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221 Copyright © Wright Group/McGraw-Hill STUDY LINK 8 1 Comparing Fractions 66–68 83–88 Name Date Time Circle the greater fraction for each pair. 1. 3 8 or 3 6 2. 2 3 or 2 9 3. 4 7 or 5 6 4. 1 29 0 or 4 8 5. 1 21 1 or 19 7 6. 4 7 or 16 1 7. Explain how you got your answer for Problem 5. Write the decimal equivalent for each fraction. 8. 3 4 9. 2 3 10. 5 8 11. 17 0  12. 1 21 0 13. 2 21 5 14. Explain how you can do Problem 10 without using a calculator. Use , , or to make each number sentence true. 15. 1 2 5 8 1 16. 2 3 2 6 1 17. 7 9 3 5 1 18. 1 16 0 25 0 19. 1 3 8 4 9 20. 1 6 7 1 8 21. Explain how you found the answer to Problem 20. Practice 22. 675 42  23. 28,350 675  24. 67.5 0.42  25. 28,350 42 67.08 

222 Copyright © Wright Group/McGraw-Hill LESSON 8 1 Name Date Time Exploring Least Common Multiples One way to find a common denominator is to use the least common multiple. The LCM is the smallest number that is a multiple of the given denominators. You can find the least common multiple by making lists of multiples. Find the least common multiple for 4 9, 5 6, and 1 4. List the multiples of each denominator. Multiples of 9: Multiples of 6: Multiples of 4: Least common multiple: Another way to find the least common multiple is to use prime factorization. Find the least common multiple for 8 and 6. Step 1Use factor trees to find the prime factorization. Step 2Count the appearance of each different prime number. Note only the largest counts. 2 appears 3 times in the prime factorization of 8. 3 appears once in the prime factorization of 6. Step 3Write a multiplication expression using these counts. 2 2 2 3 24 so 24 is the least common multiple of 8 and 6. Use the prime factorization method to find the LCM. 1. 9, 6, and 4 2. 20 and 90 3. 15 and 49 4. 12, 15, and 25 LCM: LCM: LCM: LCM: 5. What might be an advantage or disadvantage to using the prime factorization method to find the least common multiple? 2 2 º 4 8 2 2 º º 6 2 3 º

223 Copyright © Wright Group/McGraw-Hill STUDY LINK 8 2 Adding Mixed Numbers 61 63 70 Name Date Time 17. 3,540 6  18. 1,770 3  19. 7,080 / 12  20. (590 5) 2  Rename each mixed number in simplest form. 1. 36 5 2. 1 86 3. 95 3 4. 17 5 5. 46 4 6. 51 60 Add. Write each sum as a whole number or mixed number in simplest form. 7. 31 42 3 4 8. 41 53 4 5 9. 91 34 2 3 10. 35 78 6 7 11. 1 853 3 8 12. 42 95 5 9 Add. 13. 25 8 14. 71 2 15. 46 9 16. 53 4 6 3 4 3 2 3 3 17 2 2 4 5 4 1 5 Practice

Copyright © Wright Group/McGraw-Hill 224 STUDY LINK 8 3 Subtracting Mixed Numbers 71 72 Name Date Time Fill in the missing numbers. 1. 33 82 —8 2. 45 6 1 61 3. 21 91 —9 4. 63 7 1 70 5. 43 53 —5 6. 72 3 —3 Subtract. Write your answers in simplest form. 7. 53 4 8. 62 3 9. 54 5  3 1 4  4 1 3 3 3 5 10. 4 3 8  11. 6 5 9  12. 52 13 0  13. 7 4 3 4  14. 32 51 3 5 15. 43 83 7 8 16. 654 205  17. 654 502  18. 654 250  19. 654 520  Practice

225 Copyright © Wright Group/McGraw-Hill LESSON 8 3 Name Date Time Addition and Subtraction Patterns Add. 1. a. 1 1 1 2 b. 1 2 1 3 c. 1 3 1 4 d. 1 4 1 5 e. 1 5 1 6 2. What pattern do you notice in Problems 1a–1e? 3. Use the pattern above to solve these problems. a. 1 6 1 7 b. 11 0 11 1 c. 91 9 11 00  4. Do you think this pattern also works for problems like 1 8 1 3? Explain. 5. The plus signs in Problem 1 have been replaced with minus signs. Find each answer. a. 1 1 1 2 b. 1 2 1 3 c. 1 3 1 4 d. 1 4 1 5 e. 1 5 1 6 f. Describe the pattern.

