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Problem Solving opportunities in Everyday Mathematics Grade 5 (2004) Unit 1 Pencils are packed 18 to a box. How many pencils are there in 9 boxes? Show and explain how you got your answer. Complete the table of Divisibility: Number By 2? By 3? By 6? By 9? By 5? By 10? 998,876 5,890 72,344 36,540 861 33,015 1,098 45,369 4,009,721 Explain how you said yes for one number in each column. Math class is dismissed at 2:20 P.M. It is 1:53 P.M. How many more minutes before math class is dismissed? Show and explain how you got your answer. How many crayons are there in 10 boxes, if each box contains 48 crayons? Show and explain how you got your answer. How many crayons are there in 1,000 boxes? Show and explain how you got your answer. In the morning, I need 30 minutes to shower and dress, 15 minutes to eat, and another 15 minutes to ride my bike to school. School begins at 8:30 A.M. What is the latest I can get up and still get to school on time? Show and explain how you got your answer. How many marbles are there in 7 bags, if each bag contains 8 marbles? How many marbles are there in 700 bags? Show and explain how you got your answer. Unit 2 At the start of an experiment, the temperature in a box was 27 ° C. The temperature was increased by 32 degrees. Next it was decreased by 43 degrees. What was the temperature in the box then? Show and explain how you got your answer. Maria had 2 decks of cards. One of the decks had only 36 cards instead of 52. The rest were missing from the deck. How many cards were missing? Show and explain how you got your answer. Anthony got a new bike. He rode 18 miles the first week, 27 miles the second week, and 34 miles the third week. How many miles did he ride altogether? Show and explain how you got your answer. 1 Regina has $23.08. Her sister has $16.47. Her brother has only $5.00. How much more money does Regina have than her sister? Show and explain how you got your answer. Lucas was having 12 friends over for breakfast. He started with 19 eggs. He bought 1 dozen more eggs. How many eggs did he have to cook for breakfast? Show and explain how you got your answer. Nicholas earned $48 mowing lawns one weekend. With the money he earned, he bought 2 CDs that cost a total of $23. How much money did he have left? Show and explain how you got your answer. Patrick’s hobby is to paint color-by-number pictures. He spent 24 hours painting in June and 37 hours painting in July. The last picture he painted had 18 different colors. How many hours did he paint in the two months? Show and explain how you got your answer. Sue walked 2 miles to Jan’s house. Then both girls walked 2 miles to Tad’s house. Sue took 28 minutes to get to Jan’s house. The girls took 45 minutes to get to Tad’s house. How much longer did it take to get to Tad’s house than to Jan’s house? Show and explain how you got your answer. The temperature at midnight was 25°F. The wind chill temperature was 14°F. How much warmer was the actual temperature than the wind chill temperature? Show and explain how you got your answer. Althea and her brother collect baseball cards. Althea has 149 cards. Her brother has 127 cards. How many cards do they have altogether? Show and explain how you got your answer. Julie was driving from Chicago, Illinois to Topeka, Kansas. Before she started, she filled her tank with 10 gallons of gas. She paid $14.08. After driving about 305 miles, she stopped for gas in Iowa. Again, she got 10 gallons of gas and paid $11.85. How much more did she pay for gas in Chicago than in Iowa? Show and explain how you got your answer. Mark paid for his burger and fries with a $20 bill. His burger cost $3.89. his fires cost $1.49. How much change did he receive? Show and explain how you got your answer. Ralph and Adeline saved their money for 6 weeks. Ralph saved $27.23. Adeline saved $34.98. How much more did Adeline save than Ralph? Show and explain how you got your answer. Lucas was comparing prices on a pair of min-speakers. At one store, the pair of speakers cost $19.95. At a second store, the same speakers cost $24.70. At a third store, they cost $18.50. If he buys the speakers at the lowest price, how much will he save over the highest price? Show and explain how you got your answer. 2 Linell and Ben pooled their money to buy a video game. Linell had $12.40 and Ben had $15.88. How much money did they have in all? Show and explain how you got your answer. Make a magnitude estimate. 7 * 326 = _____ 95 * 48 = _____ 5 * 4,127 = _____ 46 * 414 = _____ Show and explain how you got your answer. Certain varieties of sea horses can move 10.5 inches per minute. Would these sea horses be able to travel 6 yards in 1 hour? Show and explain how you got your answer. Orville Wright completed the first successful airplane flight on December 17, 1903. He traveled 120 feet in 12 seconds. If he had been able to stay in the air for a full minute, would he have traveled 1 mile? (Hint 1 mile = 5,280 feet) Show and explain how you got your answer. In 1960, the Triton became the first submarine to circumnavigate the world. It covered 36,014 miles in 75 days. Is that more or less than 100 miles per day? Show and explain how you got your answer. Unit 3 Jeanne practiced her multiplication facts for 3 weeks. The first week she practiced for 45 minutes, the second week for 37 minutes, and third week for 32 minutes. How many minutes did she practice in all? [How many hours is this?] Show and explain how you got your answer. The shortest book Martha read one summer was 57 pages. The longest book was 243 pages. She read a total of 36 books. How many pages longer was the longest book than the shortest book? Show and explain how you got your answer. Chesa collects marbles. He had 347 marbles. Then he played in two tournaments. He lost 34 marbles in the first tournament. He won 23 marbles in the second tournament. How many marbles did he have after playing in both tournaments? Show and explain how you got your answer. Unit 4 Roger had saved $10.05 from his allowance. Then he bought a paint-by-numbers kit for $7.39. How much does he have left? Show and explain how you got your answer. Show and explain how you got your answer. Larry spent $4.82 on a notebook, $1.79 on paper to fill it, and $2.14 on a pen. How much did he spend in all? Show and explain how you got your answer. 