, 19, 22, 25, 28, 31, … 34
6. 2, 4, 8, 16, 32, …
Complete the pattern.
5. A tennis tournament starts with 16 people. The number in each round is shown in the table. How many players will be in the 4th round? 2
16 8 4 ?
Mathematics: Applications and Concepts, Course 1
25, 30, 20, 25
1st Round 2nd Round 3rd Round 4th Round
4. COMMERCIALS The highest average cost of a 30-second commercial in October, 2002 is $455,700. How much is this commercial worth per second? $15,190 per second
3. MONEY The Palmer family wants to purchase a DVD player in four equal installments of $64. What is the cost of the DVD player? $256
2. POPULATION In 1990, the total population of Sacramento, CA was 369,365. In 2000, its population was 407,018. How much did the population increase? 37,653
1. GEOGRAPHY The president is going on a campaign trip to California, first flying about 2,840 miles from Washington D.C. to San Francisco and then another 390 to Los Angeles before returning the 2,650 miles back to the capital. How many miles will the president have flown? 5,880 mi
Use the four-step plan to solve each problem.
A Plan for Problem Solving
Practice: Skills
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-1)
Lesson 1–1
© Glencoe/McGraw-Hill
A4 3
Mathematics: Applications and Concepts, Course 1
8. BUS SCHEDULE A bus stops at the corner of Elm Street and Oak Street every half hour between 9 A.M. and 3 P.M. and every 15 minutes between 3 P.M. and 6 P.M. How many times will a bus stop at the corner between 9 A.M. and 6 P.M.? 25
7. SHOPPING Josita received $50 as a gift. She plans to buy two cassette tapes that cost $9 each and a headphone set that costs $25. How much money will she have left? $7
© Glencoe/McGraw-Hill
6. PATTERNS Complete the pattern: 5, 7, 10, 14, ___, ___, ___ 19, 25, 32
4. SPORTS Samantha can run one mile in 8 minutes. At this rate, how long will it take for her to run 5 miles? 40 min
50 mi
2. How many miles is it from Klamath Falls to Crater Lake National Park?
Directions from Klamath Falls: Take U.S. Highway 97 north 21 miles, then go west on S.R. 62 for 29 miles.
90 miles of trails 26 miles of shoreline Boat tours available Open 24 hours
Visit Crater Lake National Park
5. SPORTS On a certain day, 525 people signed up to play softball. If 15 players are assigned to each team, how many teams can be formed? 35 teams
3. SPORTS Jasmine swims 12 laps every afternoon, Monday through Friday. How many laps does she swim in one week? 60 laps
1. How many more miles of trails are there than miles of shoreline in Crater Lake National Park? 64 mi
poster information about Crater Lake National Park in Oregon.
GEOGRAPHY For Exercises 1 and 2, use the
Use the four-step plan to solve each problem.
A Plan for Problem Solving
Practice: Word Problems
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill
See students’ work. 4
Mathematics: Applications and Concepts, Course 1
7. Think about the four steps in the problem-solving plan: Explore, Plan, Solve, Examine. Write a sentence about something you like to help you remember the four words. For example, “I like to explore caves.”
Helping You Remember
6. In the four-step plan for problem solving, think about the term examine. Does examine come before or after the solution? (Hint: What are you examining?) after the solution
5. If you were doing an exploratory, when do you think this would happen? Before or after the thing you were exploring? before
work.
4. Think of how you use the word explore. When was the last time you did some exploring of your own? Write a definition of the word explore that matches what you did during your exploration. Or maybe you would like to consider someone from history who was an explorer. Write a definition of the word explore that matches what that person did. See students’
Reading the Lesson
up quarters along a foot ruler and count how many are in a foot. Then multiply by 5,280.
3. Explain how you could use the answer to Exercise 1 to estimate the number of quarters in a row one mile long. Sample answer: Line
dollar, divide 84,480 by 100. The value of the pennies is $844.80.
2. Explain how to find the value of the pennies in dollars. Then find the value. Sample answer: Since there are 100 pennies in one
1. How many pennies are in a row that is one mile long? (Hint: There are 5,280 feet in one mile.) 84,480 pennies
Write your answers below.
Pre-Activity Read the introduction at the top of page 6 in your textbook.
A Plan for Problem Solving
Reading to Learn Mathematics
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-1)
Mathematics: Applications and Concepts, Course 1
Lesson 1– 1
© Glencoe/McGraw-Hill
A5
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
5
Erase r $0.55
Penc Pack ils of 1 $2.39 0
Ball-P oint Pen $3.69
Filler P Pack aper of 1 $1.29 00
Three -Rin Binde g r $4.75
Spira l No Large tebook Small $2.29 $1.59
Mathematics: Applications and Concepts, Course 1
three packs of filler paper, one pack of pencils
8. Select five items whose total cost is as close as possible to $10, but not more than $10. Sample answer: one pen,
7. Lee bought three items and spent exactly $8.99. What were the items? three-ring binder, pen, eraser
6. What is the greatest amount of filler paper that you can buy with $5? 3 packs, or 300 sheets
5. What is the greatest number of erasers you can buy with $2? 3
yes
4. Kevin has $10 and has to buy a pen and two small spiral notebooks. Will he have $2.50 left to buy lunch?
3. Rosita has $10. Can she buy a large spiral notebook and a pen and still have $5 left? no
2. Andreas wants to buy a three-ring binder and two packs of filler paper. Will $7 be enough money? no
1. Jamaal has $5. Will that be enough money to buy a large spiral notebook and a pack of pencils? yes
Use the prices at the right to answer each question.
So $5 will not be enough money.
• The notebook costs $1.59 and the pen costs $3.69. • $1 $3 $4. I have $5 $4, or $1, left. • $0.59 and $0.69 are each more than $0.50, so $0.59 $0.69 is more than $1.
There are many times when you need to make an estimate in relation to a reference point. For example, at the right there are prices listed for some school supplies. You might wonder if $5 is enough money to buy a small spiral notebook and a pen. This is how you might estimate, using $5 as the reference point.
Using a Reference Point
Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
2, 4, 6, 8, 10, 12, 14, 16, … 3, 6, 9, 12, 15, 18, 21, 24, … 4, 8, 12, … , 104, 108, 112, … 5, 10, 15, 20, 25, 30, … 6, 12, 18, 24, 30, 36, … 9, 18, 27, 36, 45, … 10, 20, 30, 40, 50, …
A whole number is divisible by: • 2 if the ones digit is divisible by 2. • 3 if the sum of the digits is divisible by 3. • 4 if the number formed by the last two digits is divisible by 4. • 5 if the ones digit is 0 or 5. • 6 if the number is divisible by both 2 and 3. • 9 if the sum of the digits is divisible by 9. • 10 if the ones digit is 0.
2, 4; even
2, 5, 10; even
3; odd
9. 665
13. A number that is divisible by both 2 and 3 is also divisible by 6.
Tell whether each sentence is sometimes, always, or never true.
5; odd
© Glencoe/McGraw-Hill
6
Mathematics: Applications and Concepts, Course 1
14. Any number that is divisible by 10 is also divisible by 2 and 5. always
always
2, 3, 4, 6, 9; even 6. 23,512 2, 4; even
3. 324
11. 7,000 2, 4, 5, 10; even 12. 24,681 3; odd
8. 268
2, 3, 4, 6; even 7. 48
10. 3,579 3; odd
5. 650
2. 93
3, 9; odd
2, 4, 5, 10; even 4. 81
1. 80
Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd.
The number 112 is even because it is divisible by 2.
2: Yes; the ones digit is divisible by 2. 3: No; the sum of the digits, 4, is not divisible by 3. 4: Yes; the number formed by the last two digits, 12, is divisible by 4. 5: No; the ones digit is not a 0 or a 5. 6: No; the number is not divisible by 2 and 3. 9: No; the sum of the digits, 4, is not divisible by 9. 10: No; the ones digit, 2, is not 0.
Tell whether 112 is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd.
Examples
Rule
A whole number is divisible by another number if the remainder is 0 when the first is divided by the second. A whole number is even if it is divisible by 2. A whole number is odd if it is not divisible by 2.