Copyright © Wright Group/McGraw-Hill 226 STUDY LINK 8 4 More Fraction Problems 66–68 Name Date Time 1. Circle all the fractions below that are greater than 3 4. 4 5 1 23 0 1 2 1 28 5 19 2 1 25 05 0 17 1 Rewrite each expression by renaming the fractions with a common denominator. Then decide whether the sum or difference is greater than 1 2, less than 1 2, or equal to 1 2. Circle your answer. 2. 11 0 2 7  1 2  1 2  1 2 3. 5 6 1 4  1 2  1 2  1 2 4. 1 28 0 2 5  1 2  1 2  1 2 5. 3 4 1 3  1 2  1 2  1 2 Fraction Puzzle 6. Select and place three different numbers so the sum is as large as possible. Procedure:Select three different numbers from this list: 1, 2, 3, 4, 5, 6. Write the same number in each square. Write a different number in the circle. Write a third number in the hexagon. Add the two fractions. Example: 8 4  2   2 42 3 Practice 7. 3 2.564  8. 3 2.564  9. 16 5.438  10. 3,049 / 15 

227 Copyright © Wright Group/McGraw-Hill LESSON 8 4 Name Date Time Charting Common Denominators Find the least common denominator.Use the QCD.Is one denominator a factor of the other denominator? START Common denominator? No NoYes Yes Rename both fractions. Rename the fraction. Add numerators. Write the solution number sentence. STOP

228 Copyright © Wright Group/McGraw-Hill LESSON 8 4 Name Date Time Exploring Equivalent Fractions 1. Do equivalent fractions convert to the same decimal? 2. Complete the fraction column in the table so there are 10 equivalent fractions. 3. Use your calculator to convert each fraction to a decimal. Write the display in the decimal column. (Don’t forget to use a repeat bar, if necessary.) Fractions Decimals 4. Explain your results. Describe the relationship between the equivalent fractions and their decimal form.

229 Copyright © Wright Group/McGraw-Hill STUDY LINK 8 5 Fractions of a Fraction Name Date Time Example: The whole rectangle represents ONE.Shade 3 8of the interior.Shade 1 3of the interior in a different way. 1. Shade 3 4of the interior. Shade 1 3of the interior in a different way. The double shading shows that 1 3of 3 4is . 3. Shade 4 5. Shade 3 4of the interior in a different way. The double shading shows that 3 4of 4 5is . 2. Shade 3 5of the interior. Shade 2 3of the interior in a different way. The double shading shows that 2 3of 3 5is . 4. Shade 5 8. Shade 3 5of the interior in a different way. The double shading shows that 3 5of 5 8is . The double shading shows that 1 3of 3 8is 23 4, or 1 8. In each of the following problems, the whole rectangle represents ONE. 5. Nina and Phillip cut Mr. Ferguson’s lawn. Nina worked alone on her half, but Phillip shared his half equally with his friends, Ezra and Benjamin. What fraction of the earnings should each person get? 76 243

230 Copyright © Wright Group/McGraw-Hill LESSON 85 Name Date Time Equivalent Fractions Use the fraction stick to find equivalent fractions. A whole stick is worth 1. 1. Divide the fraction stick into 4 equal parts. Find the equivalent fraction. 1 2 2. Divide the fraction stick into 8 equal parts. Find the equivalent fractions. 1 2 3. Divide the fraction stick into 16 equal parts. Find the equivalent fractions. 1 2 4 4 4 8 8 16

231 Copyright © Wright Group/McGraw-Hill LESSON 8 6 Name Date Time An Area Model for Fraction Multiplication 1. Use the rectangle at the right to find 2 3º 3 4. 2 3º 3 4 Your completed drawing in Problem 1 is called an area model. Use area models to complete the following. 2. 3. 4. 2 3º 1 5 3 4º 2 5 1 4º 5 6 5. 6. 7. 3 8º 3 5 1 2º 5 8 5 6º 4 5 8. Explain how you sketched and shaded the rectangle to solve Problem 7.