3 Compact discs are on sale for $9, including tax. Part A. How many can you buy with $30? Part B. What does the remainder represent? Part C. What did you do about the remainder? Show and explain how you got your answer. Rebecca and her three sisters bought their mother a bread machine for her birthday. The machine cost $219, including tax. The sisters split the bill evenly. Part A. How much did each sister contribute? Part B. What does the remainder represent? Part C. What did you do about the remainder? Show and explain how you got your answer. You are organizing a trip to a museum for 110 students, teachers, and parents. Part A. If each bus can seat 25 people, how many buses do you need? Part B. What does the remainder represent? Part C. What did you do about the remainder? Unit 5 In a school election, 141 fifth graders voted. One-third voted for Shira and two-third voted by Bree. How many votes did Shira get? How many votes did Breeget? Show and explain how you got your answer. Bob, Liz, and Eli drove the 1,050 miles from Chicago to Denver. Bob drove 1/10 of the distance. Liz drove 4/10 of the distance. Eli drove ½ of the distance. How many miles did each person drive/? Check to make sure that the total is 1,050 miles. Show and explain how you got your answer. Carlos and Rick paid $8.75 for a present. Carlos paid 2/5 of the total amount and Rick aid 3/5 of the total. How much did Carlos pay? How much did Rick pay? Show and explain how you got your answer. A pizza costs $12.00, including tax. Scott paid 1/4 of the total cost. Trung paid 1/3of the total cost. Pritish paid 1/6. Bill [aid the rest. How much did each person pay? Scott _____ Trung ______ Pritish ______ Bill ______ Show and explain how you got your answer. Chris made pizza dough with 5/8 cup of white four and ¼ cup of whole wheat flour. How much flour did he use in all? Show and explain how you got your answer. Sheryl’s puppy weighed 1 ½ pounds when it was born. After two weeks, the puppy had gained 3/8 pounds. How much did the puppy weigh after two weeks? Show and explain how you got your answer. Fran had $6.48 to spend on lunch. She bought a hamburger for $2.83. How much did she have left to spend after buying the hamburger? Show and explain how you got your answer. 4 The large rhombus on your Geometry Template is worth 1. Use your Template to draw a shape worth 2 ½. Show and explain how you got your answer. Sophie went to the ball game. She spent $8.50 on the ticket, $2.72 on a hot dog, $1.99 on a soft drink, and $0.15 on a souvenir pencil. How much did she spend in all? Show and explain how you got your answer. Number of times that each of the following players won the four “Grand Slam” tennis tournaments. Player Australian Wimbledon French Open U.S. Open Total Open Chris Evert 2 3 7 6 18 Lloyd Monica Selles 4 0 3 2 6 Steffi Graf 4 7 6 5 22 Jimmy 1 2 0 5 8 Connors Pete Sempras 2 6 0 6 14 How many times did Jimmy Connors win Wimbledom? What is the total number of times he won the four tournaments listed above? Show and explain how you got your answer. How many times did Chris Evert Lloyd win the U.S. Open? What is the total number of times she won the four tournaments listed above? What fraction of this total were won at the U.S. Open? Show and explain how you got your answer. How many times has Monica Selles won the Australian Open? What fraction is this of her total number of wins for these four tournaments? Show and explain how you got your answer. How many times has Steffi Graf win the French Open? What fraction is this of her total number of wins for these four tournaments? Show and explain how you got your answer. Linell got 80% correct on a spelling test. If the test had 20 questions, how many did Linell get correct? Show and explain how you got your answer. Jamie spent 50% of his money on a baseball cap. The cap cost $15. How much money did Jamie have at the beginning? Show and explain how you got your answer. Hunter got 75% correct on a music test. If he got 15 questions correct, how many questions were on the test? Show and explain how you got your answer. The total number of horses in the world is about 60,800,000. China is the country with the greatest number of horses (about 8, 900,000). What percent of the world’s horses live in China? Show and explain how you got your answer. 5 In the United States, about 45% of the population has blood type O. About how many people out of every 100 have blood type O? Show and explain how you got your answer. About 11 out of every 100 households in the United States has a parakeet. How would you express this as a percent? Show and explain how you got your answer. I am a number. If you double 1/3 of me, you get 14. What number am I? Show and explain how you got your answer. Class survey of favorite snacks: Cookies – 8 Granola bar – 4 Candy bar – 10 Fruit – 2 Other – 1 Add all of the votes and the total is ______. That total is the number of students who voted. Make a bar graph showing the results. Label appropriately. Show and explain how you got your answer. Another fifth grade class with 20 students collected snack-survey data. The class made a circle graph of the results. Cookies – 5 Granola bar – 4 Candy bar – 7 Fruit – 3 Other – 1. Make a circle graph to represent this data. Show and explain how you got your answer. Complete. a. 1 hour = ___ minutes b. 3 hours = ___ minutes c. 5 weeks = ____ days d. 4 years = ___ months e. 2 ½ years = ___ months Show and explain how you got your answer. Concrete is an artificial stone. It is made by first mixing cement and sand with gravel or other broken stone. Then enough water is mixed in to cause the cement to set. After drying (or curing), the result is a hard piece of concrete. The cement, sand, and gravel are commonly mixed using this recipe. Recipe for Dry Mix for Concrete Material Fractional Part of Mix Percent Part of Mix Cement 1/6 16 2/3% Sand 1/3 33 1/3% Gravel ½ 50% Use the Percent Circle to make a circle graph for the above recipe. Label each section of the graph, and give it a title. Show and explain how you got your answer. 