M A T H N A V I G A T O R ASSESSMENT RESOURCES Percents
This work is protected by United States copyright laws and is provided solely for the use of teachers and administrators in teaching courses and assessing student learning in their classes and schools. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. Copyright 2012 Pearson Education, Inc., or its affiliate(s). All Rights Reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. The publisher hereby grants permission to reproduce these pages, in part or in whole, for classroom use only, the number not to exceed the number of students in each class. Notice of copyright must appear on all copies. For information regarding permissions, write to Pearson Curriculum Group Rights & Permissions, One Lake Street, Upper Saddle River, New Jersey 07458. America s Choice, the America s Choice A logo, Math Navigator, the Pearson logo, and the Pearson Always Learning logo are trademarks, in the U.S. and/or other countries, of Pearson Education, Inc. or its affiliate(s). ISBN: 978-1-40261-354-8 1 2 3 4 5 6 7 8 9 10 16 15 14 13 12
Contents Teacher Materials Pre-Test/Post-Test Administration........................................ 1 Checkpoint Test Administration.......................................... 4 Student Materials Lesson 5: Checkpoint 1................................................ 7 Checkpoint 1A Answer Sheet.................................. 11 Checkpoint 1 Answer Key.................................... 13 Lesson 10: Checkpoint 2............................................... 15 Checkpoint 2A Answer Sheet................................ 20 Checkpoint 2 Answer Key.................................... 22 Lesson 15: Checkpoint 3............................................... 24 Checkpoint 3A Answer Sheet................................ 28 Checkpoint 3 Answer Key.................................... 30 Image Credits............................................................. 32 PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. iii
Pre-Test/Post-Test Administration test administration Pre-test: Let students know that this test will help you determine what they already know. Explain that the module will help students learn how to solve problems on the test that seem difficult now. Post-test: Explain that this test will help you determine what students have learned about percents. Online Testing Once your testing window has started, you can begin testing. Seat students individually in front of a computer. Give each student a piece of scratch paper. Make sure that students have pencils. Have students use their access codes to log in to the pre-test. Before each student begins the test, confirm that he or she is taking the correct test. Tell students that: Each question will be displayed on the computer screen. Students should select the answer they think is best by clicking on the option choice and then clicking to confirm the choice. After students answer a question, the next question will appear on the computer screen. Students may opt to skip a question and flag it to come back to before ending the test. During the test: Observe students as they work to make sure that they are actively engaged in the testing process. Support any students who seem to find the material challenging. Encourage them to make a good estimate for any problem they find difficult. You may wish to provide manipulatives. Once students have answered all the questions, they should follow the online prompts to conclude the test. Pre-test: If any students finish the test early, group them into pairs. Give each of the students a Student Book. Tell them to read the instructions on page 1 and start working with their partners. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 1
Pre-Test/Post-Test Administration Paper-and-Pencil Test Print copies of the test and answer sheet from ARO for each student. Seat students individually. Distribute tests, answer sheets, and scratch paper. Make sure that students have #2 pencils. Instruct students to fill in the answers on their answer sheets. During the test: Observe students as they work to make sure that they are actively engaged in the testing process. Support any students who seem to find the material challenging. Encourage them to make a good estimate for any problem they find difficult. You may wish to provide manipulatives. After students finish, collect their tests, answer sheets, and scratch paper. You will need to upload students answers to the ARO system so you can analyze the results. Pre-test: If any students finish the test early, group them into pairs. Give each of the students a Student Book. Tell them to read the instructions on page 1 and start working with their partners. analyzing results Irrespective of the method (online or paper-and-pencil) that you chose to administer the test, your students must be enrolled in the ARO system in order for you to obtain computer-generated reports. These reports: Offer rich, instructionally-relevant information to teachers and administrators at the individual student, class, grade, school, and district levels Include total test score performance information and item-level analysis for each student and for all students combined Are important references in helping you assess the misconceptions your students are struggling with and decide what concepts to focus on during the module For results: Online Testing: ARO will automatically generate performance reports. Paper-and-Pencil Test: Upload students data to ARO. Once you have uploaded the data, ARO will generate performance reports. Additional information about the online test reporting can be found on ARO. Remember to give a copy of the reports to students regular mathematics teachers to help them plan subsequent instruction. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 2