Copyright © Wright Group/McGraw-Hill 232 STUDY LINK 8 6 Multiplying Fractions 74 76 Name Date Time Write a number model for each area model. Example: 1. 2. 3. Multiply. 4. 3 7º 12 0 5. 5 6º 2 3 6. 1 2º 1 4 7. 4 5º 3 5 8. 2 3º 3 8 9. 1 7º 5 9 10. Matt is making cookies for the school fund-raiser. The recipe calls for 2 3cup of chocolate chips. He decides to triple the recipe. How many cups of chocolate chips does he need? cups 11. The total number of goals scored by both teams in the field-hockey game was 15. Julie’s team scored 3 5of the goals. Julie scored 1 3of her team’s goals. How many goals did Julie’s team score? goals How many goals did Julie score? goals 1 4 º 2 5  22 0  ,or 11 0  Reminder: a bº dc ba ºº dc 

233 Copyright © Wright Group/McGraw-Hill LESSON 8 6 Name Date Time Fraction Multiplication Problem 1 a. How many squares are in this grid? b. How many squares represent 1 3of 1 2of the grid. Shade these squares. c. Think of the total number of squares in the grid as the denominator and the shaded squares as the numerator, and write the fraction. 1 3of 1 2 d. Write the number model you would use to find the area of this rectangle. Reminder:Area length ºwidth Area  e. The number model to find the fractional part of the rectangle is the same as the number model to find the area of the rectangle. Write the number model you would use to find the fractional part of the rectangle. Problem 2 Linda bakes a peach pie. She serves 1 2of the pie for dessert. She saves 1 3of what is left for her mom. a. Shade the circle to represent the piece of the pie that should be saved. b. Think of the total number of pie pieces as the denominator and the shaded piece as the numerator, and write the fraction. c. Write a number sentence to show how you could find the fractional part of the pie that was saved without counting pie pieces. To find a fraction ofa fraction, multiply. 4 3 Try This Write and solve a number model to find the fractional part of the pie left after subtracting dessert and the piece saved for Linda’s mom.

234 Copyright © Wright Group/McGraw-Hill LESSON 8 6 Name Date Time Using Area Models to Multiply Fractions Use area models to complete the following problems. 1. 2. 3. 3 4º 1 6 2 3º 1 2 3 4of 1 2 4. 5. 6. 3 8º 3 4 1 6of 3 4 3 5º 1 6 Make up your own fraction multiplication problems. Use area models to help you solve them. 7. 8.  

235 Copyright © Wright Group/McGraw-Hill STUDY LINK 8 7 Multiplying Fractions and Whole Numbers Name Date Time Use the fraction multiplication algorithm to calculate the following products. 1. 5 3º 9  2. 3 8º 12  3. 1 8º 5  4. 20 º 3 4 5. 5 6º 14  6. 27 º 2 9 7. Use the given rule to complete the table. 8. What is the rule for the table below? 9. Make and complete your own “What’s My Rule?” table on the back of this page. Rule º 4 in ( )out ( ) 2 3 4 5 8 9 5 4 7 3 in ( )out ( ) 2 1 2 3 3 4 5 6 25 4 2 3 1 6 73 Rule

236 Copyright © Wright Group/McGraw-Hill LESSON 8 7 Name Date Time Simplifying Fraction Factors The commutative property lets us write ba ºº dc  as dcº ºa b  . Study the examples. Example 1: 7 8º 1 26 1 7 8º º1 26 1   1 11 62 8; 1 11 62 8  8 8 1 24 1, or 2 3 Example 2: 7 8º 1 26 1 7 8º º1 26 1   1 86º 27 1 2 1º 1 3 2 1º º1 3   2 3 1. Describe the similarities and differences between Examples 1 and 2. Example 3: 2. Describe the similarities and differences between Examples 2 and 3. Use what you have discovered to solve the following problems. Show your work. 3. 1 64 0º 1 22 1 4. 3 86 8º 3 73 2 5. 2 55 4º 3 46 5 7 8 2 3 16 21 1 º 2 1 º 3 1 12 3 º An Algorithm for Fraction Multiplication a bº dc ba ºº dc  The denominator of the product is the product of the factor denominators, and the numerator of the product is the product of the factor numerators.