Divisibility Patterns
Study Guide and Intervention
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 1-1 and 1-2)
Lesson 1– 1
© Glencoe/McGraw-Hill
no
6. 860; 5
yes
10. 13,509; 5
no
no
5. 305; 10
no
9. 816; 3
yes
no
11. 2,847; 2
no
7. 4,672; 9
yes
3. 693; 9
yes
12. 192; 6
yes
8. 2,310; 6
yes
4. 1,974; 2
A6 2, 3, 4, 6; even
23. 33,324
2; even
20. 6,598
2, 4; even
17. 104
3, 9; odd
14. 27
3, 5, 9; odd
24. 16,335
3; odd
21. 399
5; odd
18. 205
2, 3, 5, 6, 9, 10; even
15. 90
0, 5
29. 31,45__ is divisible by 5
© Glencoe/McGraw-Hill
7
Mathematics: Applications and Concepts, Course 1
2, 5, 8
28. 5,__32 is divisible by 6
0, 2, 4, 6, 8
1, 4, 7
27. 1,25__ is divisible by 3
30. 1,679,83__ is divisible by 2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
6
26. 1,__24 is divisible by 4
25. 1__2 is divisible by 9
Use divisibility rules to find each missing digit. List all possible answers.
3; odd
22. 27,453
2, 4, 5, 10; even
19. 1,000
3, 9; odd
16. 81
2, 3, 4, 6; even
13. 24
Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. Then classify the number as even or odd.
2. 1,048; 6
1. 527; 3
Tell whether the first number is divisible by the second number.
28
31
30
31
30
© Glencoe/McGraw-Hill
4 6 24. She’ll have one bottle left.
5. RETAIL Li is stacking bottles of apple juice on the shelf at her parent’s grocery store. She has space to fit 4 bottles across and 6 bottles from front to back. She has 25 bottles to stack. Will all of the bottles fit on the shelf? Explain. No, because
4, 6
3. The total number of months in a year are divisible by which numbers? 2, 3,
1. Which month has a number of days that is divisible by 4? During a leap year, is this still true? February; no
31
8
31
30
31
30
31
Mathematics: Applications and Concepts, Course 1
Yes, because 12 9 108.
6. FARMING Sally is helping her mother put eggs into egg cartons to sell at the local farmer’s market. Their chickens have produced a total of 108 eggs for market. Can Sally package the eggs in groups of 12 so that each carton has the same number of eggs? Explain.
4. FOOD Jermaine and his father are in charge of grilling for a family reunion picnic. There will be 40 people attending. Ground beef patties come 5 to a package. How many packages of patties should they buy to provide 1 hamburger for each person? Will there by any patties left over? If so, how many? 8 packages; no
April, June, September, November; yes
2. Which months have a number of days that is divisible by both 5 and 10? During a leap year, is this still true?
31
JAN. FEB. MAR. APR. MAY JUN. JUL. AUG. SEP. OCT. NOV. DEC.
many days are in each month, excluding leap years. (Every four years, the calendar is adjusted by adding one day to February.)
MONTHS OF THE YEAR For Exercises 1–3, use the table that shows how
Divisibility Patterns
Practice: Word Problems
Practice: Skills
Divisibility Patterns
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-2)
Mathematics: Applications and Concepts, Course 1
© Glencoe/McGraw-Hill
A7
2
3
4
6
5
10
12
12
12
12
20
20
the ones digit is 0
the ones digit is 0 or 5
the number is divisible by both 2 and 3
the number formed by the last two digits is divisible by 4
the sum of the digits is divisible by 3
the ones digit is divisible by 2
because
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
sizes of computer data 9
Mathematics: Applications and Concepts, Course 1
7. Several commonplace items come in amounts that are divisible by smaller units. For example, a deck of playing cards has 4 suits of 13 cards, so 52 is divisible by 4 and 13. Name other everyday items that illustrate divisibility patterns. Sample answer: currency, time,
Helping You Remember
in meaning. Indivisible means "not divisible," "not capable of being divided."
6. The Pledge of Allegiance uses the term indivisible. How do the meanings of divisible and indivisible compare to each other? They are opposite
is divisible by
The number
5. Complete the following table.
Reading the Lesson
The sum of the digits can be divided evenly by 3.
4. the numbers that can be evenly divided by 3 (Hint: Look at both digits.)
The ones digit is 0.
3. the numbers that can be evenly divided by 10
The ones digit ends in 0 or 5.
2. the numbers that can be evenly divided by 5
The ones digit ends in 0, 2, 4, 6, or 8.
1. the numbers that can be evenly divided by 2
Describe a pattern in each group of numbers listed.
Write your answers below.
Pre-Activity Complete the Mini Lab at the top of page 10 in your textbook.
10. 2000 yes
6. 1776 yes
2. 1930 no
11. 2001 no
7. 1812 yes
3. 1960 yes
12. 2100 no
8. 1900 no
4. 1902 no
© Glencoe/McGraw-Hill
depending upon the year of birth 10
Mathematics: Applications and Concepts, Course 1
17. CHALLENGE If a person lives to be exactly 100 years old, how many leap years or parts of leap years will that person see? 24, 25, or 26,
16. George Washington was first elected president in 1789. Since 1792, United States presidential elections have been held every four years. How many presidential elections will there have been up to and including the election in the year 2000? 54
15. In 1896, the first modern Olympic games were held in Athens, Greece. After that, the officially recognized games were held every four years except for 1916, 1940, and 1944, when the world was at war. How many times were the games held from 1896 to 1992? 22
14. How many leap years were there from the Declaration of Independence in 1776 to the bicentennial celebration in 1976? (Include 1776 and 1976 in your count.) 51
13. How many leap years are there between 1901 and 2001? 25
9. 1994 no
5. 1492 yes
1. 1928 yes
Decide whether each year is a leap year. Write yes or no.
Be careful when you decide if a year is a leap year. A century year—like 1800, 1900, or 2000—is a leap year only if its number is divisible by 400.
1936 is divisible by 4 because 36 is divisible by 4. 1938 is not divisible by 4 because 38 is not divisible by 4. So 1936 was a leap year, and 1938 was not.
You probably know that a leap year has 366 days, with the extra day being February 29. Did you know that divisibility can help you recognize a leap year? That is because the number of a leap year is always divisible by 4. A number is divisible by 4 if the number formed by its tens and ones digits is divisible by 4.
Leap Years
Enrichment
Reading to Learn Mathematics
Divisibility Patterns
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 2
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill
A8
Prime
1 17
1
15
17
1
3 2 3
Except for the order, the prime factors are the same.
11. 61
P
C
C
C
© Glencoe/McGraw-Hill
1 11
15. 11
555
13. 125
11
C
C
P
Mathematics: Applications and Concepts, Course 1
2227
16. 56
9. 120
6. 23
3. 29
12. 114
2 2 11
14. 44
Find the prime factorization of each number.
C
8. 28
C
7. 54
10. 243
5. 18
C
2. 12
4. 81
1. 7 P
P
The prime factorization of 18 is 2 3 3.
Circle the prime numbers, 3 and 3.
Circle the prime number, 2. 9 is divisible by 3, because the sum of the digits is divisible by 3.
Tell whether each number is prime, composite, or neither.
6
3
Choose any pair of whole number factors of 18.
9
18
Write the number that is being factored at the top.
18 is divisible by 2, because the ones digit is divisible by 2.
Find the prime factorization of 18.
18
2 3 3
2
Composite
1 15 35
Neither
Prime or Composite?
Factors
Number
Tell whether each number is prime, composite, or neither.
11. 10
81 97
March 5
337
20. 63
© Glencoe/McGraw-Hill
12
P
Mathematics: Applications and Concepts, Course 1
24. Find the prime factorization of 81. 3 3 3 3
23. Find the prime factorization of 100. 2 2 5 5
22. Which prime number is the least prime number? 67
21. Which test scores are prime numbers? 67, 97
100
67
February 15 March 29
Test Score
Date January 28
Marisa’s History Test Scores
12. 11
8. 7 P
22233
18. 72
2333
16. 54
55
14. 25
SCHOOL For Exercises 21–24, use the table below.
5 11
19. 55
2 17
17. 34
227
15. 28
33
13. 9
C
7. 6 C
3. 2 P
Find the prime factorization of each number.