6 Recently a fifth grade class made a survey of favorite snacks. They have recorded the percent of votes each snack received. You will need to record the number of votes and the fraction that “Percent” represents. Show and explain how you got your answer. ` VOTES Snack Number Fraction Percent Cookies 32% Granola Bar 16% Candy Bar 40% Fruit 8% Other 4% TOTAL About 100% Make a circle graph of the snack-survey data. Remember to label each piece of the graph and give it a title. Show and explain how you got your answer. If 7 yards of cloth cost 21 shillings (a unit of money), how much do 19 yards of cloth cost? Show and explain how you got your answer. After studying arithmetic two hours a 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 ½ of 1/3 of 9 hours, 18 minutes? Here is a problem from around 1870 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? Show and explain how you got your answer. Complete. a. ½ hour = ___ minutes b. 2/6 hour = ___ minutes c. 1 ½ hours = ___ minutes d. 3 ½ days = ___ hours e. 2 years = ___ weeks Show and explain how you got your answer. Complete. a. ¼ hour = ___ minutes b. 20 minutes = ___ hour c. 30 minutes = ___ hour d. ¾ hour = ____ minutes e. 1/12 hour = ___ minutes Show and explain how you got your answer. 7 Unit 6 Ms. Perez’s physical education class participated in the standing long jump. These are the results rounded to the nearest inch. 24 35 33 48 33 48 27 35 27 55 43 24 55 33 52 33 29 59 26 59 48 37 42 42 Organize these data on this line plot. | | | | 20 25 30 35 40 45 50 55 60 65 70 75 Make a bar graph for the data on this line plot. Label it with a title and appropriate information. Find the following landmarks for the standing long jump data: a. Maximum (the longest distance a student jumped) = ___ in b. Minimum )the shortest distance a student jumped): ___ in. c. Model: ___ in d. Median: ___ in e. Mean (average): ___ in (You may use a calculator) d. Mode: e. Range: Mr. Hernandez’s class took a survey to find out when students prefer to do their homework. They got responses from 125 fifth grade students. The results are shown in the table below. As soon as I get home 17% After having an after-school snack 30% Right after dinner 39% Just before going to bed 14% Make a circle graph of the results, using your Geometry Template. Give the graph a title. Label the sections of the graph. Show and explain how you got your answer. When Antoinette woke up on New Year’s Day, it was –4 degrees outside. By the time the parade started, it was a cozy 18 degrees F. How many degrees had the temperature risen by the time the parade began? Show and explain how you got your answer. Randy was growing sunflowers. After eight weeks, he measured the height of his sunflowers, in inches. He recorded the heights: 31, 39, 47, 46, 49, 42,49, 52, 53 55, 52, 58, 57, 53, 65, 63, 64, 73. Record these heights in a stem-and-leaf plot. How tall is the tallest sunflower? Which landmark is the height of the tallest flower? How many sunflowers did Randy measure? What is the mode for his measurement? How would you find the median for his measurement? Show and explain how you got your answer. 1. How much is 3/5 of $1? 2. How much is 3/5 of $10? 3. How much is 3/5 of $1,000? 4. Eight counters is ½ of the set. How many countries are in the set? ___counters 5. Twenty counters is 2/10 of the set. How many counters are in the set? 6. A set has 40 counters,. How many countries are in 3/8 of the set/ 7. A set has 36 counters. How many counters are in 5/6 of the set? 8 8. Mariah shared her sandwich equally with her 3 friends. What fraction of a sandwich did Mariah get? 9. Bernice gave 2/3 of her 18 fancy pencils to her bet friends. How many people did Bernice have left? Show and explain how you got your answers. Draw a circle graph that is divided into the following sectors: 32%, 4%, 22%, 18%, and 24%. Make up a situation for the graph. Give the graph a title. Label each sector. The temperature in Chicago at 6 p.m. was 35 °F. By midnight, the temperature had dropped 48 degrees. What was the temperature at midnight? Show and explain how you got your answer. Brenda bought 4 cheeseburgers for her family for lunch. The total cost was $5.56. How much did 3 cheeseburgers cost? Show and explain how you got your answer. Thomas’s family went on a long trip over summer vacation. They drove for 5 days. The distances for the 5 days were as follows: 347 miles, 504 miles, 393 miles, 422 miles, and 418 miles. A To the nearest mile, what was the average distance traveled per day? Show and explain how you got your answer. B. Tell what you did with the remainder. Explain why. Justin’s school has 15 classrooms. On an average, there are 28 students per room. One fifth of the classrooms are for fifth graders. About how many students are in the school? Show and explain how you got your answer. Carolyn reads 45 pages of a book every night. How many pages did she read in the month of March (31 days)? Show and explain how you got your answer. Lucienne and her class made 684 note cards for a school benefit. How many boxes of eight can they fill? Show and explain how you got your answer. A. Explain what the remainder represents and what you did with it. Favorite flavors of ice cream data was gathered in a Mr. Lenard’s 5th grade class. Create a bar graph to represent these choices: vanilla – 4 chocolate – 7 Strawberry – 4 Chocolate chip – 12 Create a bar graph to represent this data. Include a title and appropriate labeling. How many students prefer the class’s favorite flavor? How many more students prefer chocolate than vanilla? Show and explain how you got your answer. A piece of ribbon is 7 ½ inches long. If a piece 2 3/16 inches long is cut off, how long is the remaining piece? Show and explain how you got your answer. Write a number sentence to show how you solved the problem. 