University of North Carolina at Charlotte



Task Analysis: Fractions1. Building Model and Comparing Fractions2. Concrete Manipulatives: Action Languagea. Additionb. Subtractionc. Multiplicationd. Division3. Representational:a. Additionb. Subtractionc. Multiplicationsd. Division4. Transitional:a. Additionb. Subtractionc. Multiplicationd. Division5. Symbolic: Algorithms and Alternative Algorithmsa. Additionb. Subtractionc. Multiplicationd. DivisionCAMMP 2014 College of EducationReading and Elementary EducationNames: Clark, M., Merritt, A., Rayburn, J.Integrated, Thematic Problem Solving Unit: A Global Quest for the World CupGrade Level: Rising 5th GradeArithmetic Topic (operation): Comparing, Addition, Subtraction, Multiplication, and Division of FractionsDay 1HIERARCHY STEP #1: Build a Model to Compare Fractions with Concrete ManipulativesTHEME PROBLEM: The FIFA World Cup? is the biggest single-event sporting competition in the world and is contested by the senior men's national teams from the 208 Member Associations of FIFA. The competition has been played every four years since the inaugural tournament in 1930, except in 1942 and 1946 when it was not held because of the Second World War. During the 2014 World Cup that is going on right now, 32 teams are competing in 8 groups, labeled A-H. Each team has an equal number of players. At the Opening Ceremony Feast, ? of MNTUSA are sitting around the team banquet table. ? of Team Brazil is sitting at the banquet table beside MNTUSA. Which team has a greater fraction of players at their banquet table? Show us using the C-Rods.Fractional parts of 12 using people -- ?, ?, ?, ?, etc. Summary TableAction Language: NoneOpen Number Sentence: >, <, =Manipulative: Cuisenaire Rods Rorange Model Quantitative Solution: ? is greaterReferential Meaning: the teamCONCRETE MANIPULATIVE: C-rods, Rorange modelREPRESENTATIONAL MANIPULATIVE: Number LinesTRANSITIONAL ACTIVITIES: Computer ActivitiesSTUDENT PROBLEMS: (some comparison, some ordering)1. ?Carlos and Sarah are eating a bowl of popcorn while watching the soccer game on television. ?Carlos eats ? of the bowl and Sarah eats 2/6 of the bowl. Who ate more popcorn, Carlos or Sarah? 2. ?Madison and Andrew were racing along the soccer field to see who could run the farthest. Madison ran 4/6 of the length of the field and Andrew ran ? of the field. ?Which person, Madison or Andrew, ran the shortest distance?3. ?During the soccer game, Jack played ? of the game, Marie played ? of the game, Susan played ? of the game and John played 5/6 of the game. Order the fractions from smallest to largest to see which player played the longest amount of time. 4. Jorgen Klinsmann, the coach of the USMNT, is judging goalies. Tim can kick the ball ? of the length of the field. Another, Jeff, can kick the ball 4/6 of the field. If Klinsmann wants to choose the goalie who will kick the ball the farthest, whom should he choose? Which is the greatest fraction? 5. The captain of the USWNT is Abby Wombach. She scored ? of the goals in the team’s most recent game. The midfielder is Tobin Heath. She scored 4/6 of the goals in the most recent game. Using the Rorange model, find an equivalent fraction for both of these fractions. 6. There are 23 members of the USMNT. 2/6 of the reserve team can play striker. ? of the reserve team can play midfield. Can more players play striker or midfield? Which is the greater fraction?7. The Estadio Nacional World Cup stadium holds 68,349 people. During the match between Switzerland and Ecuador, ? of the people in the stadium were Team Switzerland fans, and 3/6 of the people in the stadium were Team Ecuador fans. Which team had more fans in the stadium?8. Team Germany was practicing for a match. Goalkeeper Roman Weidenfeller practiced for 1 ? hours. Defender Phillip Lamb practiced for 2 ? hours. Who practiced longer?9. 