237 Copyright © Wright Group/McGraw-Hill STUDY LINK 8 8 Multiplying Fractions and Mixed Numbers 76 –78 Name Date Time 1. Multiply. a. 53 4º 2 6 b. 5 8º 2 5 c. 41 4º 5 6 d. 21 3º 3 1 8 e. 311 2º 1 3 5 f. 24 5º 3 2 8 2. Find the area of each figure below. a. b. c. Area yd 2 Area ft 2 Area ft 2 3. The dimensions of a large doghouse are 2 1 2times the dimensions of a small doghouse. a. If the width of the small doghouse is 2 feet, what is the width of the large doghouse? feet b. If the length of the small doghouse is 2 1 4feet, what is the length of the large doghouse? feet ft5 6 2ft1 2 4 ft 2ft3 4 3yd2 3 2yd1 3 Area of a Rectangle Abº hArea of a Triangle A 1 2º bº hArea of a Parallelogram Abº h 2 ft 2 ft 1 4

Copyright © Wright Group/McGraw-Hill 238 STUDY LINK 8 9 Fractions, Decimals, and Percents 26 48 51 83 89 Name Date Time 1. Complete the table so each number is shown as a fraction, decimal, and percent. Fraction Decimal Percent 45% 0.3 12 0 0.15 2. Use your percent sense to estimate the discount for each item. Then calculate the discount for each item. (If necessary, round to the nearest cent.) ItemList Percent of Estimated Calculated Price Discount Discount Discount Saguaro cactus $400.00 25% with arms Life-size wax $10,000.00 16% figure of yourself Manhole cover $78.35 10% Live scorpion $14.98 5% 10,000 $29.00 30% honeybees Dinner for one on $88.00 6% the Eiffel Tower Magician’s box for sawing a $4,500.00 18% person in half Fire hydrant $1,100.00 35% Source:Everything Has Its Price

239 Copyright © Wright Group/McGraw-Hill LESSON 8 9 Name Date Time Finding the Percent of a Number The unit percent is 1% or 0.01. For example, the unit percent of 100 is 1; the unit percent of 200 is 2; the unit percent of 10 is 0.1. Another way to think of the unit percent of a number is to think: What number times 100 equals the whole?For example, 1 100 100; 2 100 200; 0.1 100 10 To find the unit percent of a whole, multiply by 0.01 or 11 00. Solve. 1. 1% of 84  2. 1% of 35  3. 1% of 628  The unit percent can be used to find other percents of a whole. For example, if you want to find 8% of 200: Calculate the unit percent: 1% of 200 200 0.01 2 Check your answer: 2 100 200. Multiply your answer by the percent you are finding: 2 8 16; 8% of 200 16 Solve. 4. 19% of 84  5. 72% of 35  6. 37% of 628  7. Think about the steps you followed in Problems 4–6. First you multiplied the unit percent by 0.01, and then you multiplied the product by the number of percents. How can you find the percent of a number by multiplying only once? Provide an example. 20 10 1% of 200 1% of 100 1 mm 1% of 10 cm 012345678910 cm

240 Copyright © Wright Group/McGraw-Hill LESSON 8 9 Name Date Time Calculating Discounts There are 2 steps to finding a discounted total: Calculate the amount that represents the percent of discount. Subtract the calculated discount from the original total. This is the discounted total. Calculate the discounted total for the following problems. Show your work on the back of this sheet. 1. A computer store has an Internet special for their customers. If Carla spends $50.00 or more, she gets 10% off her order. The shipping and handling charge is 4% of the original total. Carla buys $68.00 in software. What is her total charge? 2. The Hartfield School District wants to get the government discount for telephone service. The discount is based on the percent of students qualifying for the National School Lunch Program. 32% of students in this urban district qualify. The district pays about $3,500 per month for telephone service. Use the table below to find how much the district would save. Percent of Students Urban Discount Rural Discount Less than 1% 20% 25% 1% to 19% 40% 50% 20% to 34% 50% 60% 35% to 49% 60% 70% 50% to 74% 80% 80% 75% to 100% 90% 90% The Hartfield School District is eligible for a discount. The district will save about per month for its telephone service. With the government discount, the district will pay about per month. 3. At the Goose Island Family Restaurant, if the original bill is $75.00 or more, the kids’ meals are discounted 3%. If the original bill is $95.70, with $23.00 for kids’ meals, what is the discounted amount? What is the discounted total?