9 Round: 489 to the nearest ten 608 to the nearest ten 23,605 to the nearest hundred 18.27 to the nearest tenth 12.17 to the nearest whole number 15.98 to the nearest tenth 200.73 to the nearest whole number Show and explain how you got your answer. Complete this table Fraction Decimal Percent 2/3 4/8 4/5 3/10 7/25 15/50 Show and explain how you got your answer. Unit 7 Regina is baking two different kinds of chocolate-chip cookies. One recipe calls for ¼ cup of chocolate chips. The other calls for ¾ cup of chocolate chips. How many cups of chocolate chips does she need in all? Write a number model. Show and explain how you got your answer. Roger found a long piece of heavy rope that was 24 ¾ feet long. It was a perfect rope for making jump ropes. If each jump rope is 8 ¼ feet long, how many can he make? Show and explain how you got your answer. Amanda collects dobsonflies (a pretty scary-looking creature, by all accounts). Below are the lengths, in millimeters for the flies in her collection. 95, 107, 119, 103, 102, 91, 115, 120, 111, 114, 115, 107, 110, 108, 98, 112 Create a stem-and-leaf plot that represents this data. Find the median: ___ minimum: ___ range: ___ mode:___ Show and explain how you got your answer. Solve the following problem to get as many different answers as possible. Write a number sentence, using parentheses, for each way. 6 * 4 – 2 / 2= ? (Hint – there are at least four ways) Show and explain how you got your answer. A grocery store received a shipment of 120 cases of apple juice. Each case contained 4 six-packs of cans. After inspection, the store found that 9 cans were damaged. [How many of the cans were NOT damaged?] Write an expression that represents the number of undamaged cans. Show and explain how you got your answer. 10 Robin asked her friends to help figure out how much money she needed to go to the movies. She asked her friends, “How much is 4 plus 5 times 8?” Frances and Sack said, “72”. Ann and Ricky said, “44”. How did they get 72 and how did they get 44? Robin’s friends couldn’t agree who was right. Finally Robin said, “I need to buy one under-12 ticket for $4 and 5 adult tickets for $8”. Then Robin’s friends knew who was right. Who do you think was right? Show and explain how you got your answer. A person breathes an average of 12 to 15 times per minute. At this rate, about how many breaths might a person take in a day? Show and explain how you got your answer. Find the whole set. a. 4 is 1/8 of the set b. 4 is 2/5 of the set c. 9 is 3/7 of the set d. 5 is 1/3 of the set e. 12 is 3/8 of the set Show and explain how you got your answer. Make a circle graph of the survey results Favorite After-School Activity Activity Percent of Students Write it as a Write it as a Choosing it fraction decimal Eat snack 18% Visit friends 35% Watch TV 22% Read 10% Play outside 15% For each temperature change in the table two number models are shown in the “Temperature after Change” column. Only one of the number models is correct. Choose the correct number model and complete that number model. Temperature Temperature Temperature after Temperature after before Change Change Change # Model ? Change # Model ? 40 º Up 7º 40 + 7 = 40 + ( -7) = 10º Down 8º 10 – (-8) = 10 – 8 = - 15º Up 10º - 15 + 10 = 15 + 10 = - 20º Down 10º - 20 – 10 = 20 – (- 10)= The Healthy Delights Candy Company specializes in candy that is wholesome and good for you. Unfortunately, they have been losing money for several years. During the year 2000, they lost $12 million, ending the year with a total debt of $23 million. Part A. What was Healthy Delights’ total debt at the beginning of 2000? Show and explain how you got your answer. Part B. Write a number model that fits this problem. In 2001, Healthy Delights is expecting to lose $8 million. Part A. What will Healthy Delights’ total debt be at the end of 2001? Show and explain how you got your answer. 11 Julie arrived 20 minutes before the race began. She started right on time. It took her 24 minutes to finish the 6-kilometer race. She stayed 10 minutes after the race to cool off; then she left. If she arrived at the race at 9:10 am, what time was it when she left? Show and explain how you got your answer. Marcus had $5.00 to spend on lunch. He bought a hot dog for $1.75 and some French fries for $0.69. How much money did he have left for dessert? Show and explain how you got your answer. A salesperson is often assigned a quota. A quota is the dollar value of the goods that the salesperson is expected to sell. Suppose a salesperson is $3,500 below quota and then makes a sale of $4,700. Show and explain how you got your answers. Part A. Did the sales person exceed or fall short of his or her quota? Show and explain how you got your answer. Part B. Write a number model to figure out by how much the salesperson exceeded or fell short. (Use negative and positive numbers. Think about a number line with the quota at 0.) Stock prices change every day. The first day, a stock’s price went up ¼ dollar per share. The next day, it went down ½ dollar. The third day, it went up 5/8 dollar. Part A. Did the value increase or decrease from the beginning of Day 1 to the end of Day 3. Show and explain how you got your answer. Part B. Write a number model to figure out by how much the stock increased or decreased over the 3-day period. (Use negative and positive numbers. Think about a number line with the Day 1 starting price at 0.) There are 36 stamps in each package. How many stamps are there in… a. ¾ of a package? b. 5/7 of a package? c. 2/9 of a package? d. 7/12 of a package? e. 2/3 of a package? Make a circle graph of the survey results Time Spent on Homework Time Percent of Students Write as a fraction Write as a decimal 0 – 29 minutes 25 30 – 59 minutes 48 60 – 89 minutes 10 90 – 119 minutes 12 2 hours or more 5 The water in Leroy’s and Jerod’s fish tank had evaporated so that it was about 5/8 inch below the level it should be. They added water and the water level went up about ¾ inch. Did the water level end up above or below where it should be? How much above or below? Write the number model. What is the answer? Show and explain how you got your answer. 