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STUDY LINK 5 1 Parts-and-Whole Fraction Practice 125 74 75 243 Name Date Time Copyright © Wright Group/McGraw-Hill For the following problems, use counters or draw pictures to help you. 1. If 15 counters are the whole set, how many are of the set? counters 2. If 18 counters are the whole set, how many are 7 9of the set? counters 3. If 20 counters are the whole set, what fraction of the set is 16 counters? 4. If 50 counters are the whole set, what fraction of the set is 45 counters? 5. If 35 counters are half of a set, what is the whole set?counters 6. If 12 counters are of a set, what is the whole set? counters 7. Gerald and Michelle went on a 24-mile bike ride. By lunchtime, they had ridden 5 8of the total distance. How many miles did they have left to ride after lunch? miles 8. Jen and Heather went to lunch. When the bill came, Jen discovered that she had only $8. Luckily, Heather had enough money to pay the other part, or , of the bill. a. How much did Heather pay? b. How much was the total bill? c. Explain how you figured out Heather’s portion of the bill. 35 34 35 Practice 9. 342 10. 3420 11. 30 420 12. 30 4,200

LESSON 5 1 Name Date Time Birthday Box 126 Copyright © Wright Group/McGraw-Hill Use only numbers from one data bank below to fill in the missing values for this number story. Reminder:oz means ounce For her birthday, Alisha got a box containing pieces of candy that weighed oz. Each piece of candy weighed oz. She ate pieces of candy. The remaining pieces of candy and the box weighed oz. The weight of the box is oz. 1. Read the problem. 2. Think about how the missing values need to relate to each other. Which values should be greater than other values? Which should be less than other values? Are there multiples that can help you? 3. Fill in the missing values. 4. Read the problem again. Make sure the number relationships make sense. Data Bank: Whole Numbers 12630366173 Data Bank: Fractions and Mixed Numbers 1 3 3 4 53 4 83 4 91524

STUDY LINK 5 2 Fraction and Mixed-Number Practice 127 Name Date Time Copyright © Wright Group/McGraw-Hill For the problems below, the hexagon is worth 1. Write the mixed-number name and the fraction name shown by each diagram. Practice 1. Mixed number Fraction 3. Mixed number Fraction 5. Mixed number Fraction 7. 71,834 9. 8984 2. Mixed number Fraction 4. Mixed number Fraction 6. Make up a mixed-number problem of your own in the space below. 8. 6196 → 10. 9651 → Unit hexagon 62 63

LESSON 5 2 Name Date Time Pattern Block Fractions 128 Copyright © Wright Group/McGraw-Hill 1. Cover Shape A with trapezoid blocks. a. How many trapezoid blocks does it take to cover Shape A? b. Write a fraction for this amount. c. What fraction of Shape A is covered by one trapezoid block? 2. Cover Shape A with rhombus blocks. a. How many rhombus blocks does it take to cover Shape A? b. Write a fraction for this amount. c. What fraction of Shape A is covered by one rhombus block? 3. Cover Shape A with triangle blocks. a. How many triangle blocks does it take to cover Shape A? b. Write a fraction for this amount. c. What fraction of Shape A is covered by one triangle block? rhombus triangle Shape A trapezoid

LESSON 5 2 Name Date Time Pattern Blocks and Fractions 129 Copyright © Wright Group/McGraw-Hill Use your , , and pattern blocks to solve these problems. 1. Choose one pattern block and give it a value. The block can be worth ONE or a fraction of ONE. Draw the block and record its value. The is worth . Use the figure you chose in Problem 1 to answer Problems 2–5. 2.3. 4.5. 6. In the space below or on another piece of paper, make a design with about 10 pattern blocks. Trace the outline of each block. (Or use the pattern-block shapes on the Geometry Template.) 7. Label each part of your design with a fraction. How much is the design worth? 8. Write a number model to show how you calculated the value of the design. A hexagon is worth . A rhombus is worth . A trapezoid is worth . A triangle is worth .