241 Copyright © Wright Group/McGraw-Hill STUDY LINK 810 Unit Fractions Name Date Time Finding the worth of the unit fraction will help you solve each problem below. 1. If 4 5of a number is 16, what is 1 5of the number? What is the number? 2. Our football team won 3 4of the games that it played. It won 12 games. How many games did it play? (unit) 3. When a balloon had traveled 800 miles, it had completed 2 3of its journey. What was the total length of its trip? (unit) 4. Grandpa baked cookies. Twenty cookies were oatmeal raisin. The oatmeal raisin cookies represent 5 8of all the cookies. How many cookies did Grandpa bake? (unit) 5. Tiana jogged 6 8of the way to school in 12 minutes. If she continues at the same speed, how long will her entire jog to school take? (unit) 6. After 35 minutes, Hayden had completed 17 0of his math test. If he has a total of 55 minutes to complete the test, do you think he will finish in time? Explain: in out 100 60 42 110 72 35 Rule out 60% of in 74 75 7. Complete the table using the given rule. 8. Find the rule. Then complete the table. in out 24 9 72 27 56 21 80 30 15 32 Rule out of in

242 Copyright © Wright Group/McGraw-Hill 1 4of 12  3 2 4of 12  6 3 4of 12  12 4 4of 12  24 LESSON 8 10 Name Date Time Fraction of and Percent of a Number George practiced finding the fraction of and the percent of a number. He completed the tables below. George thinks there is something wrong with his answers, but he doesn’t know how to fix it. 1. Study George’s tables and then explain how he should correct his work. 2. Write the correct answers. 20% of 40  6 40% of 40  12 60% of 40  18 80% of 40  24 100% of 40  30 1 4of 12  2 4of 12  3 4of 12  4 4of 12  20% of 40  40% of 40  60% of 40  80% of 40  100% of 40 

243 Copyright © Wright Group/McGraw-Hill LESSON 8 10 Name Date Time Fraction and Percent of a Number Methods 1. Alton collected 252 marbles but lost 4 7of them on his way to school. When he arrived at school, how many marbles did Alton have left? Explain how you found your answer. 2. Circle the letter of each method below that you could use to solve Problem 1. a. You can find 4 7of 252 by multiplying 252  4 7and simplifying. b. You can find 4 7of 252 by dividing 252 by 4 and multiplying the result by 7. c. You can find the unit fraction by dividing 252 by 7, and then find 4 7of 252 by multiplying the unit fraction value by 4. 3. For any method you did notcircle, explain why it will not work. 4. The regular price for rollerblades is $125 at a local store. The store was having a promotion: Buy one pair of rollerblades and get a second pair for 75% of the regular price. How much would a second pair of rollerblades cost? Explain how you found your answer. 5. Circle the letter of each method below that you could use to solve Problem 4. a. You can rename 75% as a fraction and then multiply $125 by the fraction to find 75% of $125. b. You can find the cost of the second pair by multiplying $125 by 1 4and subtracting the product from $125. c. You can find the cost of the second pair by dividing $125 by 4. 6. For any method you did notcircle, explain why it will not work.

244 Copyright © Wright Group/McGraw-Hill LESSON 8 11 Name Date Time Classroom Survey Number in Household Number of Students 1– 2 3–5 6 or more Language at Home Number of Students English Spanish Other Years at Current Address Number of Students 0 or 1 2 3 4 5 6 or more Handedness Number of Students right left