Pre-Test/Post-Test Administration reflection When students finish working on the test, ask them to open the Student Book and continue with the work time or reflection task that follows. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 3
Checkpoint Test Administration preparation Make a copy of the appropriate checkpoint lesson, answer sheet, and answer key for each student. Hand out the checkpoint lesson to each student. setting the direction Lessons 5, 10, and 15 of this module are checkpoint lessons. In checkpoint lessons, students practice skills by answering multiple choice and free response questions in a test like atmosphere, and then work in groups to debug their procedural knowledge. Each checkpoint lesson is structured as follows: 1. Students work independently on Checkpoint A. 2. Students work in groups to debug their work, concentrating on procedural knowledge. 3. Students work independently on either Checkpoint B or C, based on their success with Checkpoint A. Checkpoint C is easier than Checkpoint B. 4. Students meet in groups to debug their work. The problems in the checkpoints follow up on the week s work. When students have completed Checkpoint A, collect their answer sheets before the debug group. Enter the data from Checkpoints 1A, 2A, and 3A into ARO. The report generated by ARO will help you assess whether students are on track and making sufficient progress. checkpoint A A. Work on Checkpoint A Have students work individually to answer the multiple choice and free response problems found in Checkpoint A. Have students show their work in the checkpoint lesson and then transfer their answers to the answer sheet. Give students about 10 15 minutes to complete the checkpoint. Observe students as they work in order to identify students who are struggling. You will use this information to decide how to organize the debug groups, and to determine which students will work on Checkpoint B versus Checkpoint C later in the lesson. B. Model Debug Groups in Lesson 5 The debug groups are an important step of the checkpoint lesson because they give students additional opportunities to engage in the mathematical practice of constructing viable arguments and critiquing the reasoning of others (MP3). Many of the problems in the checkpoints ask students to reason abstractly and quantitatively (MP2) and to attend to precision (MP6). The debug discussions give students a chance to refine their understanding of the content while engaging in these mathematical practices. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 4
Checkpoint Test Administration In Lesson 5 during Checkpoint 1A, you will deviate slightly from the typical checkpoint lesson structure by first modeling the debug group routine. Spend about 5 minutes modeling this routine in front of the class. Create a model group to help you. Choose students who have been willing to share their mistakes during the first four lessons. Participate as a member of the group in order to model how students should debug their work. Model the following debug group routine, which students will use in all checkpoint lessons: Hand out the answer key for Checkpoint 1A. First, group members check their answers against the answer key. Students can check their own work or they can exchange work with a partner and check each other s work. You can determine the rules for the process, or you can decide as a group. Next, members of the group should each choose a problem that they got wrong, show their work for the problem, and ask the group, What am I doing wrong? As resources, group members can use their own work, information they have from earlier lessons, the procedural help in the back of the Student Book, and the Concept Book. As a member of the debug group, model for students. Tell them that you answered A for question 3. What did you do wrong? Listen to their advice. Hopefully, some of the students will point out that a percent means one hundredth so 0.25 is 25 hundredths and that is the same as 25 percent (answer C). Ask them where they might get more help. Hopefully some of the students might answer page 94 of the procedural help page, which describes converting decimals to percents. Any students who got all of the problems right can share something interesting or helpful about their solutions. You might not want to take the time to have all the students in the model group present their work. However, emphasize to students that in their own groups, all students should present their work. Be sure to spend the time required for your students to understand the purpose and routines of the debug process. In subsequent checkpoint lessons, you may skip Part B Model Debug Groups in Lesson 5. C. Debug Groups Divide students into groups of three or four students each and have the groups follow the debug routine. Try to balance the groups with regard to strong and weak students, based on your earlier observations. In Lesson 5, integrate students from your model group into the other groups. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 5
