[PDF] Unit 01 Introduction to Sixth Grade Everyday Mathematics.pdf | Plain Text

Copyright © Wright Group/McGraw-Hill Teaching Masters and Study Link Masters 1 Teaching Masters and Study Link Masters LESSON53 Name Date Time Sums of Angle Measures in Polygons 156 Copyright © Wright Group/McGraw-Hill A diagonalis a line segment that connects two vertices of a polygon and is nota side. You can draw diagonals from one vertex to separate polygons into triangles. 1.Draw diagonals from the given vertex to separate each polygon into triangles. Then complete the table. 2. a. Study your completed table. Use any patterns you notice to write a formula to find the sum of the angle measures in any polygon (n-gon). Formula b.Use the formula to find the sums of the angle measures in a heptagon. ° nonagon. ° dodecagon. ° Number of Number of Sum of Angle Measures Polygon Sides (n)Triangles Example:Quadrangle 4 2 2 º 180360 Pentagon º Hexagon º Octagon º Decagon º diagonal STUDY LINK113 Unit 2: Family Letter 37 Name Date Time Copyright © Wright Group/McGraw-Hill Operations with Whole Numbers and Decimals In Unit 2, your child will revisit operations with whole numbers and decimals from earlier grades and will continue strengthening previously developed number skills. We will work with estimation strategies, mental methods, paper-and-pencil algorithms, and calculator procedures with whole numbers. We will also develop techniques for working with decimal numbers. In addition to standard and number-and-word notation, we will learn new ways to represent large and small numbers using exponential and scientific notation. Your child will realize that scientific notation, which is used by scientists and mathematicians, is an easier and more efficient way to write large numbers. For example, the distance from the Sun to the planet Pluto is 3,675,000,000 miles. In scientific notation, the same number is expressed as 3.675 º10 9. To use scientific notation, your child will first need to know more about exponential notation, which is a way of representing multiplication of repeated factors. For example, 7 º7 º7 º7 can be written as 7 4. Similarly, 100,000, or 10 º10 º10 º10 º10, is also 10 5. Unit 2 also reviews multiplication and division of whole numbers. All these strategies will be extended to decimals. The partial-quotient algorithm used in fourth and fifth grade Everyday Mathematicsto divide whole numbers will also be used to divide decimals to obtain decimal quotients. This algorithm is similar to the traditional long division method, but it is easier to learn and apply. The quotient is built up in steps using “easy” multiples of the divisor. The student doesn’t have to get the partial quotient exactly right at each step. The example below demonstrates how to use the partial-quotient algorithm. Example: Partial-Quotient Algorithm 12)3270 Partial Quotients2400 200 200 º12 2,400 870 100 º12 1,200600 50 50 º12 600 270 20 º12 240240 20 10 º12 120 30 5 º12 6024 2 2 º12 24 6 272 Remainder Quotient The partial-quotient algorithm is discussed on pages 22 and 23 in the Student Reference Book. Please keep this Family Letter for reference as your child works through Unit 2. Teaching Masters and Study Link Masters

2 Introduction toSixth Grade Everyday Mathematics® The program we are using this year—Everyday Mathematics—offers students a broad background in mathematics. Some approaches in this program may differ from the ones you learned as a student. That’s because we’re using the latest research results and field-test experiences to teach students the math skills they’ll need in the 21st century. Following are some program highlights:  A problem-solving approach that uses mathematics in everyday situations  Activities to develop confidence, self-reliance, and cooperation  Repeated review of concepts throughout the school year to promote mastery  Development of concepts and skills through hands-on activities  Opportunities to communicate mathematically  Frequent practice using games as alternatives to tedious drills  Opportunities for home and school communication Sixth Grade Everyday Mathematics emphasizes a variety of content. Number Relations  Recognizing place value in whole numbers and decimals  Using exponential and scientific notation  Finding factors and multiples  Converting between fractions, decimals, and percents  Ordering positive and negative numbers Operations, Computation, and Mental Arithmetic  Solving problems involving whole numbers, fractions, decimals, and positive and negative numbers  Applying properties of addition, subtraction, multiplication, and division Data and Chance  Collecting, organizing, displaying, and analyzing data  Identifying and comparing landmarks of data sets (mean, median, mode, and range)  Using probability to represent and predict outcomes and analyze chance Measurement, Measures, and Numbers in Reference Frames  Measuring using metric and U.S. customary units  Using formulas to calculate circumference, area, and volume  Naming and plotting points on a coordinate grid Copyright © Wright Group/McGraw-Hill STUDY LINK 11 Unit 1: Family Letter Name Date Time

3 Copyright © Wright Group/McGraw-Hill Geometry  Measuring and drawing angles  Understanding properties of angles  Identifying and modeling similar and congruent figures  Constructing figures with a compass and a straightedge  Drawing to scale  Exploring transformations of geometric shapes  Experimenting with modern geometric ideas STUDY LINK 11 Unit 1: Family Letter cont. Patterns, Functions, and Algebra  Creating and extending numerical patterns  Representing and analyzing functions  Manipulating algebraic expressions  Solving equations and inequalities  Working with Venn diagrams  Applying algebraic properties  Working with ratios and proportions Throughout the year, you will receive Family Letters telling you about each unit. Letters may include definitions and suggestions for at-home activities. Parents and guardians are encouraged to share ideas pertaining to these math concepts with their child in their home language. You and your child will experience an exciting year filled with discovery. Games are as integral to the Everyday Mathematicsprogram as Math Boxes and Study Links because they are an effective and interactive way to practice skills. In this unit, your child will work on understanding place value of whole and decimal numbers, data landmarks, and order of operations by playing the following games. Detailed game instructions for all sixth-grade games are provided in the Student Reference Book. High-Number Toss (Whole Number and Decimal Versions)SeeStudent Reference Book, pages 323 and 324. Students practice reading and comparing whole numbers through hundred-millions and decimals through thousandths. Landmark SharkSeeStudent Reference Book, pages 325 and 326. Students practice finding the mean, median, mode(s), and range of a set of numbers. Name That NumberSeeStudent Reference Book,page 329. Students practice writing number sentences using order of operations. Building Skills Through Games