245 Copyright © Wright Group/McGraw-Hill STUDY LINK 8 11 Fraction Review Name Date Time Write three equivalent fractions for each fraction. 1. 7 8 2. 3 4 3. 16 2 4. 2 3 Circle the fraction that is closer to 1 2. 5. 3 8 or 4 5 6. 4 7 or 5 9 7. 7 8 or 7 9 8. 14 0 or 17 2 9. Explain how you found your answer for Problem 8. Solve. Write your answers in simplest form. 10.  5 6 3 4 11. 7 9 1 6 12. 8  2 3 13. 7 8 1 6 14. 3 4of 2 5is . 15. 4 º 5 6 Practice 16. 64,072 15,978  17. 2,297 45 ∑ 18. 1,674 1,204  19. 326 684 934  59 66 68 73 76

246 Copyright © Wright Group/McGraw-Hill LESSON 811 Name Date Time Using a Calculator with Percents Finding the percent of a number is the same as multiplying the number by the percent. Usually, it’s easiest to change the percent to a decimal and use a calculator. Example:What is 65% of 55? 65%  16 05 0 0.65 Write the fraction and decimal for each percent. 1. 18%  2. 60%  3. 89%  4. 7.5%  Use your calculator and the percents in Problem 1 to find the percent of 55 by multiplying 55 by each decimal. Example:55 0.65 5. 18% of 55  6. 60% of 55  7. 89% of 55  8. 7.5% of 55  9. Write the calculator key sequence that you used. Sometimes you know a percent and how much it’s worth, but you don’t know what the ONE is. Use a unit percent strategy first to find 1%, and then multiply by 100 to get 100%. Example:60 million is 37% of what number? 60 37 1.6216216 1.6216216 100 162.16216 Using the fix function 1.6216216 100 162 (rounded to the nearest whole number) 37% of 162 million is 59.94 million, or 60 million (rounded to the nearest ten million). Use your calculator and unit percents to solve the following problems. 10. 42% of 18 11. 87% of 65 12. 63% of 28 million

247 Copyright © Wright Group/McGraw-Hill LESSON 8 11 Name Date Time Charting Changes in Consumption Many times the information that interests you has to be located in data displays with much more data than you need. Use the information on Student Reference Book, page 363 to complete the table below. 1. Line graphs can make it easier to compare changes in data over time. Use the data from your table in Problem 1 to make a line graph of the pounds of carrots and grapes eaten per person, per year in the United States. Use one color for the carrots data and a different color for the grapes data. Indicate your choices by coloring in the boxes of the graph key. 2. 3. What is one conclusion you could draw from the data in your line graph? 1970 1980 1990 2000 0 1 2 3 4 5 6 7 8 9 10 11 Pounds per Person Carrots Grapes title Foods 1970 1980 1990 2000 Carrots Grapes (title) 363

Copyright © Wright Group/McGraw-Hill 248 STUDY LINK 8 12 Mixed-Number Review Name Date Time Fill in the missing numbers. 1. 41 43 —4 2. —5 3 7 5 Solve. Write your answers in simplest form. 3. 13 52 1 5 4. 33 81 5 8 5. 74 95 8 9 6. 32 71 4 5 7. 52 32 3 4 8. 4 1 3 4 9. 3 º 3 3 4 10. 42 3º 6 7 11. 2 1 2º 1 4 5 12. 13 0º 8 1 3 Common Denominator Division Here is one way to divide fractions and to divide whole or mixed numbers by fractions. Step 1Rename the numbers using a common denominator. Step 2Divide the numerators. Solve. Show your work. 13. 5  2 3 14. 4 7 3 5 15. 41 8 3 4 16. 62 3 7 9 62 63

249 Copyright © Wright Group/McGraw-Hill LESSON 8 12 Name Date Time Exploring the Meaning of the Reciprocal Lamont and Maribel have to divide fractions. Lamont doesn’t want to use common denominators. He thinks using the reciprocal is faster, but he’s not sure what a reciprocal is. Maribel looks it up on the Internet and finds this: One number is the reciprocal of another number if their product is 1. Example 1: Example 2: 3 º ? 1 1 2º ? 1 3 º 1 3 3 31 1 2º 2  2 21 1 3is the reciprocal of 3 2 is the reciprocal of 1 2 3 is the reciprocal of 1 3 1 2is the reciprocal of 2 1. Find the reciprocals. a. 6 b. 1 7 c. 20 d. 1 9 2. What do you think would be the reciprocal of 5 6? Reciprocals on a Calculator On all scientific calculators, you can find a reciprocal of a number by raising the number to the 1 power. 3. Write each number in standard notation as a decimal and a fraction. a. 81 , b. 52 , c. 23 , 4. Write the key sequence you could use to find the reciprocal of 36. 5. Write the key sequence you could use to find the reciprocal of 3 7. 6. What pattern do you see for the reciprocal of a fraction?