Checkpoint Test Administration Make sure all students have a copy of the answer key for the appropriate checkpoint. Some groups may need more help than others. Spend extra time with groups that need more help, but be sure to take time to monitor all of the groups. checkpoints B and C A. Work on Checkpoint B or C Give the debug groups about 15 minutes to finish. Then assign students to work on either Checkpoint B or Checkpoint C. Checkpoint C is easier than Checkpoint B, so assign Checkpoint C to any students who had difficulty with Checkpoint A. Allow 7 10 minutes for the second checkpoint. Observe students as they work to assess whether they still need help with the material either individually or as a class. B. Debug Groups Hand out the answer key for the appropriate checkpoint. If you have time, form debug groups again and have them follow the debug routine. If you run short of time, just have students check their answers using the answer keys. Spend time with students who are struggling. reflection When you have about 2 minutes left, stop the debug groups, even if they are not finished. Have students respond to the reflection prompt in the Student Book. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 6
Checkpoint 1 5 setting the direction For each problem, circle the correct answer or write your solution. Show your work. Copy your answers to the Checkpoint 1A answer sheet. Turn in your answer sheet to your teacher and get an answer key. Check your answers against the answer key. Then have each person in your group share one problem with the group. If you got one or more problems wrong, select one and ask the group, What did I do wrong in this problem? If you answered all the problems correctly, share with the group something that you did to solve a problem that you think was interesting or unusual. To help you and the members of your group, use the procedural help on pages 93 97 at the end of the Student Book or use the Concept Book pages 173 175. Then complete either Checkpoint 1B or Checkpoint 1C as instructed by your teacher. When completed, check your answers against the answer key. Have one person in your group share a problem using the routine described above. checkpoint 1A 1. What percent of this whole square is shaded? A 0.60% B 6% C 60% D 600% 2. Write 3 10 as a percent. A 3% B 0.3% C 0.03% D 30% PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 7
Checkpoint 1 5 3. Write 0.25 as a percent. A 0.25% B 2.5% C 25% D 0.0025% 4. Write 92% as a decimal. A 0.92 B 9.2 C 92 D 0.092 5. Write 9 15 as a percent. A 6% B 0.6% C 60% D 167% 6. Write 14.27% as a decimal number. 7. Write 7 10 as a percent. 8. Write 0.048 as a percent. 9. Write 67% as a decimal. 10. Write 0.47 as a percent. Check your answers using the Checkpoint 1A Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 8
Checkpoint 1 5 checkpoint 1B 1. Write 0.071 as a percent. A 7.1% B 0.71% C 0.071% D 71% 2. Write 19.05% as a decimal number. A 0.001905 B 0.1905 C 1,905 D 190.5 3. Write 9 200 as a percent. 4. Write 0.027% as a decimal number. 5. Write 2.5 as a percent. Check your answers using the Checkpoint 1B Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 9
Checkpoint 1 5 checkpoint 1C 1. Write 0.43 as a percent. A 430% B 43% C 4.3% D 0.43% 2. Write 9 10 as a percent. A 90% B 10% C 0.9% D 9% 3. What percent of this whole square is shaded? 4. Write 47% as a decimal: 5. Write 16.69% as a decimal number. Check your answers using the Checkpoint 1C Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 10
Checkpoint 1A Answer Sheet Class Information School City State Teacher (mathematics class) Student Information Grade First name Last name Date of birth (month) (day) (year) Male o Female o How many years have you been at this school? years Do you usually speak English at home? Yes o No o Does anyone in your home usually speak a language other than English? Yes o No o PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 11
Checkpoint 1A Answer Sheet Name A B C D 1. m m m m 2. m m m m 3. m m m m 4. m m m m 5. m m m m 6. 7. 8. 9. 10. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 12
Checkpoint 1 Answer Key Checkpoint 1A 1. B 6% 2. D 30% 3. C 25% 4. A 0.92 5. C 60% 6. 0.1427 7. 70% 8. 4.8% 9. 0.67 10. 47% PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 13
Checkpoint 1 Answer Key Checkpoint 1B 1. A 7.1% 2. B 0.1905 3. 4.5% 4. 0.00027 5. 250% Checkpoint 1C 1. B 43% 2. A 90% 3. 40% 4. 0.47 5. 0.1669 PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 14