LESSON 5 3 Name Date Time Fraction-Stick Chart 130 Copyright © Wright Group/McGraw-Hill 1. Using the Fraction-Stick Chart, list all the fractions that are equivalent to 1 2. a. What pattern do you notice in the numerators for these fractions? b. What pattern do you notice in the denominators for these fractions? c. Are the patterns complete? d. What fraction is missing that would make the pattern complete? 2. Using the Fraction-Stick Chart, list all the fractions that are equivalent to 1 3. a. What pattern do you notice in these fractions? b. Use this pattern to find the next 3 fractions that are equivalent to 1 3. 1 12 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 7 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 3 1 3 1 3 1 3 1 3 1 3 1 2 1 2 1 2 1 2 11 1 4 1 2 4 3 4 0 1 1 4 12 4 13 4 2 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7

STUDY LINK 5 3 Fraction-Stick Problems 131 Name Date Time Copyright © Wright Group/McGraw-Hill Shade the fraction sticks to help you find equivalent fractions. 1. 1 2 —8 2. 3 4 —16 3. —4  2 8 —16 Shade the fraction sticks to help you solve the addition problems. 4. 1 4 3 4 5. 1 2 2 8 6. 1 2 3 4 Shade the fraction sticks to help you solve the fraction number stories. 7. Joe was baking a cake. He added 3 4cup of white sugar and 3 8cup of brown sugar. How much sugar did he use in all? (unit) 8. On the back of this page, write a number story using fractions. Then write a number model to show how you solved it. Practice 59 9. 3891 10. 6891 → 11. 12 891 → 12. 24 891 →

STUDY LINK 5 4 Equivalent Fractions Copyright © Wright Group/McGraw-Hill 132 Name Date Time If the fractions are equivalent, write in the answer blank. If the fractions are not equivalent, write (not equal to) in the answer blank. 1. 3 4 19 2 2. 13 0 1 5 3. 17 4 18 5 4. 1 10 2 5 6 5. 11 06 0 58 0 6. 3 76 2 1 2 7. 17 2  2 31 6 8. 8 3 1 66 Fill in the boxes to complete and match the equivalent fractions. Example: 9. 3 5 —10 10. 2 3 —14 11. 4 54 5 —5 12. —12  13 0 13. 3 65 0 —7 14. 19 6 —45 15. 39 6 —108 16. —7  1 8 17. 13 30 5  —27 18. 1 10 6 —112 19. 7$4 9 .2 8  20. 15$ 300.45 21. 21 367 → 22. 8644 → 15 2  46 5 Practice 59

LESSON 5 4 Name Date Time Exploring Simplest Form 133 Copyright © Wright Group/McGraw-Hill A fraction is in simplest form if no other equivalent fraction can be found by dividing the numerator and the denominator by a whole number. For example, 1 2is in simplest form. 1. Use the division rule to find equivalent fractions. a. 14 0 b. 13 5 c. 24 0 d. 25 5 e. 36 0 f. 3 30 6 g. 3 45 2 h. 4 40 8 i. 4 55 4 j. 2 30 2 2. List the fractions from your answers in 3. Find and list the simplest form for the Problem 1 that are in simplest form. remaining fractions. 4. Jamie wants to be able to find the simplest form for any fraction by using the division rule and dividing only once. What should she do?