4 Copyright © Wright Group/McGraw-Hill Collection, Display, and Interpretation of Data Everyday Mathematicswill help your child use mathematics effectively in daily life. For example, the media—especially newspapers and magazines—use data. Employees and employers need to know how to gather, analyze, and display data to work efficiently. Consumers need to know how to interpret and question data presented to them so they can make informed choices. Citizens need to understand government data to participate in the running of their country. InEveryday Mathematics,data provide a context for the development of numeric skills that, in traditional programs, would be developed in isolation. In Unit 1, your child will work with data displayed in stem-and-leaf plots, circle graphs, step graphs, broken-line graphs, bar graphs, and tables. The displays above relate to earthquake magnitudes, preferred pizza crusts, postal rates, and temperatures. Real-world applications support and enrich other areas of mathematics as well. Throughout Unit 1, your child will look for graphs and tables in newspapers and magazines and bring them to school with your permission. The class will think critically about the materials collected. Students will consider the following questions:  What is the purpose of the graph or table?  Is the display clear and attractive, or can it be improved?  Does the display seem accurate, or is it biased?  Can you draw conclusions or make predictions based on the information? Finally, students will learn a new game, Landmark Shark,which will help them develop skill in finding landmarks of data in various data sets. Ask your child to teach you how to play this game. This should be a stimulating year, and we invite you to share the excitement with us! Please keep this Family Letter for reference as your child works through Unit 1. Magnitude of Earthquakes on June 28, 2004 Stems Leaves (ones) (tenths) 2 0 2 6 8 8 3 0 3 4 5 9 4 1 2 2 5 7 8 8 51 2 4 68 Postal Rates Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Degrees Fahrenheit Month Average of Daily High and Low Temperature 90°100° 80° 70° 60° 50° 40° 30° 20° 10° 0° HighLow Stem-and-leaf plot Step graphCircle graph Broken-line graph STUDY LINK 11 Unit 1: Family Letter cont. Preferred Types of Pizza Crust

5 Copyright © Wright Group/McGraw-Hill As You Help Your Child with Homework As your child brings assignments home, you might want to go over the instructions together, clarifying them as necessary. Some of the answers listed below will guide you through the unit’s Study Links. Study Link 1 2 2.90 5.Sample answers: Title: Weekly Allowance; Unit: Dollars 6.907.808.1209.80 Study Link 1 3 2. a.4.8b.2.8, 4.2, 4.8c.4.1 3.804.1105.5006.50 Study Link 1 4 1.Mia: 80; Nico: 803.Mia: 80; Nico: 75 4.Mia: 25; Nico: 45 6.$5.827.$30.27 8.$14.249.$20.50 Study Link 1 5 1. a.38b.147.5c.149.2 2. a.29b.149c.151.3 3.$9.014.$1,107.47 5.$45.876.$35.67 Study Link 1 6 2.90°F3.About 25 minutes 4.Sample answers: a.About 100 minutes b.The rate of cooling levels off to 2 1 2F every 10 min. 5. a.no b.The tea cools very quickly at first, but then the temperature drops slowly. 6.1,7287.3,3068.4,4849.2,538 Study Link 1 7 2.53.24.3 times5.2 times 6.2; 38.6,6139.8,44810.10,872 11.9, 711 Study Link 1 8 2.$1.293. a.$1.75 b.Sample answer: The price difference per ounce is $0.23. The price jumps another $0.23 for every additional part of an ounce. 5.286.457.678.55 Study Link 1 9 1.Answers vary. 3.men4. a.89%b.11% 5.10% greater6.60% greater 7.Sample answer: Because they don’t know the per- son, they don’t know how the stranger will react. 8.249.1410.3211.19 Study Link 1 10 1.Width (ft): 2; 3; 4; 6; 8; 9 Area (ft 2): 20; 27; 32; 36; 32; 27; 11 2.square 3.Length (yd): 24; 16; 12; 8; 6; 4; 2; 1 Perimeter (yd): 98; 52; 38; 32; 28; 32; 38; 98 4. a.6 yd or 8 ydb.8 yd or 6 yd5.$0.10 6.$4.007.$485.008.$2,050.00 Study Link 1 11 1.165,0002.2003 and 2004 3.Sample answer: Yes. The population in 2005 would have to be 310,000 for the claim to be true. 4.$5.005.$90.006.$13,925.007.$0.89 Study Link 1 12 1. a.30 min b.1 hr 20 min, or 1 1 3hours, or 80 min 2.2 hr 20 min, or 2 1 3hours, or 140 min 3.Sample answer: Biased. There are other ways to get to work, so not all commuters are represented. 4.$70.005.$8.456.$25.92 STUDY LINK 11 Unit 1: Family Letter cont.

LESSON 11 Name Date Time Tabbing the Student Reference Book 6 Copyright © Wright Group/McGraw-Hill Some sections of the Student Reference Bookappear in the table below. 1. Follow Steps 1–4. Then complete the table. Step 1Count out one stick-on note for each of the 5 section titles. Step 2Record a different section title on each stick-on note. Step 3Find the first page of each section. Make a tab for that section by attaching the appropriate stick-on note to the side of that first page. Step 4Record the page on which you placed each stick-on note. Use your tabs and the table above to complete Problems 2–6. 2. Find and read the definition for bar graph. 3. Using your Index tab, find the page number(s) on which bar graphs are presented. Record the page number(s). 4. Turn to the page(s) you recorded in Problem 3. What mathematical topic appears in the color strip at the top of the page? 5. Study the Check Your Understanding problem at the bottom of the page. On what page can you find the answer to the problem? To which tabbed section does this page belong? 6. Using your Contents tab, find the mathematical topic under which bar graphs is listed. (It should be the same as the one you recorded in Problem 4.) What is the last page of this topic? Section Title Page Number Answer Key Contents (Table of Contents) Games Glossary Index