10. 9 C
6. 5 P
5. 4 C
9. 8 C
2. 1 N
1. 0 N
4. 3 P
Prime Factors
Prime Factors
Factors are the numbers that are multiplied to get a product. A product is the answer to a multiplication problem. A prime number is a whole number that has only 2 factors, 1 and the number itself. A composite number is a number greater than 1 with more than two factors.
Practice: Skills
Study Guide and Intervention Tell whether each number is prime, composite, or neither.
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-3)
Mathematics: Applications and Concepts, Course 1
© Glencoe/McGraw-Hill
50
Bulls (males)
A9
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
5. GEOMETRY To find the area of a floor, you can multiply its length times its width. The measure of the area of a floor is 49. Find the most likely length and width of the room. 7, 7
3. ANIMALS Caribou calves weigh about 13 pounds at birth. Tell whether this weight is a prime or a composite number. prime
13
125
107 180
99
kilograms
Mathematics: Applications and Concepts, Course 1
257
6. GEOMETRY To find the volume of a box, you can multiply its height, width, and length. The measure of the volume of a box is 70. Find its possible dimensions.
Sample answer: Apply divisibility rules, find the prime factorization, or use a calculator to try several numbers.
4. SPEED A wildlife biologist once found a caribou traveling at 37 miles per hour. Tell whether this speed is a prime or composite number. Explain. prime;
3 3 11
400
220
pounds
Weight
2. Write the weight of caribou cows in kilograms as a prime factorization.
centimeters
1. Which animal heights and weights are prime numbers? 43, 107
43
inches
Height at the Shoulder
Cows (females)
CARIBOU
weight of caribou.
ANIMALS For Exercises 1–3, use the table that shows the height and
one of two or more numbers that are multiplied
© Glencoe/McGraw-Hill
See students’ work.
14
Mathematics: Applications and Concepts, Course 1
6. Pick a number that has two or three digits. Explain to someone else how to use a factor tree to find the prime factors of the number. In your explanation, show how the rules of divisibility help you to do the factoring.
Helping You Remember
has more than two factors (1 and 9, and 3 and 3).
5. Is 9 a prime number or a composite number? Explain. Composite; it
factors
c. factorization the process of breaking a quantity down into
b. to factorize, or to factor to break a quantity down into factors
together
a. factor
4. The word factorization is made up of factor a verb ending a noun ending. Write a definition for each of the following mathematical terms:
Reading the Lesson
and the number.
3. For the numbers in which only one rectangle is formed, what do you notice about the dimensions of the rectangle? The dimensions are 1
13, 17, 19
2. For what numbers can only one rectangle be formed? 1, 2, 3, 5, 7, 11,
10, 12, 14, 15, 16, 18, 20
1. For what numbers can more than one rectangle be formed? 4, 6, 8, 9,
Write your answers below.
Pre-Activity Complete the Mini Lab at the top of page 14 in your textbook.
Prime Factors
Reading to Learn Mathematics
Practice: Word Problems
Prime Factors
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill
2. 42
3. 12
A10 2 units
© Glencoe/McGraw-Hill
15
2 units
4. 52
3 units
23 8 cubic units
2 units
32 9 square units
3 units
Mathematics: Applications and Concepts, Course 1
7. CHALLENGE In the space at the right, draw a model for the expression 43.
e. How many small cubes have no red paint at all? 1
d. How many small cubes have red paint on exactly one face? 6
c. How many small cubes have red paint on exactly two of their faces? 12
b. How many small cubes have red paint on exactly three of their faces? 8
a. How many small cubes are there in all? 27
6. Suppose that the entire cube is painted red. Then the cube is cut into small cubes along the lines shown.
5. What expression is being modeled? 33
Exercises 5 and 6 refer to the figure at the right.
Since we read the expression 23 as two cubed, you probably have guessed that there is also a model for this number. The model, shown at the right, is a cube with sides of length 2 units. The figure that results is made up of 8 cubic units.
1. 22
Make a model for each expression.
Have you wondered why we read the number 32 as three squared? The reason is that a common model for 32 is a square with sides of length 3 units. As you see, the figure that results is made up of 9 square units. Expression
7777 999
44 5 5 5 5 5 5
Write 24 as a product. Then find the value of the product.
25; 32
35; 243
6. 10 · 10 102; 100
53; 125
92; 81 4. 5 · 5 · 5
2. 9 · 9
12. 73 7 · 7 · 7; 343
10. 55 5 · 5 · 5 · 5 · 5; 3,125
8. 43 4 · 4 · 4; 64
22 ⴛ 52
23 ⴛ 5
© Glencoe/McGraw-Hill
15. 100
13. 40
16
3 ⴛ 72
3 ⴛ 52
Mathematics: Applications and Concepts, Course 1
16. 147
14. 75
Write the prime factorization of each number using exponents.
11. 28 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2; 256
9. 84 8 · 8 · 8 · 8; 4,096
7. 72 7 · 7; 49
Write each power as a product. Then find the value of the product.
5. 3 · 3 · 3 · 3 · 3
33; 27
1. 2 · 2 · 2 · 2 · 2
Write each product using an exponent. Then find the value of the power.
The prime factorization of 225 can be written as 3 3 5 5, or 32 52.
Write the prime factorization of 225 using exponents.
The base is 2. The exponent is 4. So, 2 is a factor 4 times. 24 2 · 2 · 2 · 2 or 16
3. 3 · 3 · 3
2,401 729
Value 16 15,625
Write 6 · 6 · 6 using an exponent. Then find the value of the power.
7 to the fourth power 9 to the third power or 9 cubed
Words 4 to the second power or 4 squared 5 to the sixth power
The base is 6. Since 6 is a factor 3 times, the exponent is 3. 6 · 6 · 6 63 or 216
74 93
42 56
Powers
A product of prime factors can be written using exponents and a base. Numbers expressed using exponents are called powers.
Powers and Exponents
Study Guide and Intervention
Enrichment
Making Models for Numbers
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 3
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 1-3 and 1-4)
Mathematics: Applications and Concepts, Course 1
© Glencoe/McGraw-Hill
7. 5 · 5 · 5 · 5
A11
63; 216
35;
243
49
12. 6 · 6 · 6 · 6
64
64; 1,296
26;
34; 81
10. 2 · 2 · 2 · 2 · 2 · 2
8. 7 · 7
72;
6. 3 · 3 · 3 · 3
18. 74 7 · 7 · 7 · 7; 2,401 20. 35 3 · 3 · 3 · 3 · 3; 243 22. 27 2 · 2 · 2 · 2 · 2 · 2 · 2; 128
17. 62 6 · 6; 36
19. 23 2 · 2 · 2; 8
21. 65 6 · 6 · 6 · 6 · 6; 7,776
Mathematics: Applications and Concepts, Course 1
Answers
17
5 ⴛ 72
22 ⴛ 32
Mathematics: Applications and Concepts, Course 1
26. 245
32 ⴛ 7
25. 63
© Glencoe/McGraw-Hill
24. 36
2 ⴛ 33
23. 54
Write the prime factorization of each number using exponents.
16. 105 10 · 10 · 10 · 10 · 10; 100,000
15. 83 8 · 8 · 8; 512
13. 38 3 · 3 · 3 · 3 · 3 · 3 · 3 · 3; 6,561 14. 25 2 · 2 · 2 · 2 · 2; 32
Write each power as a product. Then find the value of the product.
11. 6 · 6 · 6
9. 3 · 3 · 3 · 3 · 3
54;
625
44; 256
5. 4 · 4 · 4 · 4
Write each product using an exponent. Then find the value of the power.
4. 56 five to the sixth power
3. 44 four to the fourth power
2. 83 eight to the third power or eight cubed
1. 72 seven to the second power or seven squared
© Glencoe/McGraw-Hill
2 in.
18
2 in.
Mathematics: Applications and Concepts, Course 1
8. SPACE A day on Jupiter lasts about 10 hours. Write a product and an exponent to show how many hours are in 10 Jupiter days. Then find the value of the power. 10 10; 102; 100 h
7. GEOMETRY The volume of the block shown can be found by multiplying the width, length, and height. Write the volume using an exponent. Find the volume. 23; 8 in3
2 in.
6. GEOGRAPHY The area of San Bernardino County, California, the largest county in the U.S., is about 39 square miles. Write this as a product. What is the area of San Bernardino County?