STUDY LINK 5 5 Decimal Numbers Copyright © Wright Group/McGraw-Hill 134 32 33 45 46 Name Date Time 1. Mark each number on the number line. The first one is done for you. 30.13 30.72 31.05 29.94 30.38 2. Round the area of each country to the nearest tenth of a square kilometer. 29.9 30.0 30.1 30.13 30.2 30.3 30.4 30.5 30.6 30.7 30.8 30.9 31.0 31.1 Practice Solve and write the fact family number sentences. 3. 327  68    Ten Smallest Area in SquareArea Rounded to Countries Kilometersthe Nearest Tenth of a Square Kilometer 1Vatican City 0.44 km 2 km 2 2Monaco 1.89 km 2 km 2 3Nauru 20.72 km 2 km 2 4Tuvalu 23.96 km 2 km 2 5San Marino 60.87 km 2 km 2 6Liechtenstein 160.58 km 2 km 2 7Marshall Islands 181.30 km 2 km 2 8St. Kitts and Nevis 296.37 km 2 km 2 9Maldives 297.85 km 2 km 2 10Malta 315.98 km 2 km 2 Source:The Top 10 of Everything 2005

LESSON 5 5 Name Date Time Renaming Fractions as Decimals 135 Copyright © Wright Group/McGraw-Hill 1. Fill in the missing numbers and shade the squares. Each large square is worth 1. Shade 4 5of the square. Shade 1 4of the square. Shade 25 5of the square. a. 4 5 —10 0. b. 1 4 —100 0. c. 25 5 —100 0. Shade 21 5of the square. Shade 54 0of the square.Write the shaded part as a fraction and as a decimal. d. 21 5 —100 0. e. 54 0 —100 0. f. 0. 2. Write each number below as a decimal. Then use the letters to mark the decimals on the number line. a. 3 4. b. 13 0 . c. 2 5. d. 12 07 0 . e. 1 21 5. f. 1 57 0. g. 6 5. h. 155 0. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Whole large square

LESSON 5 5 Name Date Time 136 Copyright © Wright Group/McGraw-Hill Draw number lines to help you round the numbers below. Example:Round 37 to the nearest ten.  Draw and label a number line from the first multiple of 10 less than 37 (that is, 30) to the first multiple of 10 greater than 37 (that is, 40). Mark and label the point halfway between these endpoints (35).  Find 37 on the number line. Mark and label it.  Since 37 is closer to 40, round 37 up to 40. 1. Round 26 to the nearest ten. 2. Round 1,256 to the nearest hundred. 3. Round 1,256 to the nearest thousand. 4. Round 2.6 to the nearest whole number. 5. Round 182.73 to the nearest ten. 6. Round 1,009 to the nearest hundred. Rounding Whole Numbers and Decimals 30 3537 40

LESSON 5 6 Name Date Time Fraction-Stick Chart and Decimal Number Line 137 Copyright © Wright Group/McGraw-Hill 1 12 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 7 1 6 1 6 1 6 1 6 1 6 1 6 1 5 1 5 1 5 1 5 1 5 1 4 1 4 1 4 1 4 1 3 1 3 1 2 1 3 1 2 1 1 4 1 2 4 3 4 0 1 7 1 7 1 7 1 7 1 7 1 7 0.0 0.1 0.2 0.3 0.50.4 0.6 0.7 0.90.8 1.0

LESSON 5 6 Name Date Time 138 Copyright © Wright Group/McGraw-Hill 1 1 2 3 4 5 Denominator 6 7 8 9 102345Numerator 678910 1.0 2.0 3.0 0.5 1.0 1.5 2.3 0.25 1.25 0.2 1.0 1.6 0.142857 0.625 0.8 0.1 Table of Decimal Equivalents for Fractions Example:To find the decimal equivalent for 1 4, use the row for the denominator 4. Go to the column for the numerator 1. The box where the row and the column meet shows the decimal 0.25.