12 Find the whole set. a. 10 is 1/5 of the set b. 12 is ¾ of the set c. 8 is 2/7 of the set d. 15 is 5/8 of the set e. 9 is 3/5 of the set Show and explain how you got your answer. Is this more or less than ½? Show and explain how you got your answer. Is this more or less than ¼? Show and explain how you got your answer. 3/8 + 1/8 = _________ Show and explain how you got your answer. Joe had 2 granola bars. He ate 1 ½ bars. a. Shade the part that he ate b. Write the part he ate as a decimal. Show and explain how you got your answer. Unit 8 Javier has $5.00 to buy school supplies. He wants one pack of pencils for $1.38, a notebook for $2.74, and some fancy writing paper for $1.29. Does he have enough money? Show and explain how you got your answer. Solve. a. If there are 12 counters in the whole set, how many are there in ¾ of the set? b. If there are 5 counters in 1/8 of the set, how many are there in the whole set c. If there are 8 counters in 4/7 of a set, how many are there in the whole set? d. If there are 15 counters in the whole set, how many are there in 2/5 of the set? e. If there are 3 counters in 2/6 of the set, how many are there in the whole set? Show and explain how you got your answer. Lydia has 7 pages of a 12-page song memorized. Has she memorized more than 2/3 of the song? Show and explain how you got your answer. A CD that normally sells for $15 is on sale for 1/3 off. What is the sale price? Show and explain how you got your answer. Christine bought a coat for ¼ off the regular price. She saved $20. What did she pay for the coat? Show and explain how you got your answer. Julie makes $4.00 per week for doing the dishes every night. She paid her sister Amy $0.75 each time Amy did the dishes for her. Is that a fair price? Show and explain how you got your answer. 13 Solve. a. If there are 18 counters in the whole set, how many are there in 5/6 of the set? b. If there are 21 counters in the whole set, how many are there in 2/3 of the set? c. If there are 6 counters in 2/7 of the set, how many are there in the whole set? d. If there are 10 counters in1/5 of the set, how many are there in the whole set? e. If there are 9 counters in 3/8 of the set, how many are there in the whole set? Show and explain how you got your answer. Amanda found a can containing 237 dominoes. A full set has 28 dominoes. What is the greatest number of complete sets that can be in the can? Show and explain how you got your answer. Raphael bought 14 pounds of meat to make hamburgers at the Fourth of July barbecue. He made 5 hamburgers from each pound. Buns come in packages of 8. How many packages of buns did Raphael need? Show and explain how you got your answer. Every moon and planet in our solar system pulls objects toward it with the force called gravity. In a recent Olympic games, the winning high jump was 7 fet8 inches, or 7 2/3 feet. The winning pole vault was 19 feet. Suppose that the Olympics were held on Earth’s Moon, or on Jupiter, Mars, or Venus. What height might we expect for a winning high jump or a winning pole vault/ 1. On the Moon, one could jump about 6 times as high as on Earth. What would be the height of the winning high jump? About ____ of the pole vault? About _____ 2. On Jupiter, one could jump about 3/8 as high as on Earth. What would be the height of the winning high jump? About _____ of the pole vault? About _____ 3. On Mars, one could jump about 2 2/3 times as high as on Earth. What would be the height of the winning high jump? About _____ of the pole vault? About _____ 4. On Venus, one could jump about 1 1/7 times as high as on Earth. What would be the height of the winning high jump? About _____ of the pole vault? About _____ 5. Is Jupiter’s pull of gravity stronger or weaker than Earth’s? Show and explain how you got your answer. The dimensions of a large doghouse are 2 ½ times 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? b. If the length of the small doghouse is 2 ¼ feet, what is the length of the large doghouse? Show and explain how you got your answer. Find the difference between the highest and lowest temperature recorded in each state. Lowest Highest Difference Alaska - 80º 100º Arizona - 40º 127º Nebraska - 47º 118º South Dakota - 58º 120º Show and explain how you got your answer. 1. If 12 counters are 1/5 of a set, how many counters are in the set? 2. If 15 counters are 1/7 of a set, how many counters are in the set? 14 3. If 31 pages are 1/8 of a book, how many pages are in the book? 4. If 13 marbles are 1% of the marbles in a jar, how many marbles are in the jar? 5. If $5.43 is 1% of the cost of a TV, what does the TV cost? 6. If 84 counters are 10 % of a set, how many counters are in the set? 7. After 80 minutes, Dorothy had read 120 pages of a 300-page book. If she continues reading at the same rate, about how long will it take her to read the entire book? 8. Eighty-four people attended the school concert. This was 70% of the number expected to attend. How many people were expected to attend? 9. (Challenge.) In its most recent game, the Lincoln Junior High basketball team made 36 baskets, which was 48% of the shots team members tried. How many shots did they try? Show and explain how you got your answers. Six jars are filled with cookies. The number of cookies in each jar is not known. For each cue given below, find the number of cokes in the jar. Clue Number of Cookies in Jar a. ½ jar contains 31 cookies b. 2/8 jar contains 10 cookies c. 3/5 jar contains 36 cookies d. 3/8 jar contains 21 cookies e. 4/7 jar contains 64 cookies f. 3/11 jar contains 45 cookies Show and explain how you got your answer. Use your percent sense to estimate the list price for each item. Then calculate the list. (Hint: First use your calculator to find what 1% is worth.) Sale Price Percent of Estimated Calculated List List Price List Price Price $120.00 60% $100.00 50% $8.00 32% $255.00 85% $77.00 55% $80.00 40% $9.00 60% $112.50 75% $450.00 90% Show and explain how you got your answer. Alan is walking to a friend’s house. He covered 6/10 of the distance in 48 minutes. If he continues at the same speed, about how long will the entire walk take? Show and explain how you got your answer. If the average coal miner world 2/3 of a month of 30 days, how many days during the month does he work? Show and explain how you got your answer. A recipe for fudge calls for ¼ of a cake of chocolate. If a cake costs 20¢, find the cost of the chocolate called for by the recipe. Show and explain how you got your answer. 