3 3 3 3 3 3 3 3 3; 19,683 mi2
9 9 9 9; 6,561 km
4. SPACE The diameter of Mars is about 94 kilometers. Write 94 as a product. Then find the value of the product.
5. SPACE The length of one day on Venus is 35 Earth days. Express this exponent as a product. Then find the value of the product:
3 3 3 3 3; 243 Earth days
10 10 10 10 10 10; one million votes
3. ELECTIONS In the year 2000, the governor of Washington, Gary Locke, received about 106 votes to win the election. Write this as a product. How many votes did Gary Locke receive?
2. WEIGHT A 100-pound person on Earth would weigh about 4 · 4 · 4 · 4 pounds on Jupiter. Write 4 · 4 · 4 · 4 using an exponent. Then find the value of the power. How much would a 100-pound person weigh on Jupiter? 44; 256 lb
Powers and Exponents
Powers and Exponents 1. SPACE The Sun is about 10 · 10 million miles away from Earth. Write 10 · 10 using an exponent. Then find the value of the power. How many miles away is the Sun? 102; 100; 100 million mi
Practice: Word Problems
Practice: Skills
Write each expression in words.
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 4
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill
A12
Expression
4 7 9 8 3
to to to to to
the the the the the
third power or 4 cubed second power or 7 squared sixth power fourth power fifth power
Words
© Glencoe/McGraw-Hill
19
Mathematics: Applications and Concepts, Course 1
(5 5 5 5) and then find the value of the product (625).
7. Explain how to find the value of 54. Write the power as a product
Helping You Remember
33333
8888
96
72
43
6. Complete the following table.
factor 5 times (3 3 3 3 3).
5. In the power 35, what does the exponent 5 indicate? The base 3 is a
called a power because it is made up of a base and an exponent. The number 2 is the base. The number 5 is the exponent.
4. Describe the expression 25. In your description, use the terms power, base, and exponent. Sample answer: The expression 25 is
Reading the Lesson
3. Write the prime factorization of the number of holes made if you folded it eight times. 2 2 2 2 2 2 2 2
same as the number of folds.
2. How does the number of folds relate to the number of factors in the prime factorization of the number of holes? The number of factors is the
1. What prime factors did you record? 2s
Write your answers below.
Pre-Activity Complete the Mini Lab at the top of page 18 in your textbook.
© Glencoe/McGraw-Hill
and 3, all prime numbers are of the form 6n 1 or 6n 5.
7. CHALLENGE Look at the prime numbers that are circled in the chart. Do you see a pattern among the prime numbers that are greater than 3? What do you think the pattern is? Except for 2
6. Continue crossing out numbers as described in Steps 2–5. The numbers that remain at the end of this process are prime numbers.
5. The number 5 is prime. Circle it. Then cross out every fifth number—10, 15, 20, 25, and so on.
4. The number 4 is crossed out. Go to the next number that is not crossed out.
3. The number 3 is prime. Circle it. Then cross out every third number—6, 9, 12, and so on.
2. The number 2 is prime. Circle it. Then cross out every second number—4, 6, 8, 10, and so on.
1. The number 1 is not prime. Cross it out.
20
56
55
116
117
111
105
99
93
87
81
75
69
63
57
51
45
39
33
27
21
15
9
3
4
118
112
106
100
94
88
82
76
70
64
58
52
46
40
34
28
22
16
10
5
119
113
107
101
95
89
83
77
71
65
59
53
47
41
35
29
23
17
11
6
120
114
108
102
96
90
84
78
72
66
60
54
48
42
36
30
24
18
12
Mathematics: Applications and Concepts, Course 1
115
110
109
98
97
104
92
103
86
80
79
91
74
73
85
68
67
62
50
61
44
38
37
49
32
31
43
26
20
19 25
14
8
7 13
2
1
Erathosthenes was a Greek mathematician who lived from about 276 B.C. to 194 B.C. He devised the Sieve of Erathosthenes as a method of identifying all the prime numbers up to a certain number. Using the chart below, you can use his method to find all the prime numbers up to 120. Just follow these numbered steps.
The Sieve of Erathosthenes
Enrichment
Reading to Learn Mathematics
Powers and Exponents
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 4
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-4)
Mathematics: Applications and Concepts, Course 1
© Glencoe/McGraw-Hill
48 6 22 48 6 4 84 4 Simplify the expression inside the parentheses. Find 22. Divide 48 by 6. Subtract 4 from 8.
A13 plus
$4 $3 $4 cost of dirt $3
5. 10 14 2 17 8. 11 (9 – 22) 55
4. 8 8 4 16
7. 80 – 8 32 8
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
(4 ⴙ 5) ⴛ $4 ⴙ $3 ⴙ $4 ⴙ $16
21
7
9. 25 5 6 (12 – 4)
6. 3 3 2 4 17
3. 16 – (4 5)
cost of fertilizer $4
53
Mathematics: Applications and Concepts, Course 1
10. GARDENING Refer to Example 2. Suppose that the gardener did not buy enough flowers and goes back to the store to purchase four more packs. She also purchases a hoe for $16. Write an expression that shows the total amount she spent to plant flowers in her garden.
2. 12 3 5 9
1. 7 2 3 13
Find the value of each expression.
plus
5 1 1
Cost Per Item Number of Items Needed
The total cost of planting flowers in the garden is $27.
5 $4 $3 $4 $20 $3 $4 $23 $4 $27
Words cost of 5 flower packs Expression 5 $4
pack of flowers bag of dirt bottle of fertilizer
Item
Write and solve an expression to find the total cost of planting flowers in the garden.
48 (3 3) 22
Find the value of 48 (3 3) 22.
1. Simplify the expressions inside grouping symbols, like parentheses. 2. Find the value of all powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.
Order of Operations
Order of Operations
Study Guide and Intervention
NAME ________________________________________ DATE ______________ PERIOD _____
7
56
© Glencoe/McGraw-Hill
19. 18 72 (8 – 2) 3 8 124
17. 48 23 25 (9 – 7)
15. 43 – 24 8 61
13. 88 – 16 5 2 – 3
11. 30 (21 – 6) 4 8
9. 13 4 – 72 8 43
7. 63 9 8 15
3
22
Mathematics: Applications and Concepts, Course 1
20. (52 33) (81 9) 10 468
18. 45 9 8 – 7 2 3 12
16. 100 52 43 256
14. (2 6) 2 4 3 16
12. 6 7 (6 8)
10. 16 2 8 3 32
8. 5 6 – (9 – 4) 25
6. (8 1) 12 – 13 95
4. 17 34 – 2 49
3. 64 – 8 21 77
5. 28 (89 – 67) 50
2. 31 19 – 8 42
1. 7 – 6 5 6
Find the value of each expression.
Order of Operations
Practice: Skills
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-5)
Lesson 1– 5
© Glencoe/McGraw-Hill
A14
© Glencoe/McGraw-Hill
23
Mathematics: Applications and Concepts, Course 1
3 $2 $1 2 $2 4 $1; $15
6. MONEY A store sells barrettes for $2 each and combs for $1. Shelby buys 3 barrettes and a comb. Kendra buys 2 barrettes and 4 combs. Write an expression for the amount the two girls spent all together. Find the total amount spent.
5. MONEY Frankie orders two hamburgers and a soda for lunch. A hamburger is $3 and a soda is $1.00. Write an expression to show how much he paid for lunch. Then find the value of the expression.
2 $3 $1; $7
4. SOCCER Eduardo is 16. Eduardo’s dad takes him and his younger sister to a soccer match. Tickets are $17 for adults and $13 for children (18 and under). Write an expression for the total cost of the tickets. What is the total cost of the tickets? $17 2 $13; $43
(1 3 2) $3; $18
2. Jan takes her three children and two neighbor’s children to a matinee. All of the children are under age 13. Write an expression for the total cost of admission. How much in all did Jan pay for admission?
3. Connor (age 13), his sister (age 7), and Connor’s parents go to a movie on Saturday night. Write an expression for the total cost. What is the total cost?
(1 2) $8 $5; $29
1. Janelle (age 12) and her cousin, Marquita (age 14), go to a 7:00 P.M. show. Write an expression for the total cost of admission. What is the total cost? $8 $5; $13
Adults: $8 Children (under 13): $5 Matinee (before 6 P.M.): $3
Movie Theater Admission
admission to a movie theater.