LESSON 12 Name Date Time Survey Data 7 Copyright © Wright Group/McGraw-Hill 0 12 345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0 12 345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0 12 345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0 12 345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0 12 345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Math Message

Copyright © Wright Group/McGraw-Hill STUDY LINK 12 Mystery Line Plots and Landmarks 134–136 Name Date Time 1. Draw a line plot for the following spelling test scores. 100, 100, 95, 90, 92, 93, 96, 90, 94, 90, 97 2. The mode of the above data is . 3. Draw a line plot below that represents data with the following landmarks. Use at least 10 numbers. range: 7 minimum: 6 median: 10 modes: 8 and 11 4. Describe a situation in which the data in the above line plot might occur. 5. Give the line plot a title and a unit. Title Unit 8 6. 540 6  7. 7,200 90  8. 84,000 700  9. 400,000 5,000  Practice

LESSON 12 Name Date Time Outliers and Gaps 9 Copyright © Wright Group/McGraw-Hill The effect of an outlier on the mean depends on the number of data values in the set and the size of the gap between the outlier and the other data values. 1. Find the mean and median for the data set above. mean median 2. Find the mean and median for the data set above without the outlier. Round each landmark to the nearest tenth. mean without outlier median without outlier 3. Explain the effect of the outlier on the mean of the set. 4. Suppose the outlier of the data set were 30 instead of 39. a. Predict the value of the mean. predicted mean b. Now calculate the mean. Round it to the nearest tenth. mean 5 10152025303540 X X XX XXX XX XX X There are no data values from 19 to 38. This is a gap. X The data value of 39 is an outlier. It is very different from the rest of the data values.

STUDY LINK 13 Stem-and-Leaf Plots Copyright © Wright Group/McGraw-Hill 10 Name Date Time Every day, there are many earthquakes worldwide. Most are too small for people to notice. Scientists refer to the size of an earthquake as its magnitude. Earthquakes are classified in categories from minor to great, depending on magnitude. The table below shows the magnitude of 21 earthquakes that occurred on June 28, 2004. 1. Construct a stem-and-leaf plot of the earthquake magnitude data. 2. Use your stem-and-leaf plot to find the following landmarks. a. range b. mode(s) c. median Class Magnitude Great 8.0 or more Major 7–7.9 Strong 6–6.9 Moderate 5–5.9 Light 4 – 4.9 Minor 3 –3.9 Magnitude of Earthquakes Occurring June 28, 2004 4.2 5.2 2.8 4.8 3.9 2.0 3.3 4.8 4.5 3.5 2.2 2.6 3.4 6.8 3.0 4.7 2.8 4.2 4.1 5.4 5.1 Stems Leaves (ones) (tenths) Magnitude of Earthquakes Occurring on June 28, 2004 135 136 3. 6,400 80  4. 121,000 1,100  5. 3,000,000 6,000  6. 600,000 12,000  Practice

LESSON 13 Name Date Time Reviewing Stem-and-Leaf Plots 11 Copyright © Wright Group/McGraw-Hill Students in Mr. Conley’s sixth-grade class measured how far they could reach and jump. Each student stood with legs together, feet flat on the floor, and one arm stretched up as high as possible. Arm reach was then measured from top fingertip to floor. 1. Using a tape measure, measure your arm reach in inches. Record this measurement. in. In the standing jump,each student stood with knees bent and then jumped forward as far as possible. The distance was measured from the starting line to the point closest to where the student’s heels came down. Students displayed their results using two different stem-and-leaf plots. Plot 1 Plot 2 Unit: inches Unit: inches arm reach jump distance Stems Leaves (10s) (1s) 44 68 5 003345677889 6 001389 Stems Leaves (10s) (1s) 617 7 0122233456666899 8 347 2. Use what you know about your arm reach to figure out which stem-and-leaf plot represents the class data for the standing jump. a. Which plot do you think it is? Plot b. Explain why you think so.

LESSON 13 Name Date Time Back-to-Back Stem-and-Leaf Plots 12 Copyright © Wright Group/McGraw-Hill You can compare two related sets of data in a back-to-back stem-and-leaf plot. In this type of plot, the stem is written in the center, with one set of leaves to the right and another set of leaves to the left. The ages of Wimbledon tennis champions in the women’s and men’s singles from 1993–2003 are shown in the back-to-back stem-and-leaf plot below. Women Men Leaves Stems Leaves (1s) (10s) (1s) 71 4322110 2 12234 76 2 56789 30 Students’ Heights (in centimeters) Girls’ Heights Boys’ Heights 162, 126, 134, 145, 127, 134, 143, 159, 154, 137, 162, 147, 145, 174, 132, 151, 147, 169, 164, 171, 163, 171, 154, 157 170, 161, 166, 136, 168, 155, 153, 143 4. The data table above shows students’ heights in centimeters. Make a back-to-back stem-and-leaf plot to display the data. Use the 2-digit stems provided.Girls Boys Leaves Stems Leaves (1s) (10s) (1s) 12 13 14 15 16 17 Ages of Wimbledon Tennis Champions 1993 – 2003 Students’ Heights 1. How many women champions were in their twenties? 2. What is the mode age for women? For men? 3. What is the median age for women? For men?