STUDY LINK 5 6 139 63 83 89 Name Date Time Copyright © Wright Group/McGraw-Hill Decimals, Fractions, and Mixed Numbers 1. Convert each decimal measurement to a mixed number. 2. The longest one-word name of any place in America is Chargoggagoggmanchauggagoggchaubunagungamaugg. This name for a lake near Webster, Massachusetts, is 45 letters long. It is a Native American name that means “You fish on your side, I’ll fish on mine, and no one fishes in the middle.” Use this word to answer the problems below. a. What fraction of the word is made up of the letter g? b. What fraction of the word is made up of the letter a? c. What fraction of the word is made up of the letter c? 3. In the space above, write the decimal equivalents for the fractions in Problem 2. Practice 4. 107 ,146 → 5. 10 84 → 6. 10 675 → Source:The Top 10 of Everything 2005 Longest Road and Rail Decimal Length Mixed-Number Length Tunnels in the U.S. Cascade Tunnel (Washington) 7.79 miles miles Flathead Tunnel (Montana) 7.78 miles miles Moffat Tunnel (Colorado) 6.21 miles miles Hoosac Tunnel (Massachusetts) 4.7 miles miles BART Transbay Tubes (San Francisco, CA) 3.6 miles miles   

LESSON 5 6 Name Date Time Fractions and Decimals 140 Copyright © Wright Group/McGraw-Hill Write the fraction name and decimal name for the shaded portion of each square. Use your transparent 100-grid to check your answer. For Problem 9, color the grid to show a fraction and then write the fraction and decimal name for the shaded portion of the square. 1. —————————————— 0. 2. —————————————— 0. 3. —————————————— 0. 3 10 3 4. —————————————— 0. 5. —————————————— 0. 6. —————————————— 0. 7. —————————————— 0. 8. —————————————— 0. 9. —————————————— 0.

LESSON 5 6 Name Date Time 100-Grids 141 Copyright © Wright Group/McGraw-Hill

STUDY LINK 5 7 Decimal Comparisons Copyright © Wright Group/McGraw-Hill 142 Name Date Time Write three numbers between each pair of numbers. 1. 0 and 1 , , 2. 2 and 3 , , 3. 0.6 and 0.8 , , 4. 0.3 and 0.4 , , 5. 0.06 and 0.05 , , Circle the correct answer to each question. 6. Which is closer to 0.6? 0.5 or 0.53 7. Which is closer to 0.3? 0.02 or 0.2 8. Which is closer to 0.8? 0.77 or 0.85 9. Which is closer to 0.75? 0.6 or 0.8  10. Which is closer to 0.04? 0.3 or 0.051 11. Arrange the decimals below in order from least to greatest. 0.12 0.05 0.2 0.78 0.6 0.043 0.1 Practice 12. 9$63.54 13. 45 287 → 14. 7567 15. 74,861 → 32 33

STUDY LINK 5 8 Percent Problems 143 52 66 83 89 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Convert the following fractions to decimals and percents. Round to the nearest whole percent. Fraction Decimal Percent 3 4 1 14 6 1 25 5 1 27 0 3 8 2. On the back of this page, explain how you could find the percent equivalent to 1 27 0without using a calculator. 3. Write the five fractions from Problem 1 in order from least to greatest. 4. Katie spent 50% of her money on shoes for soccer. The shoes cost $65. How much money did Katie start with? 5. Tom got 70% of the questions correct on a music test. If he got 7 questions correct, how many questions were on the test? Practice 6. 109 75 → 7. 209 75 → 8. 309 75 → 9. 409 75 →

LESSON 5 8 Name Date Time Solving Percent Number Stories 144 Copyright © Wright Group/McGraw-Hill Solve. 1. Paul has 150 marbles in his collection. How many marbles are about 25% of the collection? About how many marbles are 66%? 2. Beatrice decided to sell some of her doll collection. She sold 20 dolls. This was 40% of her collection. How many dolls did she have left? 3. Each day, the bakery makes pastries: 25% are chocolate donuts, 37.5% are butter cookies, 25% are breakfast buns, and the rest are the daily special. There are 90 breakfast buns. How many pastries are made each day? What percent of each day’s pastries are the daily special? How many of the daily special pastries are made? 4. After the first 85 days of school, a fifth-grade class had perfect attendance for 80% of that time. How many days did the class have perfect attendance? 5. Write a percent of story problem for your partner to solve. Remember that you must provide either the whole, or an amount and the percent of the whole that it represents.