15 In target practice the battleship Indiana shot at a target 24 times. If ¾ of the shots hit, how many successful shots were fired? Show and explain how you got your answer. A collection of mail that required 6 hours for a postman to make with a horse and wagon was made in an automobile in 5/12 the time. How long did the automobile take? Show and explain how you got your answer. How many corks per day does a machine in Spain make from the bark of the cork tree, if it makes 1/3 of a sack of 15,000 corks in that time? Show and explain how you got your answer. Write > or <. a. 50% _____ 2/3 b. 620 – 80 _____ 30 * 40 c. 7/8 _____ ¼ + 2/4 d. 20 * 19 ______ 20 to the second power e. 0.35 = 0.25 _____ 1/8 = 1/8 Show and explain how you got your answer. Finding the worth of the unit fraction will help you to solve each problem. 1. If 4/5 of a number is 16, what is ¼ of the number? What is the number? 2. Our football team won ¾ of the games that it played. It won 12 games. How many games did it platy? 3. When a balloon had traveled 800 miles, it had completed 2/3 of its journey. What was the total length of its trip? 4. Neil’s box of mixed fruit contains 15 oranges. These oranges are worth 3/5 of the total number of pieces of fruit in the box. How many pieces of fruit does Neil have? 5. Grandma baked cookies. Twenty cookies were oatmeal raisin. The oatmeal raisin cookies represent 3/8 of tall the cookies. How many cookies did Grandma bake? 6. Tiana jogged 6/8 of the way to school in12 minutes. If she continues at the same pace, how long will her entire job to school take? 7. After 35 minutes, Hayden had completed 7/10 of his math tests. If he has a total of 55 minutes to complete the test, do you think he will finish on time? 8. Ian bought a video game that was on sale for $45. He paid 75% of the original price. How much would the game have cost if it had not been on sale? 9. An ad for a computer printer stated that you could buy the printer for only $28-, or 80% of the original price. What was the original price of the printer? How much would you save? Show and explain how you got your answers. Complete the table showing how far Melissa ran during her 60-minute run. She ran at a steady rate for the entire time. Time 15 minutes 30 minutes 60 minutes Miles 4 miles 6 miles What percent of the run is 30 minutes? What percent of her total distance is 6 miles? 16 How can constructing a table help solve a percent problem? Show and explain how you got your answer. Fifteen percent of the 20 students in Ms.Swanson’s class were left-handed. How many students were left-handed? Show and explain how you got your answer. About 85% of the 600 students at Emerson Middle School speak English at home. Another 10% speak Spanish, and 5% speak other languages. About how many students speak each language at home? Show and explain how you got your answer. English? Spanish? Other? The government reported that 5 % of 90,000,000 workers do not have jobs. How many workers were jobless? Show and explain how you got your answer. Chase is packing cookies in ½-pound bags. He has 10 pounds of cookies. How many bags can he pack? Show and explain how you got your answer. Regina is cutting lanyard to make bracelets. She has 15 feet of lanyard and needs 1 ½ feet for each bracelet. How many bracelets can she make? Show and explain how you got your answer. Eric is planning a pizza party. He has 3 large pizzas. He figures each person will eat 3/8 of a pizza. How many people can attend the party, including himself? Show and explain how you got your answer. Unit 9 Create a graph to represent each number story. 1. Juanita started with $350. She saved another $25 every week. How much money does she have at the end of 5 weeks? Show and explain how you got your answer. 2. Meredith received $350 for her birthday. She deposited the entire amount in a non- interest bearing checking account in the bank. Every week she withdrew $50. How much money will she have left in this bank account after 5 weeks? Show and explain how you got your answer. Complete the “What’s My Rule?” table and state the rule. IN OUT 2 -10 0 16 4 3 -5 Show and explain how you got your answers. Will a circle with a radius of 4 inches fit inside a circle with a diameter of 5 inches? Show and explain how you got your answer. 17 Write the smallest number you can make that is less than 1 by using each of the following digits only once; 8 9 2 3 Write this number in words. Show and explain how you got your answer. A bedroom floor is 12 feet by 15 feet (4 yards by 5 yards) Floor area = _____square feet Floor area = _____square yards Imagine that you want to buy carpet for the bedroom in Problem 1. The carpet comes on a roll that is 6 feet (2 yards) wide. The carpet salesperson unrolls the carpet to the length you want and cuts off your piece. How long a piece will you need to cover the bedroom floor? Show and explain how you got your answer. Which has the greater area, a 3-ft-by-2-ft rectangle or a triangle with base 3 ft and height 5 ft? Show and explain how you got your answer. Which has the greater area, a triangle with base 10 cm and height 4 cm or a parallelogram with base 5 cm and height 6 cm. Show and explain how you got your answer. Solve the following problems. a. 10 – (-2) = b. 5 – 8 = c. 15 – (-5) = d. - 15 – (-5) = e. – 4 – 7 = Show and explain how you got your answer. Mr. Carroll’s class collected autumn leaves and sorted them by color. The class had 24 yellow leaves, 17 green leaves, 37 red leaves, 8 orange leaves, and 14 brown leaves. Make a circle graph to represent this data. Show and explain how created the graph. Sometimes it is helpful to know that 1 liter is a little more than 1 quart. In the United Stated, gasoline is sold by the gallon. If you travel in Canada or Mexico, you will find that gasoline is sold by the liter. Is 1 gallon of gasoline more or less than 4 liters of gasoline? Explain your answer. Name a number between each pair of numbers. a. 4.2 and 4.25 b. 3/8 and 3/7 c. - 12 and - 11 d. 1/10 and 0.15 e. 2/3 and 5/6 f. 7/16 and4/5 Show and explain how you got your answer. 