12 members of Team Nigeria did a commercial for Adidas. Of those, 7 had speaking parts. What fraction of the teammates doing the commercial had speaking parts?STUDENT ANSWER KEY:1. ????Quantitative Meaning: N/A????????Referential Meaning: Sarah ate more popcorn ?2. ????Quantitative Meaning: N/A????????Referential Meaning: Andrew ran the shortest distance3. ????Quantitative Meaning: ?, ?, ?, ? ????????Referential Meaning: John played the longest amount of time4. ????Quantitative Meaning: ? ????????Referential Meaning: Distance of the field Tim can kick5. ????Quantitative Meaning: 10/12, ?, 8/12 ????????Referential Meaning: Number of goals6. ????Quantitative Meaning: 2/6 > 1/4????????Referential Meaning: Striker7. ????Quantitative Meaning: ? = 3/6 ????????Referential Meaning: Each team had the same amount of fans.8. ????Quantitative Meaning: 2 ? > 1 ? ????????Referential Meaning: Phillip Lamb practiced longer.9. ?????Quantitative Meaning: 7/12 ?????????Referential Meaning: team members had speaking partsDay 2HIERARCHY STEP: #2a, #3a Addition of Fractions with Action Language, Concrete Manipulatives, and Representational ManipulativesTHEME PROBLEM: The 2014 World Cup is being contested in 12 host cities in Brazil. Last week, when Brazil played Mexico, they played in Sao Paolo. Yesterday, Brazil played Cameroon in Brasilia. The distance from Sao Paolo to Brasilia, the capital, is 630 miles. On Thursday, they drove 3/6 of the way. On Friday, they drove ? of the way. What fraction of the distance had they traveled by Friday? Summary TableAction Language: “3/6 joined with ?” Open Number Sentence: 3/6+? = ?Manipulative: Cuisenaire RodsQuantitative Solution: ?Referential Meaning: of the distanceCONCRETE MANIPULATIVE: C-Rod Rorange modelREPRESENTATIONAL MANIPULATIVE: n/aTRANSITIONAL ACTIVITIES: Computer ActivitiesSTUDENT PROBLEMS:1. While traveling around Brazil for the World Cup, Jack will spend ? of his time in Cuiaba. Another ? of his time will be spent in Porto Alegre. What fraction of Jack’s time will be spent in these 2 cities?2. During the Brazil vs. Croatia match, midfielder Luis Gustavo of Team Brazil took the ball ? of the way up the field. Then, forward Hulk of Team Brazil took the ball an additional ? of the way up the field. How far had the two players taken the ball in all?3. The Estadio do Maracana in Rio de Janeiro is one of the most famous soccer stadiums in the world. Built in 1950 for the FIFA World Cup, it could at one time hold 200,000 fans, though it now has a capacity of 74,738. Tomorrow, France will compete against Ecuador in the Maracana. Stadium officials think that the stadium will be ? full two hours before the game. They think another ? of the stadium will fill up in those two hours. What fraction of the stadium will be full at kickoff? 4. Of the 12 host cities in Brazil, ? are on the northern coast (Fortaleza, Natal, Salvador, and Recife), and ? are on the southern coast (Rio de Janeiro, Curitiba, Porto Alegre, and Sao Paolo). What fraction of the host cities are coastal cities? 5. A popular tourist destination for soccer fans to visit in Rio de Janeiro is the famous Copacabana beach. Another popular destination is the statue called “Cristo” that overlooks the city from a high mountain. Tim Howard, goalie for MNTUSA, wants to take some time to visit these two spots. He read in a guide book that he should expect to spend ? of a day at Copacabana and ? of a day at Cristo. How many days does he need to fully experience these two sites? 6. Fred of Team Brazil ordered 2 steaks at the team dinner on Saturday night. During the first 30 minutes, he ate ? steak. After 45 minutes, he had?eaten another ? steak. How much of the steaks did he eat in all?7. There are 48 total matches in the Group Stage of the World Cup. ? of the matches were played by Saturday, June 14. ? of the matches were played between Sunday, June 15 and Sunday, June 22. An additional 1/12 of the matches were played yesterday (Monday, June 23). What fraction of the total Group Stage matches have been played so far?8. Feijoada, a black bean stew with smoked meats, is the National dish of Brazil. It is?typically a very large meal which takes a full day to prepare, and is meant to be shared with family and friends. One Feijoada recipe calls for 1 lb. salt cured beef, ? lb. salt pork, 1 ? lbs. smoked ham hocks, 1 ? lbs. Spanish chorizo sausage, ?? lb. pork ribs, and 1 lb. beef stew meat, in addition to black beans, onions, oranges, peppers, collard greens, and