STUDY LINK 5 9 Graphs 145 122 124 125 Name Date Time Copyright © Wright Group/McGraw-Hill Brenda’s class made a list of their favorite colors. Here are the results. Blue 8 Red 7 Yellow 3 Green 2 Other 4 1. Circle each graph that correctly represents the data above. (There may be more than one.) Marsha kept track of low temperatures. Here are the results for the end of May: May 17 50 F May 18 63 F May 19 58 F May 20 60 F May 21 65 F May 22 57 F May 23 58 F May 24 65 F May 25 68 F May 26 70 F May 27 66 F May 28 65 F May 29 64 F May 30 68 F May 31 74 F Number of Students Green Yellow Blue Other Red 0 1 2 3 4 5 6 7 8 blue 33% red 29% yellow 13% green 8%other 17% Number of Students Green Yellow Blue Other Red 0 1 2 3 4 5 6 7 8 17 19 21 23 25 27 29 31 50 54 58 62 66 70 74 Date (in May)Temperature (°F) Line Graph 50 57 58 60 63 64 65 66 68 7074 1 0 2 3 Number of Days Temperature (°F) Bar Graph 2. Which graph do you think is more helpful for answering the question, “On how many days was the low temperature 65 F?” 3. Which graph do you think is more helpful for showing trends in the temperature for the last two weeks of May? 4. On the back of this page, explain your choices for Problems 2 and 3.

LESSON 5 9 Name Date Time Finding Equivalent Fractions 146 Copyright © Wright Group/McGraw-Hill 1. Fill in the blanks to show how the multiplication rule or the division rule is used to find equivalent fractions. a.b.c. d. 2. Fill in the blanks to make equivalent fractions. a.b.c. d.e.f. 6 8  4 52 6 42 33 2 6  8 9 4  3  29 7 1 58 6 3 4 9 12 72 81  8 9 56 63  8 9  3 4  1 3 110  1 12 1  27 36  54 72  6 8  3. Circle T or F. a. TF b. TF c. TF d. TF e. TF f. TF 1 40 4 4 4 4 1 2  3 4 1 4 1 2  2 6 2 60 00 0 9 8 8 9 19 2 3 4 5 74 2 3 4

LESSON 5 10 Name Date Time Circle Graph 147 Copyright © Wright Group/McGraw-Hill

STUDY LINK 5 10 Circle Graphs and Collecting Data Copyright © Wright Group/McGraw-Hill 148 125 126 Name Date Time 1. Estimate the percent of the circle for each piece of the graph at the right. a. A is about of the circle. b. B is about of the circle. c. C is about of the circle. 2. Draw a line connecting each data set with the most likely circle graph. A C B 30% of Michel’s class walks to school. 30% of Michel’s class rides the bus. 40% of Michel’s class rides in a car or van.25% of Jeannene’s toy cars are blue. 10% of Jeannene’s toy cars are striped. 65% of Jeannene’s toy cars are red. 1 8of Angelo’s pants are jeans. 1 8of Angelo’s pants are black dress pants. 3 4of Angelo’s pants are blue dress pants. 3. Circle the graph above that you did not use. Write a set of data to match that circle graph. Practice 4. 63,798 5. 78.145 6. 221 → 7. 8804 →