Checkpoint 2 10 setting the direction For each problem, circle the correct answer or write your solution. Show your work. Copy your answers to the Checkpoint 2A answer sheet. Turn in your answer sheet to your teacher and get an answer key. Check your answers against the answer key. Then have each person in your group share one problem with the group. If you got one or more problems wrong, select one and ask the group, What did I do wrong in this problem? If you answered all the problems correctly, share with the group something that you did to solve a problem that you think was interesting or unusual. To help you and the members of your group, use the procedural help on page 96 at the end of the Student Book or use the Concept Book pages 176 178. Then complete either Checkpoint 2B or Checkpoint 2C as instructed by your teacher. When completed, check your answers against the answer key. Have one person in your group share a problem using the routine described above. checkpoint 2A 1. 75% of 60 is: A 15 B 40 C 35 D 45 2. What percent of 125 is 10? A 0.08% B 1.25% C 8% D 12.5% PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 15
Checkpoint 2 10 Ms. Luna teaches people to drive. The table below shows how many of her pupils have passed and how many have failed the driving test. Use the table for problems 3 and 4. Driving Test Results Passed Failed Men 15 5 Women 30 0 3. What percent of the men passed? A 33% B 15% C 100% D 75% 4. What percent of the pupils who passed were men? A 75% B 33 1 % C 50% D 15% 3 5. Sally s class has 7 left handed students and 13 right handed students. What percent of the students are left handed? A 7% B 286% C 54% D 35% 6. 130% of 120 is: 7. Find 48% of $125. Write your answer to the nearest cent. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 16
Checkpoint 2 10 For problems 8, 9, and 10, use this table about flavors of frozen yogurt. Bella asked 240 students in her school about their favorite flavors of frozen yogurt. The survey results are shown here. Chocolate Vanilla Strawberry Male 69 31 21 Female 64 12 43 8. What percent of boys like chocolate yogurt? 9. What percent of girls like vanilla? 10. What percent of all 240 students like vanilla? Check your answers using the Checkpoint 2A Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 17
Checkpoint 2 10 checkpoint 2B 1. Find 20% of $16.09. Write to the nearest cent. A $0.31 B $3.22 C $3.21 D $12.87 2. Isabel s coffee shop sells regular coffee and decaffeinated coffee in the morning. She estimates that 55% of her customers order regular coffee. This week she had 860 customers. About how many orders of regular coffee did they order? A 473 B 805 C 456 D 387 3. Ann spends 10% of every day reading books. How many hours does she spend reading in one week? Mario asked 50 college students whether they own a car. The table below shows the number of students who said Yes and the number who said No. Use this table for problems 4 and 5. Yes 4. What percent of the car owners were men? No Men 30 0 Women 15 5 5. What percent of all the students said that they own a car? Check your answers using the Checkpoint 2B Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 18
Checkpoint 2 10 checkpoint 2C 1. 60% of 50 is: A 10 B 15 C 30 D 60 2. 75% of 80 is: A 50 B 75 C 65 D 60 3. Mario asked 50 college students whether or not they own a car. The table below the number of students who said Yes and the number who said No. What percent of the men own a car? Yes No Men 30 0 Women 15 5 A 66 2 % B 30% C 100% D 60% 3 4. Find 45% of $220. Write your answer to the nearest cent. 5. Jin bought some roses for her friend. She had 15 red roses and 5 white roses. What percent were white roses? Check your answers using the Checkpoint 2C Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 19
Checkpoint 2A Answer Sheet Class Information School City State Teacher (mathematics class) Student Information Grade First name Last name Date of birth (month) (day) (year) Male o Female o How many years have you been at this school? years Do you usually speak English at home? Yes o No o Does anyone in your home usually speak a language other than English? Yes o No o PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 20
Checkpoint 2A Answer Sheet Name A B C D 1. m m m m 2. m m m m 3. m m m m 4. m m m m 5. m m m m 6. 7. 8. 9. 10. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 21
Checkpoint 2 Answer Key Checkpoint 2A 1. D 45 2. C 8% 3. D 75% 4. B 33 1 3 % 5. D 35% 6. 156 7. $60.00 8. 57.025% or about 57% 9. 10.08% or about 10% 10. 17.92 or about 18% PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 22
Checkpoint 2 Answer Key Checkpoint 2B 1. B $3.22 2. A 473 3. 16.8 hours 4. 66 2 3 % 5. 90% Checkpoint 2C 1. C 30 2. D 60 3. C 100% 4. $99.00 5. 25% PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 23
Checkpoint 3 15 setting the direction For each problem, circle the correct answer or write your solution. Show your work. Copy your answers to the Checkpoint 3A answer sheet. Turn in your answer sheet to your teacher and get an answer key. Check your answers against the answer key. Then have each person in your group share one problem with the group. If you got one or more problems wrong, select one and ask the group, What did I do wrong in this problem? If you answered all the problems correctly, share with the group something that you did to solve a problem that you think was interesting or unusual. To help you and the members of your group, use the procedural help on page 97 at the end of the Student Book or use the Concept Book pages 179 183. Then complete either Checkpoint 3B or Checkpoint 3C as instructed by your teacher. When completed, check your answers against the answer key. Have one person in your group share a problem using the routine described above. checkpoint 3A 1. 55 is increased by 30%. Find the new amount. A 55.65 B 71 1 2 C 16.50 D 85 2. 75 is decreased by 25%. Find the new amount. A 18.75 B 37.78 C 56.25 D 50 3. Find 22 percent of 12.5. A 25 B 9.75 C 34.5 D 2.75 PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 24