STUDY LINK 14 Median and Mean 13 135–137 Name Date Time Copyright © Wright Group/McGraw-Hill Mia’s quiz scores are 75, 70, 75, 85, 75, 85, 80, 95, and 80. Nico’s quiz scores are 55, 85, 95, 100, 75, 75, 65, 95, and 75. 1. Find each student’s mean score. Mia Nico 2. Make a stem-and-leaf plot for each student’s scores. a. Mia’s Quiz Scores b. Nico’s Quiz Scores Stems Leaves (100s and 10s) (1s) Stems Leaves (100s and 10s) (1s) 3. Find each student’s median score. Mia Nico 4. What is the range of scores for each student? Mia Nico 5. Which landmark, mean or median, is the better indicator of each student’s overall performance? Explain. 6. $4.57 $1.25  7. $14.49 $15.78  8. $19.99 $5.75  9. $39.25 $18.75  Practice

LESSON 14 Name Date Time Defining the Mean 14 Copyright © Wright Group/McGraw-Hill The table at the right shows the number of students absent from gym class during the week. Day Students Absent Monday 6 Tuesday 2 Wednesday 5 Thursday 4 Friday 8 If you redistribute, or even out, the number of absent students so the number is the same for each day, you are finding the mean.The mean is a useful landmark when there are not one or two numbers that are far away from the rest of the data values (outliers). 2. Move the cubes on the line plot so that each day has the same number. After you’ve evened out the cubes, how many does each day have? You can use a number sentence to model how you evened out the cubes. You started with 6 2 5 4 8 25 cubes. Then you redistributed the cubes so that the total number of cubes (25) was the same for each of the 5 days, or 25 5 5. 3. Use the cubes to find the mean of the following number of absent students. Monday: 5; Tuesday: 0; Wednesday: 6; Thursday: 2; Friday: 7 Then write a number sentence to model what you did. Monday Tuesday Wednesday Thursday Friday 1. Place unit cubes on the line below to show the number of absent students for each day.

Heights were measured to the nearest centimeter for 12 boys and 12 girls. All of the students were 12 years old. Boys’ heights: 157, 150, 131, 143, 147, 169, 148, 147, 145, 163, 139, 151 Girls’ heights: 146, 164, 138, 149, 145, 167, 150, 156, 143, 148, 149, 160 1. Make a stem-and-leaf plot for the boys’ data. Then find the range, median, and mean of the boys’ heights. a. range b. median c. mean 2. Make a stem-and-leaf plot for the girls’ data. Then find the range, median, and mean of the girls’ heights. a. range b. median c. mean Name Date Time Range, Median, and Mean 15 Copyright © Wright Group/McGraw-Hill Boys’ Heights (cm) Stems Leaves (10s) (1s) Girls’ Heights (cm) Stems Leaves (10s) (1s) 3. $5.86 $3.15  4. $221.17 $886.30  5. $75.37 29.50  6. $124.35 $88.68  Practice STUDY LINK 15 135–137

LESSON 15 Name Date Time Calculating and Analyzing Landmarks 16 Copyright © Wright Group/McGraw-Hill 1. Write your seven-digit home phone number in the boxes below. – 2. Using a marker, write each digit on a separate index card. These digits will make up your data set. 3. Arrange the digits in order from least to greatest. 4. Find the following landmarks for your data set. If you need a reminder about how to find landmarks, review pages 136 and 137 of the Student Reference Book. range median mode mean 5. Explain how the range, median, and mean change if you add the three numbers of your area code to your data set.

LESSON 15 Name Date Time Mentally Calculating a Mean 17 Copyright © Wright Group/McGraw-Hill 1. Apply strategies like those above to mentally calculate the mean of the following temperatures: 43F, 52F, 37F, 48F, 40F. a. Record the sum of the temperatures. b. Record the mean. 2. Mentally calculate the sum and mean for the following data sets. Then choose one of the data sets and write a number sentence to show the strategies you used to find your answers. a.Data Set A:Number of letters in first names: 6, 9, 10, 4, 6 sum of letters mean number of letters  b. Data Set B:Lengths of standing long jumps (inches): 22, 31, 28, 20, 29 sum of lengths mean length of jumps  c. For Data Set , I used the following number sentences: Consider some of these strategies when calculating the mean of a data set. Look for easy combinations of numbers and add them. Example:12 18 30 (10 2) (10 8)  (10 2) (8 10) 10 (2 8) 10  10 10 10 30 If the data set has 5 numbers, you can divide the sum of the numbers by 10 and then multiply that number by 2. Example:If the sum of 5 test scores is 80, then the mean is (80 10) º 2 8 º 2 16. Multiply any mode(s) by the number of occurrences. Example:For 20, 15, 20, 20, 10, the mode (20) occurs 3 times. (20 º 3) 10 15 (20 º 3) 25 85

LESSON 16 Name Date Time The Climate in Omaha 18 Copyright © Wright Group/McGraw-Hill Omaha, the largest city in Nebraska, is located on the eastern border of the state on the Missouri River. Precipitationis moisture that falls as rain or snow. Rainfall is usually measured in inches; snowfall is usually translated into an equivalent amount of rain. Average Number of Days in Omaha with At Least 0.01 Inch of Precipitation These averages are the result of collecting data for more than 58 years. 1. Complete the following graph. First make a dot for each month to represent the data in the table. Then connect the dots with line segments. The result is called a broken-line graph. This type of graph is often used to show trends. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 7671012119997 57 Number of days 14 12 10 8 6 4 2 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Average Number of Days in Omaha with At Least 0.01 Inch of Precipitation Month Number of Days Source:The Times Books World Weather Guide

STUDY LINK 16 Cooling Off 19 Name Date Time Copyright © Wright Group/McGraw-Hill The graph shows how a cup of hot tea cools as time passes. 1. Use the graph to fill in the missing data in the table. 2. What is the tea’s approximate temperature after 30 minutes? 3. About how many minutes does it take for the tea to cool to a temperature of 95°F? 4. a. About how many minutes do you think it will take the tea to cool to room temperature (70°F)? b. Why do you think so? 5. a. Does the tea cool at a constant rate? b. Explain your answer. 6. 32 º 54  7. 87 º 38 8. 59 º 76  9. 94 º 27 Elapsed Time Temperature (minutes) (F) 0 (pour tea) 10 40 100 115 5 Elapsed time (minutes) 30 0 102030405060 40 50 60 70 80 90 100 110 120 130 140 150 160 room temperature Temperature (°F) Temperature of Hot Tea y x Practice