STUDY LINK 5 10 Circle Graphs and Collecting Data cont. 149 Name Date Time Copyright © Wright Group/McGraw-Hill The Number of States We’ve Been In 8. Talk with an adult at home and think of all the states you have visited. (Be sure to include the state you’re living in.) Look at the map below to help you remember. Use a pencil or crayon to mark each state you have visited. Don’t count any state that you have flown over in an airplane unless the plane landed, and you left the airport. 9. Count the number of states you have marked. I have been in states in my lifetime. 10. Now ask the adult to mark the map to show the states he or she has been in, using a different color or mark from yours. Keep a tally as states are marked. The adult I interviewed has visited states. Student and adult: This data is important for our next mathematics class. Please bring this completed Study Link back to school tomorrow. Washington Oregon IdahoMontana Wyoming Nevada CaliforniaUtah ArizonaColorado New MexicoKansas OklahomaMissouri Arkansas Texas Louisiana Mississippi Illinois North Dakota South DakotaMinnesota Wisconsin Iowa NebraskaMichigan Indiana Ohio West Virginia PennsylvaniaNew York Virginia KentuckyVermont New Hampshire Maine Rhode IslandMassachusetts Connecticut New Jersey Delaware Maryland North Carolina Tennessee AlabamaGeorgiaSouth Carolina Florida Hawaii Alaska Note: Alaska and Hawaii are not shown to scale. 125 126

STUDY LINK 5 11 What’s in a Landfill? Copyright © Wright Group/McGraw-Hill 150 Name Date Time People who study landfills have estimated the percent of landfill space (volume) taken up by paper, food, plastic, and so on. Space in landfills taken up by: Paper . . . . . . . . . . . . . . . . 50% Food and yard waste . . . . 13% Plastic . . . . . . . . . . . . . . . 10% Metal . . . . . . . . . . . . . . . . . 6% Glass . . . . . . . . . . . . . . . . . 1% Other waste . . . . . . . . . . . 20% 1. Cut out the Percent Circle. Use it to make a circle graph for the data in the table. (Remember to label the graph and give it a title.)Think of it this way: For every 100 boxes of garbage hauled to the dump, expect that about 50 boxes could be filled with paper, 6 with metal, 1 with glass, and so on. 126 5% 15% 30% 35% 40% 45% 55% 60% 65% 70%80%85%90%95% 0% 10% 20% 25% 50% 75% 1/51/6 1/101/8 1/3 3/4 1/4 2/3 1/2 2. 23 391 3. 17 391 4. 43 387 5. 37 259 Practice

STUDY LINK 5 12 Finding “Fractions of” 151 Name Date Time Copyright © Wright Group/McGraw-Hill Practice Solve. 1. Tomas ate 3 8of a bag of 24 cookies. Mona ate 2 5of a bag of 25 cookies. Who ate more cookies? Explain your answer. 2. On Thursday, 24 fifth-grade students came to school. That was only 2 3of the total class. The rest were home sick. How many students were sick? Explain your answer. 3. Mario was on a 21-mile hiking trail. He walked 3 7of the trail before stopping for lunch. How far did he walk before lunch? Explain your answer. 4. 52 156 6. 13 286 5. 24 576 7. 22 528 74

LESSON 5 12 Name Date Time Mathematics Instruction in History 152 Copyright © Wright Group/McGraw-Hill Throughout our nation’s history, students have learned mathematics in different ways and have spent their time working on different kinds of problems. This is because people’s views of what students can and should learn are constantly changing. 1. 1840sIt was discovered that children could be very good at mental arithmetic, and students began to solve mental arithmetic problems as early as age 4. A school in Connecticut reported that its arithmetic champion could mentally multiply 314,521,325 by 231,452,153 in 5 1 2minutes. After studying arithmetic two hours per day for 7 to 9 years, 94% of eighth graders in Boston in 1845 could solve the following problem. Try to solve it. What is 1 2of 1 3of 9 hours and 18 minutes? Explain your solution: 2. 1870sMany textbooks were step-by-step guides on how to solve various problems. Students were given problems and answers. They had to show how the rules in the textbook could be used to produce the given answers. Here is a problem from around 1870 (without the answer) given to students at the end of 6 to 8 years of elementary arithmetic study. Try to solve it. I was married at the age of 21. If I live 19 years longer, I will have been married 60 years. What is my age now? Explain your solution: (unit) (unit)