MONEY For Exercises 1–3, use the table that shows the price of
Order of Operations
Practice: Word Problems
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill
24
Mathematics: Applications and Concepts, Course 1
Sample answer: 1. ( ); 2. 2; 3. ; 4.
7. Using only operation symbols and grouping symbols, write the order of operations.
Helping You Remember
is 11. If you do the addition before the division, the value is 1.
6. How would the value of (7 5) 22 8 differ if you added the 8 before you divided by 4? Following the order of operations, the value
22 (4). Next, divide 12 by 4. Then add 8.
5. Using the order of operations, explain how you would find the value of (7 5) 22 8. First, add 7 and 5 (12). Then, find the value of
4. The steps for finding the value of a numerical expression are listed below. Number the steps in the correct order. _____ Find the value of all powers. 2 _____ Add and subtract in order from left to right. 4 _____ Simplify the expressions inside grouping symbols. 1 _____ Multiply and divide in order from left to right. 3
Reading the Lesson
Multiply the number of Calories for each activity by the number of hours. Then, add the two products.
3. Explain how you found the total number of Calories.
2. Find the number of Calories a person would burn by walking for 2 hours and bike riding for 3 hours. 1,060 Calories
580 Calories
1. How many Calories would you burn by walking for 2 hours?
Write your answers below.
Pre-Activity Read the introduction at the top of page 24 in your textbook.
Order of Operations
Reading to Learn Mathematics
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-5)
Mathematics: Applications and Concepts, Course 1
Lesson 1– 5
© Glencoe/McGraw-Hill
A15
6. 45 3 3 9 3
8. 72 12 4 8 3 0
5. 4 16 2 8 24
7. 36 2 3 12 2 0
with one of the digits from 1 through 9 to
9 3 5 7 1 1
14. 1, 3, 5, 7, 9
2 10 5 50 50
12. 2, 5, 10, 50
4 36 9 0
10. 4, 9, 36
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
25
Mathematics: Applications and Concepts, Course 1
9 3 8 7 5 4 2 6 1 100
make a true statement. Each digit may be used only once.
15. CHALLENGE Fill in each
8 4 2 6 10 0
13. 2, 4, 6, 8, 10
24 12 8 6 4
11. 6, 8, 12, 24
24 12 6 12
9. 6, 12, 24
statement. Each number may be used only once.
with one of the given numbers to make a true
4. 24 12 6 3 18
3. 24 12 6 3 4
Fill in each
2. 30 15 3 6
with , , , or to make a true statement.
1. 48 3 12 12
Fill in each
Now that you have learned how to evaluate an expression using the order of operations, can you work backward? In this activity, the value of the expression will be given to you. It is your job to decide what the operations or the numbers must be in order to arrive at that value.
Operations Puzzles
Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
Evaluate 4n 3 if n 2.
Replace x with 21 and y with 35. Add 35 and 21.
36
60 8. y2 18
5. 15y
34
2. y 8 12
18
© Glencoe/McGraw-Hill
19. 20m k 6
16. 3k – 4m
13. m k 13
10. 16 m 19
60
26
20. m3 2k2 227
17. 2mk
14. 7m k 31
11. 4k 40
Evaluate each expression if m 3 and k 10.
7. y2 16
4. 9y
1. 3 y 7
Evaluate each expression if y 4.
4n 2 4 5 2 Replace n with 5. 20 2 Find the product of 4 and 5. 18 Subtract 2 from 20.
Evaluate 4n 2 if n 5.
1,200
16
21. k2 (2 m) 20
18. 5k – 6m 32
15. 6k m 63
12. m k 30
9. y2 3 7 37
6. 300y
3. 4 y
Mathematics: Applications and Concepts, Course 1
Evaluate y x if x 21 and y 35.
Replace x with 6. Add 35 and 6.
4n 3 4 2 3 Replace n with 2. 83 Find the product of 4 and 2. 11 Add 8 and 3.
y x 35 21 56
35 x 35 6 41
Evaluate 35 x if x 6.
• A variable is a symbol, usually a letter, used to represent a number. • Multiplication in algebra can be shown as 4n or 4 n. • Algebraic expressions are combinations of variables, numbers, and at least one operation.
Algebra: Variables and Expressions
Study Guide and Intervention
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-5 and 1-6)
Lesson 1– 5
© Glencoe/McGraw-Hill
? w, y, s
? x, y, m
2. 5w 4y 2s
3. xy 4 3m 6
A16
17. 36 6a
16. ab 7 11 89
? 4, 3, 6
? 5, 4, 2
? 5, 2
3
15
© Glencoe/McGraw-Hill
27
32. z2 5y – 20
31. xz – 2y 8 34
4 6 249
33. 3y 40x – 1,000 11,600
30. 13y – zx 4 181
27.
Mathematics: Applications and Concepts, Course 1
119
29. x2 30 – 18 61
28. y2 – 2x2 127
274
26. 15y
9
25. 9y (2x 1) y2
24. 6z – 5z 8
23. z2 4 16
22. 4x – 3z 4
x2
21. xz 3y 101
20. x 2z 23
19. x y z 30
18. 7a 8b 2 85
15. 15a – 4b 29
12. 18 2a
9. 8a – 9
1
? , , ,
? , ,
? ,
Operations
6. 4b – 5a
Numbers
Evaluate each expression if x 7, y 15, and z 8.
2
14. ab 3 4
11. a2 1 10
13. a2 b2 144
88
8. 7a 9b 756
7. a b 12
10. b 22
5. 2a 8 14
4. 10 b 14
Evaluate each expression if a 3 and b 4.
? d, c
Variables
1. 5d 2c
Algebraic Expressions
Complete the table.
Algebra: Variables and Expressions
Practice: Skills
NAME ________________________________________ DATE ______________ PERIOD _____
253 miles 317 miles
Tucson Nogales
181 miles
117 miles
Phoenix
© Glencoe/McGraw-Hill
Sample answer: 3m
5. SHOPPING Write an expression using a variable that shows how much 3 pairs of jeans will cost if you do not know the price of the jeans. Assume each pair costs the same amount.
3. PERIMETER The perimeter of a rectangle can be w found using the formula 2 2w, where represents the length and w represents the width. Find the perimeter if 6 units and w 3 units. 18 units
68 mph
28
Nogales 64 miles
181 miles
Mathematics: Applications and Concepts, Course 1
Sample answer: 3x ⴙ 2y
6. SHOPPING Write an expression using variables to show how much 3 plain T-shirts and 2 printed T-shirts will cost, assuming that the prices of plain and printed T-shirts are not the same.
18 units; equal; Add inside the parentheses and then multiply.
4. PERIMETER Another formula for perimeter is 2( w). Find the perimeter of the rectangle in Exercise 3 using this formula. How do the answers compare? Explain how you used order of operations using this formula.
4h
2. To find the time it will take for a bicyclist to travel from Nogales to Tucson, use the expression d/s where d represents distance and s represents speed. Find the time if the bicyclist travels at a speed of 16 miles per hour.
64 miles
117 miles
Tucson
Arizona Mileage Chart
1. To find the speed of a car, use the expression d t where d represents the distance and t represents time. Find the speed of a car that travels from Phoenix to Flagstaff in 2 hours.
136 miles
Phoenix
Flagstaff
between cities in Arizona.
TRAVEL For Exercises 1 and 2, use the table that shows the distance
Algebra: Variables and Expressions
Practice: Word Problems
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-6)
Mathematics: Applications and Concepts, Course 1
Lesson 1– 6
© Glencoe/McGraw-Hill
A17
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
29
Mathematics: Applications and Concepts, Course 1
numbers and at least one operation. It has a constant value. An algebraic expression contains numbers, at least one operation, and also variables. Until you replace variables with numbers (or a set of numbers), you cannot determine the numerical value of the expression.
6. Explain the difference between a numerical expression and an algebraic expression. Sample answer: A numerical expression contains
Helping You Remember
5. Exercise 4 of the Mini Lab uses the expression unknown value, which can also be read as "value of the unknown." In the expression value of the unknown, would the expression value of the variable mean the same thing? yes
quantity that may assume any of a set of values
4. Look up the word variable in a dictionary. What definition of the word matches its use in this lesson? If classmates use different dictionaries, compare the meanings among the dictionaries. Sample answer: a
Reading the Lesson
answer: Replace the unknown value with the given value and then evaluate the expression.