Checkpoint 3 15 4. The average length of a business phone call changed from 30 seconds to 45 seconds. Is this change an increase or decrease? What is the percent change? A Increase, 50% B Increase, 150% C Increase, 40% D Increase, 60% 5. The weight of sand in a bucket changes from 37.5 kg to 51 kg. Is this change an increase or decrease? What is the percent change? A Increase, 36% B Decrease, 36% C Increase, 26.47% D Decrease, 26.47% 6. The price of a pair of socks changed from $7.50 to $10.20. Is this change an increase or decrease? What is the percent change? 7. The amount of time it takes to make a sandwich changes from 50 seconds to 15 seconds. Is this change an increase or decrease? What is the percent change? 8. In a dart game, Angela scored 24 points. Her team scored 80 points in total. What percent of the team s score did Angela score? 9. Mr. Okawa and his friends went to a restaurant for lunch. The total cost was $90, and he paid $27. What percent of the cost did Mr. Okawa pay? Check your answers using the Checkpoint 3A Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 25
Checkpoint 3 15 checkpoint 3B 1. Mrs. Abir s school raised $2,580 last year during the annual fund raising campaign. This year s target amount is 15% higher than last year s total. How much does the school have to raise this year to meet the new goal? Round to the nearest dollar if necessary. A $2,967 B $387 C $2,595 D $2,730 2. Jong ordered chicken to be delivered. The bill was $7.77. Including a tip, he paid $9.00. What percent tip did he give? Round to the nearest percent. A 1% B 16% C 30% D 14% 3. Misha worked for five hours at the movie theater. He worked two hours at the concession stand and three hours at the ticket booth. What percent of the time did he sell tickets? 4. Mrs. Lopez farm sells several kinds of vegetables. This year the farm sold 100,000 pounds of vegetables, including 3,580 pounds of carrots. What percent of the total vegetables sold were carrots? 5. The average length of a phone call in a company changed from 44 seconds to 55 seconds. Say whether this change is an increase or decrease, then find the percent of change. Check your answers using the Checkpoint 3B Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 26
Checkpoint 3 15 checkpoint 3C 1. Find the number that when decreased by 10% becomes 81. A 89.1 B 90 C 91% D 72.9% 2. 68 is decreased by 50%. Find the new number. A 34 B 51 C 136 D 18 3. 36 is increased by 20%. Find the new amount. 4. Ms. Luna grows flowers in her garden. The garden has 60 plants total, and 42 are lilies. What percent of the flowers are lilies? 5. Yesterday s soccer game was between England and Mexico. The stadium holds 100,000 people, and 89,700 attended the game. What percent of the seats were taken? Check your answers using the Checkpoint 3C Answer Key. Then share one problem with the group. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 27
Checkpoint 3A Answer Sheet Class Information School City State Teacher (mathematics class) Student Information Grade First name Last name Date of birth (month) (day) (year) Male o Female o How many years have you been at this school? years Do you usually speak English at home? Yes o No o Does anyone in your home usually speak a language other than English? Yes o No o PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 28
Checkpoint 3A Answer Sheet Name A B C D 1. m m m m 2. m m m m 3. m m m m 4. m m m m 5. m m m m 6. 7. 8. 9. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 29
Checkpoint 3 Answer Key Checkpoint 3A 1. B 71 1 2 2. C 56.25 3. D 2.75 4. A Increase, 50% 5. A Increase, 36% 6. Increase, 36% 7. Decrease, 70% 8. 30% 9. 30% PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 30
Checkpoint 3 Answer Key Checkpoint 3B 1. A $2,967 2. B 16% 3. 60% 4. 3.58% 5. Increase, 25% Checkpoint 3C 1. B 90 2. A 34 3. 43.2 4. 70% 5. 89.7% PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 31
Image Credits Grateful acknowledgement is made to the following for copyrighted material: 16 t.r. istockphoto.com 16 m.r. istockphoto.com/sean Locke 16 b.r. istockphoto.com 17 m. istockphoto.com 18 t-b #1 istockphoto.com/lisa F. Young #2 istockphoto.com/derek Latta #3 istockphoto.com/alexander Moroz #4 istockphoto.com/chris Schmidt 19 m. istockphoto.com/ Diego Cervo 19 b. istockphoto.com 25 m. istockphoto.com/jill Chen 25 b. istockphoto.com 26 t. istockphoto.com/lauri Patterson 26 m. istockphoto.com/leslie Morris 27 m. istockphoto.com/ Christopher Steer 27 b. istockphoto.com/bob Thomas Calculator icon throughout istockphoto.com Note: Every effort has been made to locate the copyright owner of material reproduced in this component. Omissions brought to our attention will be corrected in subsequent editions. PERCENTS Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 32