Name Date Time Copyright © Wright Group/McGraw-Hill Using Data; Addition and Subtraction of Fractions The authors of Everyday Mathematicsbelieve that students should work substantially with data. Unit 6 is designed to present and teach relevant data skills and concepts, allowing your child ample opportunities to practice organizing and analyzing the data that he or she collects. The data that your child collects at first will usually be an unorganized set of numbers. After organizing the data using a variety of methods, he or she will study thelandmarksof the data. The following terms are called landmarks because they show important features of the data.  Themaximumis the largest data value observed.  Theminimumis the smallest data value observed.  Therangeis the difference between the maximum and the minimum.  Themodeis the most popular data value—the value observed most often.  Themedianis the middle data value observed.  Themean,commonly known as the average, is a central value for a set of data. At the end of the unit, students will demonstrate their skills by conducting a survey of their peers, gathering and organizing the data, analyzing their results, and writing a summary report. Your child will continue the American Tour by studying Native American measurements for length and distance, based on parts of the body. Students will convert these body measures to personal measures by measuring their fingers, hands, and arms in both metric and U.S. customary units. In addition, your child will learn how to read a variety of contour-type maps, such as climate, precipitation, and growing-seasons maps. Finally, students will explore addition and subtraction of fractions by using paper slide rules, a clock face, and fraction sticks. They will learn to find common denominators and apply this skill to add and subtract fractions with unlike denominators. Please keep this Family Letter for reference as your child works through Unit 6. STUDY LINK 5 13 Unit 6: Family Letter 153

Copyright © Wright Group/McGraw-Hill Vocabulary Important terms in Unit 6: angle of separation In Everyday Mathematics,the angle measure between spread fingers. The figure shows the angle of separation between a person’s thumb and first finger. common denominator Any number except zero that is a multiple of the denominators of two or more fractions. For example, the fractions 1 2and 2 3 have common denominators 6, 12, 18, and so on. contour line A curve on a map through places where a certain measurement (such as temperature or elevation) is the same. Often, contour lines separate regions that have been colored differently to show a range of conditions. cubit An ancient unit of length, measured from the point of the elbow to the end of the middle finger. A cubit is about 18 inches. decennial Occurring every 10 years. fair game A game in which each player has the same chance of winning. If any player has an advantage or disadvantage, then the game is not fair. fathom A unit used by people who work with boats and ships to measure depths underwater and lengths of cables. A fathom is now defined as 6 feet. great span The distance from the tip of the thumb to the tip of the little finger (pinkie), when the hand is stretched as far as possible. landmark A notable feature of a data set. Landmarksinclude the median, mode, maximum, minimum,andrange. line plot A sketch of data in which check marks, Xs, or other marks above a labeled line show the frequency of each value. map legend (map key) A diagram that explains the symbols, markings, and colors on a map. mode The value or values that occur most often in a set of data. normal span The distance from the tip of the thumb to the tip of the first (index) finger of an outstretched hand. Also called span. population In data collection, the group of people or objects that is the focus of the study. range The difference between the maximumand minimumin a set of data. sample A part of a population chosen to represent the whole population. simplest form A fraction less than 1 is in simplest form if there is no number other than 1 that divides its numerator and denominator evenly. A mixed number is in simplest form if its fractional part is in simplest form. stem-and-leaf plot A display of data in which digits with larger place values are “stems” and digits with smaller place values are “leaves.” Data list: 24, 24, 25, 26, 27, 27, 28, 31, 31, 32, 32, 36, 36, 36, 41, 41, 43, 45, 48, 50, 52 survey A study that collects data. Angle of separation great span normal span Unit 6: Family Letter cont. STUDY LINK 513 154 Stem-and-leaf plot Stems Leaves (10s) (1s) 2 4456778 3 1122666 4 11358 502