STUDY LINK 17 Using Bar Graphs Copyright © Wright Group/McGraw-Hill 20 138 Name Date Time Every week, Ms. Penczar gives a math quiz to her class of 15 students. The table below shows the class’s average scores for a six-week period. 1. Draw a bar graph that shows the same information. Give the graph a title and label each axis. Use the graph you drew to answer the following questions. 2. The highest average score occurred in Week . 3. The lowest average score occurred in Week . 4. How many times did scores improve from one week to the next? 5. How many times did scores decline from one week to the next? 6. The greatest one-week improvement occurred between Week and Week . 7. Name a possible set of scores for Ms. Penczar’s 15 students that would result in the class average given for Week 2. Week Class Average 168 266 379 489 591 688 Practice 8. 389 º 17  9. 176 º 48 10. 453 º 24  11. 249 º 39

LESSON 17 Name Date Time Reviewing Bar Graphs 21 Copyright © Wright Group/McGraw-Hill A school board conducted a survey in which 70 ninth graders were asked how many hours they spend doing homework each day. The bar graph displays the survey results. Less than 1 1–2 2–3 More than 3 0 10 20 30 40 50 Number of Students Hours per Da y Average Time Spent on Homework Decide whether each of the following statements about the survey results is true or false. If a statement is false, explain why. 1. All students spend some time each day doing homework. 2. About half of the students spend more than 3 hours on homework. 3. More than 15 students spend 1–2 hours per day on homework. 4. The number of students spending 2–3 hours on homework is about 3 times as many as the number of students who spend 1–2 hours on homework.

STUDY LINK 18 The Cost of Mailing a Letter Copyright © Wright Group/McGraw-Hill 22 Name Date Time The cost of mailing a first-class letter in the United States depends on how much the letter weighs. The table at the right shows first-class postal rates in 2004: 37 cents for a letter weighing 1 ounce or less; 60 cents for a letter weighing more than 1 ounce but not more than 2 ounces; and so on. A step graph for these data has been started on page 23. Notice the placement of dots in the graph. For example, on the step representing 60 cents, the dot at the right end, above the 2, shows that it costs 60 cents to mail a letter weighing exactly 2 ounces. There is no dot at the left end of the step—that is, at the intersection of 1 ounce and 60 cents—because the cost of mailing a 1-ounce letter is 37 cents, not 60 cents. 1. Continue the graph for letters weighing up to 6 ounces. 2. Using the rates shown in the table, how much would it cost to send a letter that weighs 4 1 2ounces? Weight (oz) Cost 1 $0.37 2 $0.60 3 $0.83 4 $1.06 5 $1.29 6 $1.52 3. a. Using the rates shown in the table, how much would it cost to mail a letter that weighs 6 1 2ounces? b. How did you determine your answer? 4. Continue the graph on page 23 to show the cost of mailing a first-class letter weighing more than 6 ounces, but not more than 7 ounces. 5. 25 92  6. 83 60 7. 46 79  8. 94 95 Try This Practice 2004 First-Class Postal Rates

STUDY LINK 18 The Cost of Mailing a Letter continued 23 Name Date Time Copyright © Wright Group/McGraw-Hill Cost Ounces 1 0 567234 Cost of Mailing a First-Class Letter in the United States in 2004 $0.20 $0.10 $0.50 $1.00 $1.50 $0.00 $0.30 $0.40 $0.60 $0.70 $0.80 $0.90 $1.10 $1.20 $1.30 $1.40 $1.60 $1.70 $1.80 $0.77

LESSON 18 Name Date Time Identifying Jumps in Data Values 24 Copyright © Wright Group/McGraw-Hill Set by Congress, minimum wage is the minimum rate per hour that can be paid to workers. Some historical values of the U.S. minimum wage appear in the table below. U.S. Minimum Wage, 1986–2003 Year Minimum Wage Year Minimum Wage Year Minimum Wage 1986 $3.35 1992 $4.25 1998 $5.15 1987 $3.35 1993 $4.25 1999 $5.15 1988 $3.35 1994 $4.25 2000 $5.15 1989 $3.35 1995 $4.25 2001 $5.15 1990 $3.80 1996 $4.75 2002 $5.15 1991 $4.25 1997 $5.15 2003 $5.15 Source:Economic Policy Institute Use the table above to answer the following questions. 1. Name the years at which a jump in the values occurs. 2. Name the number of years for which the minimum wage is $3.35 $3.80 $4.25 $4.75 $5.15 3. Is the number of years between jumps the same? Explain.

LESSON 18 Name Date Time Parking Lot Charges 25 Copyright © Wright Group/McGraw-Hill 1. A parking lot charges $3.00 for the first hour or fraction of an hour and $2.00 for each additional hour or fraction of an hour. a. Complete the table at the right. b. What is the cost of parking for 2 1 2hours? 2. Draw a step graph of the parking lot charges. Remember: The parking lot charges $3.00 for the first hour or fraction of an hour and $2.00 for each additional hour or fraction of an hour. 3. What is the cost of parking for 1 hour and 15 minutes? 4. What is the cost of parking for 3 hours and 45 minutes? Time Cost 30 min $3.00 1 hr $3.00 21 2 hr 3 hr 59 min 5 hr 5 hr 15 min $0 $5 $10 $15 0123 Number of Hours Parking Lot Charges Cost 456 141

LESSON 19 Name Date Time Sports Team Survey 26 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Math Message I am a girl boy. (Place an X next to your gender.) Circle your answer to each of the following questions. 1. Should girls be allowed to play on boys’ teams? yes no 2. Should boys be allowed to play on girls’ teams? yes no LESSON 19 Name Date Time Sports Team Survey Math Message I am a girl boy. (Place an X next to your gender.) Circle your answer to each of the following questions. 1. Should girls be allowed to play on boys’ teams? yes no 2. Should boys be allowed to play on girls’ teams? yes no LESSON 19 Name Date Time Sports Team Survey Math Message I am a girl boy. (Place an X next to your gender.) Circle your answer to each of the following questions. 1. Should girls be allowed to play on boys’ teams? yes no 2. Should boys be allowed to play on girls’ teams? yes no