18 Make up a set of 15 numbers that has the following landmarks. Maximum: 152 Range: 25 Mode: 139 Median: 142 Make a stem-and-leaf plot of the data you created. Show and explain how you got your answer. Unit 10 Name a number between each pair of numbers. a. – 1.30 and – 1.20 b. 8.05 and 8.10 c. – 0.26 and – 0.25 d. 1/3 and 7/8 e. ¼ and 0.3 f. 0.2 and 2/9 Show and explain how you got your answer. Make a stem-and-leaf plot of the following numbers; 120, 111, 137,144,121,120,95, 87, 120, 110, 135, 90, 86, 137, 144, 121, 120, 95, 87, 120, 110, 135, 90, 86, 143, 95, 141 Find the landmarks: Mode: ____ Median: _____ Range: _____ Show and explain how you created the plot and got your answers. The table shows how Robert spent his allowance for the month of April. Complete the table and make a circle graph of the data. Type of Expense Amount Spent Percent of Allowance Snacks $2.50 Movie $5.50 Gum $0.50 Baseball Cards $1.50 Total Show and explain how you got your answers and how you created the graph. Solve. a. 1/3 of 36 = b. 2/5 of 75 = c. 3/8 of 88 = d. 5/6 of 30 = e. 2/7 of 28 = Show and explain how you got your answers. 19 Mr. Kim’s art class asked 50 people each to name their favorite kind of movie. The results are shown in the table. Complete the table and then make a circle graph of the results. Kind of Movie Number of people Percent of Total Action 20 Comedy 14 Romance 2 Thriller 7 Mystery 4 Total Show and explain how you got your answer and created the graph. Ms. Hopheart’s class asked 50 people to name their favorite kind of fruit The results are shown in the table. Complete the table and then make a circle graph of the results. Kind of fruit Number of People Percent of Total Apples 20 Bananas 12 Grapes 5 Oranges 8 Other 5 Total 50 Show and explain how you got your answers and how you created the graph. Janet wanted to know how long it would take her to drive 525 miles. She was traveling at about 65 miles per hour. Explain how she might solve these problems using a graph, a formula, or a table. Unit 11 Complete the following table. Polyhedron Number of Faces Number of Vertices Number of Edges (f) (v) (e) Rectangular prism 6 Tetrahedron 4 Triangular prism 9 Rectangular pyramid Octahedron Show and explain how you got your answer. Theresa is y years old. Write an algebraic expression for the age of each person below. a. Nancy is four years older than Theresa b. Frank is twice as old as Theresa. c. Jose is 1/3 as old as Theresa. d. Lucianna is 8 years younger than Theresa e. If Theresa if 12, who is the oldest person above? How old is that person? Show and explain how you got your answer. To calculate the volume of any prism or cylinder, you multiply the area of the base by the height. How would you calculate the volume of a Pyramid or Cone? 20 The Pyramid of Cheops is near Cairo, Egypt. It was built about 2600 B.C. It is a square pyramid. Each side of the square base is 756 feet long. Its height is 449.5 feet. The pyramid contains about 2,300,000. A. Calculate the volume of this pyramid. [Show your work.] B. What is the average volume of one limestone block? [Show and Explain how you got your answer.] You have 12 white tiles. If you add some black tiles so that the ratio of white tiles to black tiles is 1 to 3, how many black tiles will you need? How many tiles will you have in all? Show and explain how you got your answer. You have 15 white tiles. If you add some black tiles so that 3 out of 4 tiles are white, how many black tiles will you need? How many tiles will you have in all? Show and explain how you got your answer. You have a total of 24 tiles. Five out of 8 tiles are black. How many black tiles do you have? Show and explain how you got your answer. Draw 12 shaded tiles. Then draw some unshaded tiles so that 3 out of 5 tiles are shaded. Show and explain how you got your answer. 5/7 of a set contains 22522 objects. How many objects are in the whole set? Show and explain how you got your answer. 4/9 of a set contains 36 objects. How many objects are in the whole set? Show and explain how you got your answer. 111/12 of a set contains 88 objects. How many objects are in the whole set? Show and explain how you got your answer. If 15 marbles are 3/5 of the marbles in a bag, how many marbles are in the bag? Show and explain how you got your answer. If 14 pennies are 7% of a pile of pennies, how many pennies are in the pile? [Show and explain how you got your answer. 75 students are absent today. This is 10% of the students enrolled at the school. How many students are enrolled at the school? Show and explain how you got your answer. Jane paid $90 for a new radio. It was on sale for ¾ of the regular price. What is the regular price of the radio? Show and explain how you got your answer. Unit 12 1. Mica reads about 44 pages in an hour. About how many pages will she read in 2 ¾ hour? Show and explain how you got your answer. 21 2. If Mica starts reading a 230-page book at 3:30 P.M., and she reads straight through the book (without stopping), about what time will Mica finish the book? [Show and Explain how you found your answer. Tryee and Jake built a tower of centimeter cubes. The bottom floor of tower is rectangular. It is 5 cubes wide and 10 cubes long. The completed tower is the shape of a rectangular prism. They began building at 2 P.M. They built for about 1 hour. They used approximately 200 cubes every 10 minutes. How tall was the final tower? Show and explain how you got your answer. The students in Mrs. Dillard’s class took a survey of their favorite colors. Complete the table. Then make a circle graph of the data. Favorite Color Number of Percent of Students Class Red 6 Blue 10 Orange 4 Yellow 2 Purple 3 Total Show and explain how you got your answer. It rained 2 out of 4 days in the month of April. On how many days did it rain that month? Show and explain how you got your answer. For every 4 times