155 Copyright © Wright Group/McGraw-Hill Do-Anytime Activities In this unit, your child will work on his or her understanding of angles and the addition and subtraction of fractions by playing the following games. For detailed instructions, see the Student Reference Book. Divisibility DashSeeStudent Reference Book,page 302. This is a game for two or three players. Game materials include 4 each of the number cards 0–9 as well as 2 each of the number cards 2, 3, 5, 6, 9, and 10. This game provides practice in recognizing multiples and using divisibility rules in a context that also develops speed. Frac-Tac-ToeSeeStudent Reference Book,pages 309–311. This is a game for two players. Game materials include 4 each of the number cards 0–10, pennies or counters of two colors, a calculator, and a gameboard. The gameboard is a 5-by-5 number grid that resembles a bingo card. Several versions of the gameboard are shown in the Student Reference Book. Frac-Tac-Toehelps students practice converting fractions to decimals and percents. In Unit 6, students practice fraction/decimal conversions. Fraction CaptureSeeMathJournal,page 198.This is a game for two players and requires 2 six-sided dice and a gameboard. Partners roll dice to form fractions and then attempt to capture squares on a Fraction Capturegameboard. This game provides practice in finding equivalent fractions and in adding fractions. Building Skills through Games To work with your child on the concepts taught in this unit and in previous units, try these interesting and rewarding activities. 1.Have your child design and conduct an informal survey. Help him or her collect and organize the data, and then describe the data using data landmarks. Challenge your child to create different ways to present the data. 2.Encourage your child to develop his or her own set of personal measures for both metric and U.S. customary units. Unit 6: Family Letter cont. STUDY LINK 513

156 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. The answers listed below will guide you through this unit’s Study Links. Study Link 6 1 3. a.59b.24c.33 d. 36 e. 39.5 5.18.436.16 Study Link 6 2 2. a.cm; ftb.ounces; gal; liters c.m; milesd.cm; ft; mm e.kg; lb; grams 3.2,6866.141.63 Study Link 6 3 1.73; maximum2.193.53 4.Sample answer: Cross off the highest and lowest values—31 and 73. Continue by crossing off the highest and lowest values remaining, so that only one number, 53, remains. 5.3,2868.65,250 Study Link 6 4 1.Tapes and CDs2.Books and magazines 3.Movie tickets4.5,593 5.16,5396.582 R37.75,896 Study Link 6 5 Sample answers given for Problems 1–3. 1.5, 7, 7, 8, 8, 9, 10, 13, 14, 15, 15, 15, 20 2.3.The number of minutes it takes to get ready for bed 5.4437.1,839 Study Link 6 6 1.Sample answer: Ages of the oldest people we know Title: The Oldest People Our Class Knows Unit: Years 4. a.32b.99c.66d.78.5 5.12,4957.8,484 Study Link 6 7 1.California; Arizona2.Montana; Washington 4.2,0866.81 Study Link 6 8 1. 1 10 4, or 5 7 3. 16 5, or 2 5 5.9,3847.2,952 Study Link 6 9 1. 2 12 5, or 1 17 5 2. 11 8 3. 9 4, or 2 1 4 4.4; 7 3 4 5.5 5 6 Study Link 6 10 1. 1 28 2 1 21 2 27 2 2. 2 30 6 39 6 1 31 6 3. 2 31 0 38 0 2 39 0 4. 2 31 0 38 0 1 33 0 5. 1 19 8, or 1 11 8 6. 5 49 2, or 1 1 47 2 7. 1 6 8. 3 4 9. 12 2, or 1 6 10. 1 2 11. 1 3 12. 2 13 2, or 1 1 11 2 13. 2 13 2, or 1 1 11 2 14. 1 19 2, or 1 17 2 Minutes Minutes Needed to Get Ready for Bed (title) Number of Students 2 1 0 56 78910 11 12 13 14 15 16 17 18 19 20 4 3 6 5 8 7 Unit 6: Family Letter cont. STUDY LINK 513