Copyright © Wright Group/McGraw-Hill 250 STUDY LINK 8 13 Unit 9: Family Letter Name Date Time Coordinates, Area, Volume, and Capacity In the beginning of this unit, your child will practice naming and locating ordered number pairs on a coordinate grid. Whole numbers, fractions, and negative numbers will be used as coordinates. Your child will play the game Hidden Treasure,which provides additional practice with coordinates. You might want to challenge your child to a round. In previous grades, your child studied the perimeters (distances around) and the areas (amounts of surface) of geometric figures. Fourth Grade Everyday Mathematicsdeveloped and applied formulas for the areas of rectangles, parallelograms, and triangles. In this unit, your child will review these formulas and explore new area topics, including the rectangle method for finding areas of regular and irregular shapes. Students will also examine how mathematical transformations change the area, perimeter, and angle measurements of a figure. These transformations resemble changes and motions in the physical world. In some transformations, figures are enlarged in one or two dimensions; in other transformations, figures are translated (slid) or reflected (flipped over). In the Earth’s Water Surface exploration, students locate places on Earth with latitude and longitude. Then they use latitude and longitude in a sampling experiment that enables them to estimate, without measuring, the percent of Earth’s surface that is covered by water. In the School’s Land Area exploration, students use actual measurements and scale drawings to estimate their school’s land area. The unit concludes with a look at volume (the amount of space an object takes up) and capacity (the amount of material a container can hold). Students develop a formula for the volume of a prism (volume area of the base the height). They observe the metric equivalents 1 liter 1,000 milliliters 1,000 cubic centimeters, and they practice making conversions between U.S. customary measures (1 gallon 4 quarts, and so on). Please keep this Family Letter for reference as your child works through Unit 9. Rectangular prism height area of base Trapezoidal prismarea of base height height area of base Hexagonal prism

251 Copyright © Wright Group/McGraw-Hill Vocabulary Important terms in Unit 9: area The amount of surface inside a 2-dimensional figure. Area is measured in square units, such as square inches (in 2) and square centimeters (cm 2). axis of a coordinate grid Either of the two number lines that intersect to form a coordinate grid. capacity The amount of space occupied by a 3-dimensionalshape. Same as volume.The amount a container can hold. Capacity is often measured in units such as quarts, gallons, cups,or liters. coordinate A number used to locate a point on a number line, or one of two numbers used to locate a point on a coordinate grid. coordinate grid A reference frame for locating points in a plane using ordered number pairs, or coordinates. formula A general rule for finding the value of something. A formula is usually an equation with quantities represented by letter variables. For example, the formula for the area of a rectangle may be written as Aºw,where Arepresents the area of the rectangle, represents the length, and w represents the width. latitude A measure, in degrees, of the distance of a place north or south of the equator. longitude A measure, in degrees, of how far east or west of the prime meridian a place is. ordered number pair Two numbers that are used to locate a point on a coordinate grid.The first number gives the position along the horizontal axis; the second number gives the position along the vertical axis. Ordered number pairs are usually written inside parentheses: (2,3). perpendicular Two lines or two planes that intersect at right angles. Line segments or rays that lie on perpendicular lines are perpendicular to each other. The symbol means is perpendicular to. rectangle method A method for finding area in which one or more rectangles are drawn around a figure or parts of a figure. transformation Something done to a geometric figure that produces a new figure. Common transformations are translations (slides), reflections (flips), and rotations (turns). volume The amount of space occupied by a 3-dimensional shape. Same as capacity.The amount a container can hold. Volume is usually measured in cubic units, such as cubic centimeters (cm 3), cubic inches (in 3), or cubic feet (ft 3). To find the area of triangle XYZ,first draw rectangle XRYS through its vertices. Then subtract the areas of the two shaded triangles from the area of rectangle XRYS. XY Z R S 1 2 31231 2 3 1 2 3 0 (2, 3) (2,3) (2,3) (2,3) Rectangular coordinate grid Unit 9: Family Letter cont. STUDY LINK 813