John was at bat, he got 1 hit. If he got 7 hits, how many times did he bat? Show and explain how you got your answer. There are 20 students in Mrs. Kahlid’s fifth-grade class. Two out of 8 students have no brothers or sisters. How many students have no brothers or sisters? Show and explain how you got your answer. Rema eats 2 eggs twice a week. How many eggs will she eat in the month of February? How many weeks will it take her to eat 32 eggs? Show and explain how you got your answer. David took a survey of people’s favorite flavors of ice cream. Of the people he surveyed, 2 out of 5 said that they like fudge swirl best. 1 out of 8 chose vanilla, 3 out of 10 chose maple walnut, and the rest chose another flavor. a. If 16 people said that fudge swirl is their favorite flavor, how many people took part in David’s survey? b. If 80 people participated in David’s survey, how many preferred a flavor that is not fudge swirl, vanilla, or maple walnut? Show and explain how you got your answers. Draw 20 tiles so that 2 out of 10 tiles are white and the rest are shaded. a. How many tiles are white? b. How many tiles are shaded? Show and explain how you got your answers. 22 Of the 42 animals in the Children’s Zoo, 3 out of 7 are mammals. How many mammals are there in the Children’s Zoo? Show and explain how you got your answer. Five out of 8 students at Kenwood School plan an instrument. There are 224 students at the school. How many students play an instrument? Show and explain how you got your answer. Mr. Lopez sells subscriptions to a magazine. Each subscription costs $18. For each subscription he sells, he earns $8. One week, he sold $198 worth of subscriptions. How much did he earn? Show and explain how you got your answer. There are 48 students in the fifth grade a Roberts’s school. Three out of 8 fifth graders read two books last month. One out of 3 students read just one book. The rest of the students read no books at all. How many booking all did the fifth graders read last month? Show and explain how you got your answer. Mrs. Porter’s students took a survey of their favorite movie snacks. Complete the table. Then make a circle graph of the data. Favorite Snack Number of Students Percent of Class Popcorn 11 Chocolate 5 Soft drink 6 Fruit chews 2 Candy with nuts 1 Total Show and explain how you got your answer. Of the 115 students in the sixth grade, 2 out of 5 belong to the Drama Club. How many students are members of the Drama Club? Show and explain how you got your answer. Three out of 4 student at Highland School ordered a hot lunch today. There re 150 students at the school. How many students ordered a hot lunch? Show and explain how you got your answer. Gina and the other members of her troop sell cookies for $3 a box. For each box they sell, the troop earns $1.50. One week, Gina’s troop sold $90 worth of cookies. How much did the troop earn? Show and explain how you got your answer. Challenge 30% of the tickets sold by a movie theater for the Friday night show were children’s tickets t $4 each. The rest of the tickets were sold at the full price of $8.50. The movie theater collected $252 for the children’s tickets. How many tickets did they sell in all? Show and explain how you got your answer. 23 It would take 27,000 spiders, each spinning a single web, to produce a pound of spider web. Number of 27,000 54,000 spiders Pounds of 1 2 3 4 5 Spider Web At this rate, how many spiders, each spinning a single web, would be needed to produce 10 pounds of spider web? Show and explain how you got your answer. The deer botfly flies so fast that it is almost invisible to the human eye. In 1 minute it can travel 13 miles. Miles 13 Minutes 1 2 3 4 5 At this rate, how far could a deer botfly travel in 1 hour? Show and explain how you got your answer. To celebrate her birthday, Ms.Hahn decided to give each of the fifth graders one strand of her favorite kid of licorice whip. There are 179 fifth graders. The whips come 15 strands to a package at a cost of $1.19 per package. Show and explain how you got your answer. a. How many packages of licorice whips does Ms. Hahn need to buy? b. How much will she spend? In the Malagasay Indian tribes, it is against the law for a son to be taller than his father. If a son is taller, he must give his father money or an ox. Suppose a father is 5 feet 10 ½ inches tall and his son is 5 feet 6 ¾ inches tall. How many more inches can the son grow before he is as tall as his father? Show and explain how you got your answer. In the state of Indiana, it is illegal to travel on a bus within 4 hours of eating garlic. If you lived in Indiana and had eaten a bowl of pasta with garlic bread 2 1/3 hours ago, how many more hours would you need to wait before you could legally travel on a bus? Show and explain how you got your answer. In Idaho, it is against the law to give a person a box of candy that weighs more than 50 pounds. It is Valentines Day, and you give your mother a box of candy that weighs 48 ¼ pound. How much more could the box weigh without breaking the law? Show and explain how you got your answer. The body of an average jelly fish is about 9/10 water. What fraction of the jellyfish is not water? Show and explain how you got your answer. The world record for a jump by a frog is 19 feet 3 1/8 inches. How much farther would a frog need to jump to set a new world record of 7 yards? Show and explain how you got your answer. The maximum length for a typical king cobra is about 5 4/5 meters. If 6 of these snakes were lined up end to end, how far would they stretch? Show and explain how you got your answer. 24 An average trumpeter swan weighs about 16 4/5 kilograms. What is the approximate weight of 3 average trumpeter swans? Show and explain how you got your answer. Cherie lives on a chicken farm. Every morning she collects the eggs from the hen house. She collected 162 eggs on Monday, l04 eggs on Tuesday, and 157 eggs on Wednesday. She packed them into cartons, each containing 12 eggs. How many egg cartons can she fill completely? Show and explain how you got your answer. 25

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