white rice. How much meat does the recipe require in all?9. ?There are many local fruits that are popular in Brazil, like oranges, papaya, guava, acai, pineapple and passion fruit. ?At the local market, I buy 1 ? lbs of oranges, ? lb of acai, ? lbs of pineapple, and ? lbs of passion fruit. ?How many pounds of fruit did I buy all together?STUDENT ANSWER KEY:1. ?????Quantitative Meaning: 7/12 ??????????Referential Meaning: of his time2. ?????Quantitative Meaning: ? ?????????Referential Meaning: of the field3. ?????Quantitative Meaning: ?? ?????????Referential Meaning: of the stadium?4. ?????Quantitative Meaning: ? ?????????Referential Meaning: coastal cities5. ???????Quantitative Meaning: 1 ? ?????????? Referential Meaning: days6. ???????Quantitative Meaning: 1 ??????????? Referential Meaning: steaks7. ???????Quantitative Meaning: ? ?????????? Referential Meaning: Group Stage matches8. ???????Quantitative Meaning: 5?????????? Referential Meaning: lbs of meat9. ???????Quantitative Meaning: 3 1/4?????????? Referential Meaning: pounds of fruitDay 3HIERARCHY STEP: #2a, #2b Subtraction of Fractions with Action Language, Concrete Manipulatives, and Representational Manipulatives?THEME PROBLEM: At the soccer training facility in Fortaleza, Brazil, where Germany is practicing, and each World Cup team is given coolers filled with water to stay hydrated. Each cooler is 11/12 full. The German team drank ? a cooler of water during their warm-ups. How much is left over in the cooler? ?Summary TableAction Language: “11/12 takeaway ?”Open Number Sentence: 11/12 - ? = ?Manipulative: C-rodsQuantitative Solution: ?Referential Meaning: coolerCONCRETE MANIPULATIVE: C-rodsREPRESENTATIONAL MANIPULATIVE: Number linesTRANSITIONAL ACTIVITIES: Computer ActivitiesSTUDENT PROBLEMS:1. The German National team prepared 1 ? plates of curryworst, the German national dish, as their pre-game meal. By the end of the meal, the team had eaten ? of the plate. What fraction of the plate did they have left over? 2. The German National Team took a charter bus from Fortaleza to Recife. Striker Miroslav Klose and Midfielder Schweinsteiger are both reading Harry Potter and the Sorcerer’s Stone. Miroslav has read ? of the book. Schweinsteiger has read 8/12 of the book. How much more of the book has Schweinsteiger read? 3. Goalkeeper Manuel Neuer has 2 ? water bottles filled for practice. He drinks 1 ? bottle. How much water remains in his water bottle? 4. The manager of the German National Team is Joachim Low. He is a fan of two of the best musicians Germany has produced: J.S. Bach and Friedrich Handel. Low does not have an iPhone. Instead, he uses his old discman to play CDs he burned, each one with about 60 minutes of music on it. He has 3 ? CDs full of classical music to listen to in Brazil. He has listened to 2 3/12 of the CDs so far. How many more CDs worth of classical music does he have to listen to? 5. The German team ordered pizza after their 4-0 victory over Portugal. They ordered 3 whole pizzas. The team ate 1 7/12 pizza. How much pizza is left over? 6. 8/12 of the soccer balls Germany is using at practice are full of air. The other ones are flat. What fraction of the soccer balls are flat? 7. When the team’s charter bus departs from Fortaleza, the tank is 11/12 full. On the way to Recife, the bus uses ? a tank of gas. How much gas is left over at the end of the trip? 8. To help replace electrolytes during the game, Midfielder Lukas Podolski has packed 5 1/12 bottles of Gatorade. At halftime, he drank 3 ? bottles. How many bottles does he have left?9. The German national team has several trainers traveling with them. They help with injuries and warming up the players so that they can avoid injuries. Presently, they are on the bus from Belo Horizonte to Fortaleza. Some are men and some are women. All are asleep on the plane. ? of the trainers are women. What fraction of the trainers are men? STUDENT ANSWER KEY:1. ?????Quantitative Meaning: 1 1/12?????????Referential Meaning: Plate2. ?????Quantitative Meaning: 1/6??????????Referential Meaning: of the book ?3. ?????Quantitative Meaning: 3/4???????? Referential Meaning: water bottle?4. ?????Quantitative