LESSON 19 Name Date Time A Magazine Survey 27 Copyright © Wright Group/McGraw-Hill An issue of a sports magazine for kids featured a readers’ survey. In the survey, readers were asked to respond to the following three questions: 1. Should girls be allowed to play on boys’ teams? 2. Should boys be allowed to play on girls’ teams? 3. On how many organized sports teams do you play during a year? Readers’ responses are represented by the circle graphs below. Question 1:Should girls be allowed to play on boys’ teams? Question 2:Should boys be allowed to play on girls’ teams? Question 3:On how many organized sports teams do you play during a year? Boys say: Graph D Yes No Girls say: Graph C Yes No Boys say: Graph B Yes No Girls say: Graph A Yes No 23 4 5+ 0 Graph E 1

STUDY LINK 19 Analyzing Circle Graphs Copyright © Wright Group/McGraw-Hill 28 145 Name Date Time 1. Would you be willing to tell strangers that they had smudges on their faces? yes no food stuck between their teeth? yes no dandruff? yes no A marketing research company asked men and women these same questions. The results are summarized in the circle graphs below. Use the legend to read the graphs. yes, would tell no, would not tell 2. Write estimates for the percents represented by each graph. Source: America by the Numbers Men Men Men Smudge on Face Women Food in Teeth Women Dandruff Women Estimates: Estimates: Estimates: yes no yes no yes no Estimates: Estimates: Estimates: yes no yes no yes no

STUDY LINK 19 Analyzing Circle Graphs continued 29 Name Date Time Copyright © Wright Group/McGraw-Hill Cut out the Percent Circle at the right and poke a hole in the center with a pencil. Use the Percent Circle to find the percent represented by each sector mentioned in the questions below. 3. According to the survey, are men or women more likely to alert strangers to an embarrassing situation? 4. a. About what percent of men say they would tell strangers that they had food stuck between their teeth? b. About what percent of men would not be willing to tell? 5. In the survey, how much greater is the percent of men who would be willing to alert strangers to smudges on their faces than the percent of women who would be willing to do so? 6. How much greater is the percent of women who would be willing to tell strangers about food in their teeth than the percent of women who would tell strangers about dandruff? 7. Why do you think people might be hesitant to alert strangers to such situations? Practice 8. 3 13 46  9. 507 00 10. 9 39 12  11. 295 51 0% 10% 90% 80% 70% 60% 40%30%20% 50%

LESSON 110 Name Date Time Using a Graph to Find the Largest Area 30 Copyright © Wright Group/McGraw-Hill 5 10 15 20 25 30 35 01234567891011 Length (ft) Areas of Rectangles Area (ft 2)

STUDY LINK 110 Perimeter and Area 31 Name Date Time Copyright © Wright Group/McGraw-Hill The student council is preparing the gym floor for the annual talent show. They will use 24 feet of tape to mark the seating area for the judges. The table below lists the lengths of some rectangles with perimeters of 24 feet. Complete the table. You may want to draw the rectangles on grid paper. Let the side of each grid square represent 1 foot. 1. 2. How would you describe the rectangular region that will provide the largest seating area for the judges? The stage area for the talent show will be 48 square yards. The table below lists the lengths of some rectangles with areas of 48 yd 2. Complete the table. 3. 4. What is the length and width of the rectangular region that will take the least amount of tape to mark off? a. length b. width Length (ft) 109876543 2 1 Width (ft) 5 7 10 11 Perimeter (ft) 24 24 24 24 24 24 24 24 24 24 Area (ft 2) 35 35 20 Length (yd) 48 3 Width (yd) 1 2 3 4 6 8 12 16 24 48 Perimeter (yd) 28 52 Area (yd 2) 48 48 48 48 48 48 48 48 48 48 5. $0.01 º 10  6. $0.40 º 10  7. $48.50 º 10  8. $205.00 º 10  Practice 212, 214, 215

LESSON 110 Name Date Time Grid-Paper Perimeters 32 Copyright © Wright Group/McGraw-Hill Work with a partner. Use page 408 for Problems 1 and 2. Suppose one side of a centimeter square on the grid paper is 1 unit. 1. Use the lengths of the sides that appear in the first row of the table to draw a rectangle with a perimeter of 12 units. 2. Now make two different rectangles that also have perimeters of 12 units. Record the lengths of the sides for these rectangles. (Remember:A square is also a rectangle.) 3. Write a number sentence for the perimeter of the rectangle. For example, two possible number sentences for the first rectangle are 1 1 5 5 12 OR 2 º (1 5) 12. 4. Complete the table. Shorter Longer Perimeter Side SideNumber Sentence 12 units 1 unit 5 units 1 5 1 5 12 OR 2 º (1 5) 12 12 units units units 12 units units units 14 units units units 14 units units units 14 units units units 16 units units units 16 units units units 16 units units units 16 units units units Use your completed table to complete Problems 5 and 6 on page 33. 1 unit 1 unit

LESSON 110 Name Date Time Grid-Paper Perimeters continued 33 Copyright © Wright Group/McGraw-Hill 5. Look for a pattern or rule in the results of your table. Then apply this rule to find the lengths of the sides of a rectangle with a perimeter of 20 units without using your grid paper. Record the lengths of the shorter and longer sides of this rectangle and a number sentence for its perimeter. shorter side units longer side units number sentence 6. What are the side lengths of the rectangle in your table that has the largest area? (Ashorter side º longer side) shorter side units longer side units Try This 7. Find the lengths of sides xand y.Then find the perimeter and area of the polygon. a. xcm b. ycm c. perimeter cm d. area cm 2 8 cm 7 cm 18 cm 16 cm x y

STUDY LINK 111 The Population of River City Copyright © Wright Group/McGraw-Hill 34 Name Date Time The way a graph is constructed affects how fairly the data are represent\ ed. The mayor of River City is trying to convince the city council that the \ city needs more schools. She claims that the city’s population has doubled since\ 1998. The mayor used the graph below to support her claim. 1. According to the graph, what was the population in 2000? 2. Between which 2 years was the increase in population the least? 3. Is the mayor’s claim misleading? Explain. Practice 4. $0.05 º 100  5. $0.90 º 100  6. $139.25 º 100  7. º 100 $89.00 140 155 160 165 170 175 180 185 190 1998 1999 2000 2001 2002 2003 2004 2005 Year Population of River City Population (thousands)