3. Write a sentence explaining how to evaluate an expression like the sum of some number and seven when the unknown value is given. Sample
2. Find the value of the expression if the unknown value is 4. 9
1. Model the sum of five and some number. See students’ work.
Write your answers below.
Pre-Activity Complete the Mini Lab at the top of page 28 in your textbook.
Algebra: Variables and Expressions
Reading to Learn Mathematics
NAME ________________________________________ DATE ______________ PERIOD _____
1 2 3 4 5 6 7
H I J K L M N
8 9 10 11 12 13 14 O P Q R S T
15 16 17 18 19 20
U 21 V 22 W 23 X 24 Y 25 Z 26
427,680
6. ALGEBRA
15,120
72,000
630 4. CATTLE
2. CUBE
10. RIGHT or WRITE
neither
8. MARCH or CHARM
14. 6,000 TOT (value ⴝ 6,000)
12. 2,000 USE (value ⴝ 1,995)
© Glencoe/McGraw-Hill
30
13 (M) 1 (A) 13 20 (T) 260 8 (H) 2,080
Mathematics: Applications and Concepts, Course 1
Samples: CAB (value ⴝ 6); WOW (value ⴝ 7,935)
15. CHALLENGE What is the least possible value that you can find for a threeletter word? the greatest possible value? Answers may vary.
13. 3,000 JOT (value ⴝ 3,000)
11. 1,000 JET (value ⴝ 1,000)
Find a three-letter word that has a value as close as possible to the given number. Sample answers are given.
9. THOUGHT or THROUGH
7. PRINCIPAL or PRINCIPLE
Circle the word that has the greater value. (Hint: Do you have to evaluate the entire word, or is there a shortcut?)
5. VARIABLE
2,400
720
3. TABLE
1. BOX
Use the code above to evaluate each word.
To evaluate a word using this code, you replace each letter with its code number, then multiply. For instance, at the right you see how to find the value of the word MATH, which is 2,080.
A B C D E F G
Suppose you use the following code for the letters of the alphabet.
What’s in a Word?
Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-6)
Lesson 1– 6
© Glencoe/McGraw-Hill
Try 6. 14 – p ⱨ 6 14 – 6 8 no
Try 8. 14 – p ⱨ 6 14 – 8 6 yes
A18
47
25
5. 88 41 s; 46, 47, 48
7. 69 – j 44; 25, 26, 27
7
© Glencoe/McGraw-Hill
15. y – 26 3 29
12. 31 – h 24
9. j 3 9 6
27
16
31
16. 14 n 19
5
37
Mathematics: Applications and Concepts, Course 1
17. 100 75 w 25
14. 35 – a 25 10
11. 23 x 29 6
8. h 19 56; 36, 37, 38
6. 34 – b 17; 16, 17, 18 17
4. m – 12 15; 27, 28, 29
2. 31 x 42; 9, 10, 11 11
13. 18 5 d 13
10. m – 5 11
Solve each equation mentally.
21
17
3. 45 24 k; 21, 22, 23
1. k – 4 13; 16, 17, 18
Identify the solution of each equation from the list given.
The solution is 8 because replacing p with 8 results in a true sentence.
Try 7. 14 – p ⱨ 6 14 – 7 6 no
Guess the value of p, then check it out.
Solve 14 – p 6 using guess and check.
m 12¬ 15 Think: What number plus 12 equals 15? 3 12¬ 15 You know that 12 3 15. m¬ 3 The solution is 3.
Solve m 12 15 mentally.
An equation is a sentence that contains an equals sign, =. Some equations contain variables. When you replace a variable with a value that results in a true sentence, you solve the equation. The value for the variable is the solution of the equation.
Algebra: Solving Equations
Study Guide and Intervention
NAME ________________________________________ DATE ______________ PERIOD _____
false
8
6
7
19
© Glencoe/McGraw-Hill
31. 28 v 92; 64, 65, 66 64
29. 54 f 70; 16, 17, 18 16
27. 66 – d 44; 21, 22, 23 22
25. 69 50 s; 17, 18, 19
23. 24 – k 3; 21, 22, 23 21
21. s 12 17; 5, 6, 7 5
17
53
25
17
21
100
Mathematics: Applications and Concepts, Course 1
32. 56 c 109; 52, 53, 54
30. 47 72 – b; 25, 26, 27
28. h 39 56; 15, 16, 17
26. 34 – b 13; 20, 21, 22
24. h – 15 31; 44, 45, 46 46
22. 59 – x 42; 15, 16, 17
32
8
5
9
13
15. 175 w 75
12. 49 – c 41
9. 20 r 25
6. 16 z 25
3. 23 – x 10
Identify the solution of each equation from the list given.
20. If p – 8 45, then p 51. false
19. If 98 – g 87, then g 11. true
18. If 17 – x 9, then x 7. false
17. If 48 40 k, then k 8. true
16. If 31 h 50, then h 29.
True or False?
14. 64 n 70
13. 45 r 59
14
11. 26 – d 19
10. 18 – v 9 9
7. y – 25 3 28
8. 7 f 15
5. 18 20 – b 2
10
4. 31 – h 21
7
2. 4 k 11
1. 9 – m 8 1
Solve each equation mentally.
Algebra: Solving Equations
Practice: Skills
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-7)
Mathematics: Applications and Concepts, Course 1
Lesson 1– 7
© Glencoe/McGraw-Hill
15
10
7
Giant weta
Harlequin beetle
A19
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
Mathematics: Applications and Concepts, Course 1
6. BEETLES A harlequin beetle lays eggs in trees. She can lay up to 20 eggs over 2 or 3 days. After the first day, the beetle has laid 9 eggs. If she lays 20 eggs in all, how many eggs will she lay during the second and third day? 11 eggs
5. CICADAS The nymphs of some cicada can live among tree roots for 17 years before they develop into adults. One nymph developed into an adult after only 13 years. The equation 17 – x 13 describes the number of years less than 17 that it lived as a nymph. Find the value of x in the equation to tell how many years less than 17 years it lived as a nymph.
4 years less
4. BUTTERFLIES A Monarch butterfly flies about 80 miles per day. So far it has flown 60 miles. In the equation 80 – m 60, m represents the number of miles it has yet to fly that day. Find the solution to the equation. 20 mi
3. Bradley found a silkworm moth that was 2 centimeters longer than average. The equation m – 4 2 represents this situation. Find the length of the silkworm moth that Bradley found.
m ⴝ 6 cm
flower mantis
33
3
Flower mantis 2. The equation 7 y 13 gives the length of a Harlequin beetle and one other insect. If y is the other insect, which insect makes the equation a true sentence? giant water bug
4
Silkworm moth
5
6
Giant water bug Katydid
Length (cm)
Insect
1. The equation 15 – x 12 gives the difference in length between a walking stick and one other insect. If x is the other insect, which insect is it?
15
Goliath beetle
Length (cm)
Walking stick
Insect
of several unusual insects in centimeters.
INSECTS For Exercises 1–3, use the table that gives the average lengths
Algebra: Solving Equations
Practice: Word Problems
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill
34
Mathematics: Applications and Concepts, Course 1
c represents the change from the transaction.
11. Suppose you are buying a soda for $0.60 and you are going to pay with a dollar bill. Write an equation that represents this situation. What does your variable represent? An equation is: 1.00 ⴚ 0.60 ⴝ c;
Helping You Remember
equal." An equation shows that two values are equal; the two values are connected by an equals sign.
10. Look up the word equate in a dictionary. How does it relate to the word equation? Sample answer: The word equate means "to make
When you solve a problem, you find a solution.
9. How are the words solve and solution related? Sample answer:
values on both sides of the equals sign are the same
8. In this lesson, what makes a mathematical sentence true? when the
same number of centimeter cubes on both sides of the scale
7. In the Mini Lab, how did you make the scale balance? placed the
Reading the Lesson
6. x 2 2 0
5. x 7 8 1
4. x 3 5 2
3. x 1 4 3
students’ work.
Let x represent the cup. Model each sentence on a scale. Find the number of centimeter cubes needed to balance the scale. 3– 6. See
2. Replace the cup with centimeter cubes until the scale balances. How many centimeter cubes did you need to balance the scale? 5
1. Suppose the variable x represents the number of cubes in the cup. What equation represents this situation? 3 ⴙ x ⴝ 8
Write your answers below.