Meaning: 1 1/4?????????Referential Meaning: CD5. ?????Quantitative Meaning: 1 5/12?????????Referential Meaning: pizza6. ?????Quantitative Meaning: 4/12?????????Referential Meaning: soccer balls7. ?????Quantitative Meaning: 1/6?????????Referential Meaning: tank8. ?????Quantitative Meaning: 1 7/12?????????Referential Meaning: bottle of Gatorade9.??? Quantitative Meaning: ? Referential Meaning: menDay 4HIERARCHY STEP: #2c, #3c Multiplication of Fractions with Action Language, Concrete Manipulatives, and Representational Manipulatives?THEME PROBLEM: ?Clint Dempsey, forward for the MNTUSA, was bragging about his chili recipe to three of his teammates. ?They challenged him to make the recipe and they would judge how it tasted. ?His teammates ate ? of the chili for lunch and ate ? of the remaining ? chili for dinner. How much chili did they eat for dinner? ??Summary TableAction Language: ? sets of ? Open Number Sentence: ? x ? = ?Manipulative: C-Rods - Rorange ModelQuantitative Solution: ? Referential Meaning: of the chili CONCRETE MANIPULATIVE: C-Rods using the Rorange model REPRESENTATIONAL MANIPULATIVE: N/ATRANSITIONAL ACTIVITIES: Computer ActivitiesSTUDENT PROBLEMS:1. ?Before their match against Ghana, MNTUSA was running sprints down the field in order to warm-up. ?They were starting at the ? way point of the field and running toward the goal line. John Brooks ran ? of that distance and the rest of the team ran the full distance. ?How much of the field did John run?2. ?The team trainer fills 30 Gatorade bottles ? full with water before every match. During the match with Portugal on Sunday, Goalkeeper Tim Howard only drank ? of the water. What fraction of the water did Tim drink? 3. ?Fans were arriving early for the Portugal vs. USA match on Sunday. One-half of the fans were cheering for Team Portugal. ?Of those ?, ? of them were wearing green. ?What portion of the stadium is wearing green? ???4. ?Players on the US Team have to train for many hours a week to be ready for the work required during the World Cup. All players train in different places before coming together to practice. Two-thirds of the team train in the eastern part of the country. Of those players, ? of them train in the southern states. ?What fraction of the team trains in the southeastern part of the country?5. ?After halftime, ? of the team comes back on to the field before everyone else. ?Of those players, ? of them start kicking the ball around for practice. ?What portion of the team was warming-up by kicking the soccer balls around? 6. ?In order to successfully run the World Cup venues, many workers have to be present to run concession stands, merchandise stands, and act as security. ?Of these workers, ? of the workers live in Rio De Janeiro, Brazil, but only 5/9 of them were born in Rio. ??What portion of the workers were born in Rio De Janeiro?7. ?Defender, Matt Besler, likes to make energy shakes with fruits and vegetables for him and his teammates. ?One batch of the recipe calls for ? cups of strawberries. ?If Matt needs to make 2 ? batches to give to the whole team, how many cups of strawberries will he use?8. ?Forward, Jozy Altidore’s favorite food is Philly Cheese Steak sandwiches. ?The sandwiches call for ? cups of green peppers. ?If he eats 1 ? sandwiches, how many cups of green peppers did he eat with his sandwiches?9. ?Midfielder, Jermaine Jones, likes to eats almonds before every game for good luck. ?Each serving of almonds contains 1 ? ounces. ?Before the Portugal match, he eats 1 ? servings of almonds. How many ounces of almonds does he eat before the game? ??STUDENT ANSWER KEY:1.??? Quantitative Meaning: ? ? Referential Meaning: of the field?2.??? Quantitative Meaning: ? ???????Referential Meaning: of the water in the bottle3.??? Quantitative Meaning: 1/6???????Referential Meaning: of the fans in the stadium4.??? Quantitative Meaning: 3/6 ???????Referential Meaning: portion of the team5.??? Quantitative Meaning: 5/12 ?????? Referential Meaning: of the team6.??? Quantitative Meaning: 5/12???????Referential Meaning: of the workers7. ??????Quantitative Meaning: ? ??????????Referential Meaning: cups of strawberries8. ??????Quantitative Meaning: 