LESSON 111 Name Date Time Persuasive Graphs 35 Copyright © Wright Group/McGraw-Hill Create a persuasive graph for one of the two situations below or make up a situation of your own. You want to present your case in a way most favorable to you and your cause. Be sure that your graph does not contain false information. Remember that you are merely presenting the information in a way that will be of the greatest benefit to you. You have been in charge of sales at the school store this year. Each month profits have increased—from $10 in September to $18 in June. You would like to have the same job again next year and want to show your principal why you are the best candidate for the position. For health reasons, you have been encouraging your uncle to lose weight. Over the past 8 weeks, he has gone from 300 pounds to 291 pounds. You are proud of your uncle and want to show him how much progress he has made.

STUDY LINK 112 Survey Results Copyright © Wright Group/McGraw-Hill 36 Name Date Time A sample of 2,000 working adults was surveyed to determine how much time they spend performing certain weekly activities and how much time they would prefer to spend on these activities. For example, the average time adults spend on household chores is 4 hr 50 min, while the average time they prefer to do household chores is 2 hr 30 min. The survey results are shown in the side-by-side bar graph below. Actual vs. Preferred Times for Daily Activities Commuting to Work Working on the Job Sleeping Visiting with Family/Friends Pursuing Interests/Hobbies Doing Household Chores 2 hr 8 hr 6 hr 1 hr 40 min 4 hr 30 min 30 min 1 hr 20 min 4 hr 50 min 2 hr 30 min7 hr 9 hr 40 min 0246810 Hours Actual Time Preferred Time 4. $700.0010  5. $84.5010 6. $259.2010 Practice 1. a. What is the actual time spent pursuing interests/hobbies? b. How much time would adults prefer to spend pursuing interests/hobbies? 2. What is the difference between the actual time and preferred time for doing household chores? 3. For this survey, researchers interviewed every 25th rider who boarded a commuter train on a Monday morning. Do you think this sampling method provides a random or biased sample? Explain.

STUDY LINK 113 Unit 2: Family Letter 37 Name Date Time Copyright © Wright Group/McGraw-Hill Operations with Whole Numbers and Decimals In Unit 2, your child will revisit operations with whole numbers and dec\ imals from earlier grades and will continue strengthening previously developed numb\ er skills. We will work with estimation strategies, mental methods, paper-and-pencil\ algorithms, and calculator procedures with whole numbers. We will also develop techniques for working with decimal numbers. In addition to standard and number-and-word notation, we will learn new \ ways to represent large and small numbers using exponential and scientific no\ tation. Your child will realize that scientific notation, which is used by scient\ ists and mathematicians, is an easier and more efficient way to write large numbe\ rs. For example, the distance from the Sun to Pluto is 3,675,000,000 miles. \ In scientific notation, the same number is expressed as 3.675 º10 9. To use scientific notation, your child will first need to know more about\ exponential notation, which is a way of representing multiplication of r\ epeated factors. For example, 7 º7º 7º 7 can be written as 7 4. Similarly, 100,000, or 10 º10 º10 º10 º10, is also 10 5. Unit 2 also reviews multiplication and division of whole numbers. All th\ ese strategies will be extended to decimals. The partial-quotient algorithm used in fou\ rth and fifth grade Everyday Mathematics to divide whole numbers will also be used to divide decimals to obtain decimal quotients. This algorithm is similar to the t\ raditional long division method, but it is easier to learn and apply. The quotient is built up in steps using “easy” multiples of the divisor. The student doesn’t have to get the partial quotient exactly right at each step. The example below demonstrates how \ to use the partial-quotient algorithm. Example: Partial-Quotient Algorithm 12 ) 3270 Partial Quotients  2400 200 200 º12 2,400 870 100 º12 1,200  600 50 50 º12 600 270 20 º12 240  240 20 10 º12 120 30 5 º12 60  24 2 2 º12 24 6 272 Remainder Quotient The partial-quotient algorithm is discussed on pages 22 and 23 in the Student Reference Book. Please keep this Family Letter for reference as your child works through Unit 2.

38 dividend In division, the number that is being divided. For example, in 35 57, the dividend is 35. divisor In division, the number that divides another number (the dividend). For example, in 35  57, the divisor is 5. exponent A small, raised number used in exponential notationto tell how many times the base is used as a factor.For example, in 5 3, the base is 5, the exponent is 3, and 5 35 5 5. Same as power. exponential notation A way of representing repeated multiplication by the same factor. For example, 2 3is exponential notation for 2 º2º2. Theexponent3 tells how many times the base 2 is used as a factor. factor (1) Each of two or more numbers in a product. For example, in 6 º0.5, 6 and 0.5 are factors. Compare to factor of a counting numbern. (2) To represent a number as a product of factors. For example, factor 21 by rewriting as 7 º3. number-and-word notation A notation consisting of the significant digits of a number and words for the place value. For example, 27 billion is number-and-word notation for 27,000,000,000. power Same as exponent. power of 10 (1) In Everyday Mathematics,a number that can be written in the form 10 a, where ais a counting number. That is, the numbers 10 10 1, 10010 2, 1000 10 3, and so on, that can be written using only 10s as factors. Same as positive power of 10. (2) More generally, a number that can be written in the form 10 a, where ais an integer. That is, all the positive and negative powers of 10 together, along with 10 01. precise Exact or accurate. precise measures The smaller the scale of a measuring tool, the more precisea measurement can be. For example, a measurement to the nearest inch is more precise than a measurement to the nearest foot. A ruler with 11 6-inch markings can be more precise than a ruler with only 1 4-inch markings, depending on the skill of the person doing the measuring. precise calculations The more accurate measures or other data are, the more preciseany calculations using those numbers can be. quotient The result of dividing one number by another number. For example, in 10 5 2, the quotient is 2. remainder An amount left over when one number is divided by another number. For example, in 16 / 3 ∑ 5 R1, the quotient is 5 and the remainder R is 1. scientific notation A way of writing a number as the product of a power of 10and a number that is at least 1 and less than 10. Scientific notation allows you to write large and small numbers with only a few symbols. For example, in scientific notation, 4,300,000 is 4.3 º10 6, and 0.00001 is 1 10 –5. Scientific calculators display numbers in scientific notation. Compare to standard notationand expanded notation. standard notation Our most common way of representing whole numbers, integers, and decimals. Standard notation is base-ten place-value numeration. For example, standard notation for three hundred fifty-six is 356. Same as decimal notation. Vocabulary Important terms in Unit 2: Copyright © Wright Group/McGraw-Hill dividend / divisor  quotient  quotient dividend divisor Unit 2: Family Letter cont. STUDY LINK 113