Pre-Activity Complete the Mini Lab at the top of page 34 in your textbook.
Algebra: Solving Equations
Reading to Learn Mathematics
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-7)
Lesson 1– 7
© Glencoe/McGraw-Hill
so b
so c
so d
so e
ab 14,
16 b c,
14 d c,
e d 3,
h i 18, so i j i 9,
6 .
18 .
A20 w x 2y, so y xy z 40, so z
45 .
40 .
p q 10 r, so r z ⫺ v 2 → Check: 32 30 2
32 .
9 .
8 .
10 .
30 .
© Glencoe/McGraw-Hill
35
Mathematics: Applications and Concepts, Course 1
Sample answer: 12 a 2; a b 4; 3b c; c d 6; a d 7
5. CHALLENGE Create your own equation chain using these numbers for the variables: a 10, b 6, c 18, and d 3. Answers will vary.
r ⫺ m 8 → Check: 40 32 8
q 40 p,
so x
so q
so p
np 100,
80 wx,
so n
m n 12,
so w
4. 18 v 12,so v
5 .
32 . v w 3,
so m
20 .
3. m ⫼ 4 8,
20 .
11 .
7 .
9 .
4 .
j f 5 → Check: 20 4 5
so j
63 g h, so h
8 .
so f
g 13 f, so g
2. 9f 36,
2 .
7 .
a e 25 → Check: 7 18 25
so a
1. 5 a 12,
Complete each equation chain.
In an equation chain, you use the solution of one equation to help you find the solution of the next equation in the chain. The last equation in the chain is used to check that you have solved the entire chain correctly.
Equation Chains
Enrichment
NAME ________________________________________ DATE ______________ PERIOD _____
24 square units
2.
8 ft
40 square feet
5 ft
3.
21 square centimeters
7 cm
3 cm
4.
36
Mathematics: Applications and Concepts, Course 1
6. What is the area of a rectangle with a length of 35 inches and a width of 15 inches? 525 square inches
© Glencoe/McGraw-Hill
5 yd
30 square yards
6 yd
5. What is the area of a rectangle with a length of 10 meters and a width of 7 meters? 70 square meters
1.
Find the area of each rectangle.
Aw Area of a rectangle A65 Replace with 6 and w with 5. A 30 The area is 30 square inches.
Find the area of a rectangle with width 5 inches and length 6 inches.
Aw Area of a rectangle A87 Replace with 8 and w with 7. A 56 The area is 56 square feet.
Find the area of a rectangle with length 8 feet and width 7 feet.
The area of a figure is the number of square units needed to cover a surface. You can use a formula to find the area of a rectangle. The formula for finding the area of a rectangle is A w. In this formula, A represents area, represents the length of the rectangle, and w represents the width of the rectangle.
Geometry: Area of Rectangles
Study Guide and Intervention
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lessons 1-7 and 1-8)
Mathematics: Applications and Concepts, Course 1
Lesson 1– 7
Geometry: Area of Rectangles
Geometry: Area of Rectangles
© Glencoe/McGraw-Hill
6 3
A21
54
6 in.
60 ft2
12 ft
5 ft
11 m
9 in.
Mathematics: Applications and Concepts, Course 1
Answers
© Glencoe/McGraw-Hill
12.
in2
22 m2
9. 2 m
6.
13.
10.
7.
ft2
360 m2
24 m
7 yd
14 ft
37
15 m
21 yd2
3 yd
140
10 ft
Find the area of each rectangle.
49 cm2
7 cm
7 cm
9 in.
cm2
72 in2
8 in.
512
32 cm
16 cm
Mathematics: Applications and Concepts, Course 1
14.
11.
8.
12 ft
Kitchen
Hall
Bath
6 ft
2 ft
© Glencoe/McGraw-Hill
Bedroom 2
10 ft
38
14 ft
13 ft
Mathematics: Applications and Concepts, Course 1
6. How much larger is Bedroom 2 than Bedroom 1? 13 sq ft larger
117 sq ft
4. Find the area of Bedroom 1.
252 sq ft
2. Find the area of the living/dining room.
18 ft
Living/Dining Room
5. Which two parts of the house have the same area? the 2 closets
42 sq ft
3. What is the area of the bathroom?
1. What is the area of the floor in the kitchen? 168 sq ft
14 ft
Bedroom 1
7 ft
2 ft Closet
5. Find the area of a rectangle with a width of 54 centimeters and a length of 12 centimeters. 648 cm2
4. Find the area of a rectangle with a length of 3 miles and a width of 7 miles. 21 mi2
9
13 ft
9 ft
plan for a house.
Closet
3. Give the dimensions of another rectangle that has the same area as the one in Exercise 2. Sample answer: 2 9; 2
Sample answer:
2. Draw and label a rectangle that has an area of 18 square units.
1. Give the formula for finding the area of a rectangle. A ᐉ w
FLOOR PLANS For Exercises 1–6, use the diagram that shows the floor
Practice: Word Problems
Practice: Skills
Complete each problem.
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 8
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-8)
© Glencoe/McGraw-Hill 3 8
4 8
flag game board
12 64
Squares Needed to Cover the Surface
A22
© Glencoe/McGraw-Hill
students’ work.
39
Mathematics: Applications and Concepts, Course 1
7. With a partner, measure a surface in your classroom. Explain how to find its area. Then find the area in the appropriate square units. See
Helping You Remember
square meter; a square that measures 1 meter on each side
6. What unit of measure is indicated by m2? How large is one unit? a
square inches
5. On page 39, the textbook says that the area of a figure is the number of square units needed to cover a surface. If the length and width are measured in inches, in what units will the area be expressed?
4. In order to find the area of a surface, what two measurements do you need to know? the length and the width
units equal in measure to the surface
3. Look up the word area in a dictionary. Write the meaning of the word as used in this lesson. Sample answer: the number of square
Reading the Lesson
length and width is equal to the number of squares needed to cover the surface.
2. What relationship exists between the length and the width, and the number of squares needed to cover the surface? The product of the
Squares Along the Width
Squares Along the Length
Object
1. Complete the table below.
your answers below.
Pre-Activity Complete the activity at the top of page 39 in your textbook. Write
$1,006.74
10. tile: rectangle, 1 foot by 2 feet cost of one tile: $7.99
$756
8. tile: square, 2 feet by 2 feet cost of one tile: $12
$957.60
6. tile: square, 6 inches by 6 inches cost of one tile: $0.95
© Glencoe/McGraw-Hill
Exercise 7
40
Mathematics: Applications and Concepts, Course 1
11. Refer to your answers in Exercises 5-10. Which way of tiling the floor costs the least? the most? least: tiles in Exercise 8; most: tiles in
$880.74
9. tile: square, 1 foot by 1 foot cost of two tiles: $6.99
$1,134
7. tile: square, 4 inches by 4 inches cost of one tile: $0.50
$882
5. tile: square, 1 foot by 1 foot cost of one tile: $3.50
Use the given information to find the total cost of tiles for the floor.
4. Suppose each tile is a square with a side that measures six inches. How many tiles will be needed? 1,008
3. Suppose each tile is a square with a side that measures one inch. How many tiles will be needed? 36,288
2. Suppose each tile is a square with a side that measures one foot. How many tiles will be needed? 252
252 square feet
1. What is the area of the floor?
The figure at the right is the floor plan of a family room. The plan is drawn on grid paper, and each square of the grid represents one square foot. The floor is going to be covered completely with tiles.
Tiling a Floor
Enrichment
Reading to Learn Mathematics
Geometry: Area of Rectangles
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson 1– 8
NAME ________________________________________ DATE ______________ PERIOD _____
Answers (Lesson 1-8)
Mathematics: Applications and Concepts, Course 1
Chapter 1 Assessment Answer Key Form 1 Page 41
13.
2.
B
F
14.
G
15.
A
16. 3.
4.
5.
6.
7.
17.
D
18.
G
C I
19.
20.
3.
C
4.
F
5.
D
6.
H
7.
B
8.
H
9.
A
10.
H
11.
D
A H
B H
A D
H F
B 25.
12.
F
G
24. 11.
2.
A
23. 10.
B
G
22. 9.
1.
H
D
21. 8.