Copyright © Wright Group/McGraw-Hill 252 Do-Anytime Activities To work with your child on concepts taught in this unit, try these interesting and rewarding activities: 1.Find an atlas or map that uses letter-number pairs to locate places. For example, an atlasmight say that Chattanooga, Tennessee, is located at D-9. Use the letter-number pairs to locate places you have visited or would like to visit. 2.Estimate the area of a room in your home. Use a tape measure or ruler to measure the room’s length and width, and multiply to find the area. Make a simple sketch of the room, including the length, the width, and the area. If you can, find the area of other rooms or of your entire home. Unit 9: Family Letter cont. STUDY LINK 813 In Unit 9, your child will develop his or her understanding of coordinates and coordinate grids by playing the following games. For detailed instructions, see the Student Reference Book. Frac-Tac-ToeSeeStudent Reference Book,pages 309–311. Two players use a set of number cards 0–10 (4 of each), a gameboard, counters, and a calculator to play one of many versions. Students practice converting between fractions, decimals, and percents. Hidden TreasureSeeStudent Reference Book,page 319. This game for 2 players provides practice usingcoordinates and coordinate grids. It also offers the opportunity for players to develop good search strategies. Each player will need a pencil and two 1-quadrant playing grids with axes labeled from 0 to 10. Polygon CaptureSeeStudent Reference Book,page 328. This game involves two to four players. Materials include polygon pieces and property cards. Players strengthen skills with identifying attributes of polygons.Players may also use 4-quadrant grids with axes labeled from 7 to 7. Practice is extended to coordinates and grids that include negative numbers. Building Skills through Games

253 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 some of the Study Links in this unit. Study Link 9 1 2.Rectangular prism 3. a.(11,7)4.13,297 5.872.3556.10 2 8, or 10 1 4 Study Link 9 2 1.Sample answers: (8,16); (0,5); (16,5) 2.isosceles4.quadrangle 6.28.718. 1 81, or 1 3 8 Study Link 9 3 2.The first number 3. 4.26,3206. 1 24 4, or 17 2 Study Link 9 4 1.150 sq ft; 12 hr 30 min2.114 square feet 3.80 yd 2 4.33 ft 2 5. 6. Study Link 9 5 1.4 cm 2 2.6 cm 2 3.16 cm 2 4.10 cm 2 5.15 cm 2 6.4 cm 2 Study Link 9 6 1.4.5 cm 2; 1 2º3 º3 4.5 2.7.5 cm 2; 1 2º5 º3 7.5 3.3 cm 2; 1 2º2 º3 3 4.24 cm 2; 6 º4 24 5.12 cm 2; 4 º3 12 6.8 cm 2; 4 º2 8 Study Link 9 7 1.yd 2 2.cm 2 3.cm 2 4.in 2 5.ft 2 6.A 1 2º20 º13; 130 ft 2 7.A8 º2;16 cm 2 8.A 1 2º22 º7; 77 yd 2 9.A8 º9 1 2;76 m 2 Study Link 9 8 1.15 cm 2;15cm 3; 45 cm 32.8 cm 2; 8 cm 3; 16 cm 3 3.9 cm 2; 9 cm 3; 27 cm 3 4.14 cm 2; 14 cm 3; 56 cm 3 5. 43 0 6.9607.3,840 Study Link 9 9 1.72 cm 3 2.144 cm 3 3.70 in 3 4.162 cm 3 5.45 in 3 6.140 m 3 7.48.– 2459.160 Study Link 9 10 2.A 1 2º7 º6; 21 cm 2 3.A8 º6; 48 in 2 198 m 2 33 m 33 m 6 m 6 m 3,000 cm 2 50 cm 60 cm 60 cm 50 cm ?1 ?2 ?3 ?4 ?5 ?7 ?8 ?9 ?10 ?11 ?12 ?13 ?14 ?15 ?6 1234567891011121314151 2 4 3 5 6 7 8 9 10 11 12 13 14 15 0 y x Unit 9: Family Letter cont. STUDY LINK 813