39 Do-Anytime Activities Consider using the suggested real-life applications and games that not only promote your child’s understanding of Unit 2 concepts, but also are easy, fun, and rewarding to do at home. 1.Encourage your child to incorporate math vocabulary in everyday speech. Help your child recognize the everyday uses of fractions and decimals in science, statistics, business, sports, print and television journalism, and so on. 2.Have your child help you measure ingredients when cooking or baking at home. This will usually involve working with fractional amounts. Furthermore, your child could assist you with adjusting the amounts for doubling a recipe or making multiple servings.3.Extend your child’s thinking about fractions and decimals to making connections with percents. By using money as a reference, you could help your child recognize that one-tenth is equal to 11 00 0or 10%, one-quarter is the same as 0.25, 12 05 0, or 25%, and so on. 4.Ask your child to use mental math skills to help you calculate tips. For example, if the subtotal is $25.00 and the tip you intend to pay is 15%, have your child first find 10% of $25 ($2.50) and then find 5% of $25 by taking half the 10% amount ($2.50 / 2 $1.25). Add $2.50 and $1.25 to get the tip amount of $3.75. Copyright © Wright Group/McGraw-Hill Several math games develop and reinforce whole number and decimal concepts in Unit 2. Detailed game instructions for all sixth-grade games are provided in the Student Reference Book. Encourage your child to play the following games with you at home. Scientific Notation TossSeeStudent Reference Book,page 331. Two players can play this game using a pair of 6-sided dice. Winning the game depends on creating the largest number possible using scientific notation. Advanced Scientific Notation Toss,mentioned at the bottom of page 331, adds more excitement to the original game. Doggone DecimalSeeStudent Reference Book,page 310. In this game, two players compete to collect the greatest number of cards. You will need number cards, 4 index cards, 2 counters or coins, and a calculator. The skill practiced here is estimating products of whole and decimal numbers. Building Skills through Games Unit 2: Family Letter cont. STUDY LINK 113

40 Study Link 2 1 1. a. 2b. 5c.1d.6e. 8f. 0 2. a. 430,000b.90,105,000 c.170,000,065d.9,500,243,000 3. a.(3º100,000)(2º10,000)(1º1,000) 4. a.1,000b.1,000,000c.1,000,000,000 5. a.48 millionmilesb.25.7 million miles 6. a.44,300,000,000b.6,500,000,000,000 c.900,000d.70 7.416,3008.230,0009.1,900,000 10.7,000,000 Study Link 2 2 1.38.4692.1.34063.eight-tenths 4.ninety-five hundredths5.five-hundredths 7.four and eight hundred two ten-thousandths 11.(1º0.01)(3º0.001) 12.(1º100)(9º1)(3º0.1)(5º0.01) (2º0.001)(7º0.0001) 13.8.63014.0.36815.D16.A 17.C18.B19.0.6320.0.0168 21.0.740222.45.00923.0.5801 Study Link 2 3 1.0.297 minutes 2.5.815 meters 3.1.339 mph4.1.38 goals 7.$0.718.0.859.1.510.$6.75 Study Link 2 4 1.0.00492.0.0783.3.04.0.07 5.150.06.1907.3,7608.0.0428 9. a.100b.10 100 10.0.000000001 11.10 7 12.$5.2513.$6.0214.$9.11 Study Link 2 5 1.2,0012.1,2883.11,9044. a.20.01b.20.01c.200.1 5. a.1,190.4b.11.904c.11.904 7.$5.008.$11.009.34.510.0.07 Study Link 2 6 1.24.32.11.483.0.8274.756.3 5.18.0126.29.827.49.928.10.241 9.76.7 miles; 11.8 º6.576.7 12.$16.0013.$11.0014.9615.24 Study Link 2 7 6. ∑ 66 R6; 66 6 8 7. ∑ 65 R1; 65 11 5 8. 49 9. ∑18 R15; 18 1 45 6 10. ∑ 158 R20; 158 2 30 8 11. ∑126 R42; 126 4 42 4 12.$3.9813.$11.8414.$74.9415.$499.95 Study Link 2 8 1.Sample estimate: 2; Answer: 2.47 2.Sample estimate: 20; Answer: 19.7 5.2.836.$7.207.1.998.4.22 Study Link 2 9 1.12,4003.0.0000085.1.1802º10 10 6.0.000167.4.3º10 –3 8.2,835,000 9. 10.11. 12. 13.10 is raised to a negative power. 14.7,62415.3.7116.90017.200 Study Link 2 10 1.493.645.0.00001 7.3 9 9.11 –3 14.8 532,768 Study Link 2 11 1.3.6º10 –3 3.8º10 4 5.50,000 7.48,100,0009.1º10 –3; 0.00111.3.9º10 3 13.5.2º10 –1 16.6,7633,9292,834 17.71,146 – 4,876 66,270 As You Help Your Child with Homework As your child brings assignments home, you might want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through the unit’s Study Links. Copyright © Wright Group/McGraw-Hill Unit 2: Family Letter cont. STUDY LINK 113