D
G
B:
B 23
(continued on the next page) © Glencoe/McGraw-Hill
A23
Mathematics: Applications and Concepts, Course 1
Answers
1.
Form 2A Page 43
Page 42
Chapter 1 Assessment Answer Key Form 2A (continued) Page 44 12.
I
13.
B
14.
F
Form 2B Page 45
1.
2. 15.
D
16.
H
17.
18.
19.
20.
3.
D
4.
14.
H
15.
C
16.
F
17.
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18.
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19.
A
20.
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21.
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23.
A
24.
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6.
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G D
A 10.
24.
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25.
B
B:
G
A
9. 23.
B
D
5.
8. 22.
13.
F
7. 21.
Page 46
11.
36
© Glencoe/McGraw-Hill
12.
H A I
B:
A24
23
Mathematics: Applications and Concepts, Course 1
Chapter 1 Assessment Answer Key Form 2C Page 47 1.
Page 48
23
2.
19, 22, 25
3.
32 yd2
16.
37
17.
1 31
18.
2 2 2 11
19.
2255
20.
18
4.
2, 4, 5, 10; even
21.
26
3, 9; odd
22.
8
5.
23.
88
24.
2
25.
11
26.
21
27.
126
28.
6
29.
28
6.
2, 4, 5, 10; even
7. 2, 3, 4, 6, 9; even
9. 10.
112; 121 53;
125
104; 10,000
11.
83;
12.
3 3; 9
30.
10
31.
15
13.
4 4 4; 64
32.
2
33.
5
B:
2
512
10 10 10 10 10; 100,000 14. 15.
5 5; 25
© Glencoe/McGraw-Hill
A25
Mathematics: Applications and Concepts, Course 1
Answers
8.
Chapter 1 Assessment Answer Key Form 2D Page 49 1.
Page 50
49
2.
19, 23, 27
3.
96 m2
4.
2, 3, 4, 6, even
5.
5; odd
6.
2, 4, 5, 10; even
7.
3, 5, 9; odd
16.
35
17.
1 29
18.
3 3 11
19.
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20.
17
21.
28
22.
14
23.
11
24.
3
25.
19
26.
20
27.
33
8.
122; 144
9.
33; 27
10.
103; 1,000
28.
18
11.
45; 1,024
29.
40
30.
10
31.
16
32.
3
33.
7
B:
0
12.
11 11; 121
13.
3 3 3; 27
14.
10 10 10 10 10 10; 1,000,000
15.
9 9; 81
© Glencoe/McGraw-Hill
A26
Mathematics: Applications and Concepts, Course 1
Chapter 1 Assessment Answer Key Form 3 Page 51
35 14.
2.
$145
3.
162 ft2
4.
2 2 31
15. 2 2 2 2 3
16.
111
17.
7
18.
17
19.
21
20.
8
21.
13
22.
33
168 in.2
5.
2, 5, 10; even
6.
3, 5, 9; odd
7. 2, 3, 4, 6, 9; even
122; 144
23.
15
8. 9.
35; 243
24.
56 mph
25.
6
B:
$1– 35 prizes, $7– 5 prizes, $5– 7 prizes
10. 11.
10 10 10; 1,000 22222 2; 64
12. 1, 2, 4, 7, 8, 14, 28, 56 13.
prime
© Glencoe/McGraw-Hill
A27
Mathematics: Applications and Concepts, Course 1
Answers
1.
Page 52
Chapter 1 Assessment Answer Key Page 53, Extended Response Assessment Scoring Rubric
Level
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.
© Glencoe/McGraw-Hill
A28
Mathematics: Applications and Concepts, Course 1
Chapter 1 Assessment Answer Key Page 53, Extended Response Assessment Sample Answers In addition to the scoring rubric found on page A28, the following sample answers may be used as guidance in evaluating open-ended assessment items. 1. The four steps are explore, plan, solve, and examine. In the explore step you try to understand what the problem is asking and what information you need. In the plan step, you look at the facts you know and how they may be related. You plan a strategy for solving the problem and estimate the answer. In the solve step, you use your plan to solve the problem. If your plan doesn’t work, you revise your plans or make a new plan. In the examine step, you look at the problem again. You compare your answer to your estimate and decide if your answer makes sense. 2. First you simplify the expressions inside parentheses. Next you find the value of all the powers. Then you multiply and divide in order from left to right. Finally, you add and subtract in order from left to right. 3. a. Use a factor tree to find two factors of a number. Then find factors of these factors and the following factors until all factors are prime.
120
12
2
5 2
2
5 2 23
4. a. To use divisibility rules, look at the digits in the number 300 and follow the rules. 2: the ones digit is divisible by 2. 3: the sum of the digits is divisible by 3. 4: the number formed by the last two digits is divisible by 4. 5: the ones digit is 0 or 5. The club can use any of the types of tents. b. To write 105 as a product, you know that 10 is the base and 5 is the exponent. So 10 is a factor five times. 105 10 10 10 10 10 100,000. The Milky Way is 100,000 light years wide.
b. The prime factorization of 120 is: 120 2 2 2 3 5.
10
c. You know that the area of a rectangle is A w. You can set up an algebraic equation to find possible formations and then substitute numbers and use mental math or guess and check to solve the equation. 120 w. Start with w 2. To find , find what times 2 equals 120. Then try w 3, and so on. The possible formations are: 2 by 60, 3 by 40, 4 by 30, 5 by 24, 6 by 20, 8 by 15, and 10 by 12.
6
Answers
120 2 2 2 3 5
© Glencoe/McGraw-Hill
A29
Mathematics: Applications and Concepts, Course 1
Chapter 1 Assessment Answer Key Vocabulary Test/Review Page 54
Quiz (Lessons 1-1 and 1-2) Page 55
Quiz (Lessons 1-5 and 1-6) Page 56
1. exponent 2. factor
1.
$375
3. solution 4. formula
2.
$160
5. equation 6. area
3.
9. variable 10. powers
4.
2, 3, 4, 5, 6, 10; even
5.
3, 5, 9; odd
11. expressing a
composite number as a product of prime numbers 12. when one number
can be divided by another number and the remainder is 0
6
2.
31
3.
13
4.
41
5.
16
6.
7
7.
43
8.
63
9.
32
10.
B
28, 33, 38
7. prime number 8. cubed
1.
Quiz (Lessons 1-3 and 1-4) Page 55 1.
1, 2, 3, 6, 9, 18
2.
composite
4.
1 13 2237
5.
2 3 11
3.
6. 7.
8.
82;
64 54; 625
2 · 2 · 2; 8
Quiz (Lessons 1-7 and 1-8) Page 56 1.
13
2.
9
3.
17
4.
27 ft2
5.
110 in2
9. 10 · 10 · 10 · 10; 10,000 10. © Glencoe/McGraw-Hill
72; 49 A30
Mathematics: Applications and Concepts, Course 1
Chapter 1 Assessment Answer Key Mid-Chapter Test Page 57
D
1.
12, 18, 21, 80
2.
2,540
3.
40 421
4. 5.
2.
6.
G
7. 3.
8.
A
17 208 42 2,504
4.
H
10.
10 12
5.
B
11.
2, 3, 6, 9; even
12.
3; odd
9.
6.
I
13. 1, 2, 5, 10; composite
7.
3 hr
8.
19, 21, 23
9.
odd
10. 11. 12. 13.
102; 100 34; 81
14.
4 4 4; 64
15.
73
16.
63
17.
14
18.
15 ft2
19.
5
20.
8
neither composite
14.
prime
15.
48 min
© Glencoe/McGraw-Hill
A31
Mathematics: Applications and Concepts, Course 1
Answers
1.
Cumulative Review Page 58
Chapter 1 Assessment Answer Key Standardized Test Practice Page 59
Page 60
12. 1.
A
B
C
52
D
2.
F
G
H
I
3.
A
B
C
D
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
14. 4.
F
G
H
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
A
B
C
D
6.
F
G
H
I
7.
A
B
C
D
8.
F
G
H
I
9.
A
B
C
D
10.
F
11.
A
3333
15.
25; 32
41
I
5.
13.
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
16. a. 3 $18 2 $14 G
H
I
16. b. $82
B
C
D
© Glencoe/McGraw-Hill
A32
Mathematics: Applications and Concepts, Course 1