1/2??????????Referential Meaning: cups of green peppers9. ??????Quantitative Meaning: 1 ? ??????????Referential Meaning: ounces of almondsDay 5HIERARCHY STEP: #2d, #3d Division of Fractions with Action Language, Concrete Manipulatives, and Representational ManipulativesTHEME PROBLEM: Fufu is one of the most common traditional foods of Ghana. It is made from mashed yams, plantains, corn, flour, or other starchy foods. If defender Daniel Opare of Team Ghana made ? lb. of fufu and wanted to divide it into servings of ? lb., how many team members would be able to eat a serving of fufu?Summary TableAction Language: ? grouped into sets of ? how many times?Open Number Sentence: ? ÷ ? = ??Manipulative: C-rodsQuantitative Solution: 4 sets of 1/6Referential Meaning: team membersCONCRETE MANIPULATIVE: C-rods?REPRESENTATIONAL MANIPULATIVE: N/ASTUDENT PROBLEMS:1. Addae wants to raise money to buy a local Ghanan family plane tickets to Brazil to see Team Ghana compete in the World Cup. He has been collecting donations for 1 week, but still needs to raise ? of the cost. ?If he is asking each donor to contribute 1/12 of the total cost, how many more donors will he need to ask?2. Team Portugal and Team Ghana are playing a match. Forward Christiano Ronaldo of Team Portugal kicks a corner kick, but Defender Samuel Inkoom of Team Ghana intercepts it at ? of the field from their goal. Team Ghana now has to move the ball the remaining ? of the field to Team Portugal’s goal. If the ball is passed to a different Team Ghana player at 1/12 field distance each pass, how many passes will Team Ghana need to reach Team Portugal’s goal?3. Serwa’s dream is to be on Ghana’s Women’s National Football Team when she grows up. She has been playing soccer for 2 years. Every ? year she changes her practice routine so that she can continually challenge herself. How many times has she changed her routine so far?4. A regulation soccer game lasts 1 ? hours. ?If each play period lasts ? hour, how many play periods are there per game?5. Little Manu loves to watch Team Ghana practice for the World Cup. Every day he walks to the practice field, which is 1 ? miles from his village. If he walks at a rate of ? mile per hour, how many hours will it take for him to reach the field?6. Coach Appiah James of Team Ghana was filling up containers with Gatorade for practice time. He had 2 ? gallons of Gatorade. If each container holds ? gallon of Gatorade, how many containers will he be able to fill?7. Forward Majeed Waris was trying to stay hydrated during practice. He had 1 full bottle of Gatorade and one bottle that was ? full, for a total of 1 ? bottles. ?If he?drank ? bottle each break and had none left over, how many breaks did he take?8. Forward Kevin Prince Boateng was running laps around his neighborhood to work on his endurance. His goal was to run for 2 ? hours. If each lap took him ? hour, how many laps did he run?9. Jollof rice is a popular dish in Ghana. It is made of tomato-flavored rice with meat and fish. Nanyanika made a pot of Jollof rice for her and her husband to eat while watching the match between Team Ghana and Team Germany. The pot contained 1 ? lbs of jollof rice. If each serving is 9/12 lbs., how many servings will the pot yield?STUDENT ANSWER KEY:1. ???????Quantitative Meaning: 9 (sets of 1/12)?????????? Referential Meaning: donors2. ???????Quantitative Meaning: 10 (sets of 1/12)?????????? Referential Meaning: players?3. ???????Quantitative Meaning: 4 (sets of ?)?????????? Referential Meaning: times she has changed her routine4. ???????Quantitative Meaning: 2 (sets of ?)?????????? Referential Meaning: play periods per game5. ???????Quantitative Meaning: 2 ? (sets of ? miles per hour)?????????? Referential Meaning: hours to reach the field6. ???????Quantitative Meaning: 3 ? (sets of ?)?????????? Referential Meaning: containers7. ???????Quantitative Meaning: 2 (sets of ?)?????????? Referential Meaning: breaks8. ???????Quantitative Meaning: 4 ? (sets of ?)?????????? Referential Meaning: laps9. ???????Quantitative Meaning: 2 ? (sets of 9/12) ?????????? Referential Meaning: servings ................
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