2. FRACTION FREEWAY Problem Solving In this tutorial you will review Problem Solving Steps, learn five different Problem Solving Strategies, and then play a game called Fraction Freeway using the problem solving steps and strategies to solve word problems containing fractions. - - - - - - - - - - - - - - - - - - Main Menu STOP Click here to see a video on how to navigate through Fraction Freewaynavigate through Fraction Freeway. Navigation Road

3. Main Menu Suggested Order of Navigation 1. Problem Solving Steps – Click on the arrow on the sign to review the steps for solving problems. 2. Problem Solving Strategies – Click on the arrow on the sign to go to the strategies home page to choose different strategies to review. 3. Fraction Freeway – Click on the arrow on the sign to play the game of solving problems on the road to your chosen destination. - - - - - - - - - - - - - - - - - - Georgia Performance Standards References Objectives You are here - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

4. Objectives The student will be able to: Successfully navigate to the problem solving tutorial, Fraction Freeway Successfully complete the problem solving tutorial, Fraction Freeway Identify the problem solving steps in order Identify five problem solving strategies that can be used in solving story problems Match the problems solving strategy with the problem in which that particular strategy was used Correctly solve problems using problem solving strategies Main Menu STOP - - - - - - - - - - - - - - - - - - Navigation Road

5. Main Menu Georgia Performance Standards Problem Solving  Build new mathematical knowledge through problem solving  Apply and adapt a variety of appropriate strategies to solve problems  Monitor and reflect on the process of mathematical problem solving Fractions  Students will further develop their understanding of the meaning of common fractions and use them in computations.  Add and subtract fractions and mixed numbers with common denominators. STOP - - - - - - - - - - - - - - - - - - Navigation Road

6. Credit and References Alessi, S. & Trollip, S. (2001). Multimedia for learning: Methods and development. Boston: Allyn & Bacon. Burns, M. (2000). About teaching mathematics: A k – 8 resource. Sausalito, California: Math Solutions Publications. Discovering Math: Problem Solving (Grades 3-5). Discovery Channel School (2005). Retrieved October 25, 2008, from Discovery Education: http://streaming.discoveryeducation.com/ Georgia Standards. (2006). Retrieved September 20, 2008, from Georgia Standards.org: http://www.georgiastandards.org/math.aspx Harcourt Math. (2008). United States of America: Harcourt School Publishers. STOP - - - - - - - - - - - - - - - - - - Navigation Road Main Menu

7. Problem Solving Steps 1.Understand - Read the problem very carefully. –What is the problem about? –What information is given? –What is the question? 2. Plan –What problem-solving strategy should I use? –Consider different strategies, then choose the one that will best solve the problem. More Steps You are here - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

8. Problem Solving Steps 3. Solve –How can I solve this problem? –How can I state my answer in a complete sentence? 4. Check –How do I know whether my answer is reasonable? –Does my answer make sense? You are here Click on the sign Problem Solving Strategies to learn the strategies. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

9. Problem Solving Strategies Problem Solving Strategies - - - - - - - - - - - - - - - - - - Strategy 1 Draw a Picture or Diagram Strategy 2 Construct a Table Strategy 3 Write an Equation Strategy 4 Look for a Pattern Strategy 5 Work Backward Problem solving strategies are useful for analyzing and solving problems. Many problems can be solved by using a combination of strategies. Click on a strategy below to review and work practice problems. You are here - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Video

10. Example: Kate, Joe, and Ralph wanted to see who could run the farthest. Kate ran 1 / 2 meter, Joe ran 2 / 3 meter, and Ralph ran 1 / 4 meter. Who ran the greatest distance? Click on the traffic light to see the solution. Strategy #1 Draw a Picture or Diagram Use this strategy to help you “see” a problem. Draw a picture of the information given. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

11. Solution This problem can be solved by drawing a picture using fraction bars and then compare the fractions. The fraction bars are the same length because each bar represents 1 whole. Each whole is divided into halves, thirds, and fourths. The bar with the longest shaded part is the greatest fraction and represents who ran the farthest. Answer: Joe ran the farthest. 1/4 2/3 1/2 1/3 3/4 Kate Joe Ralph Practice Problem Click on the orange practice problem sign to solve another problem. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

12. PRACTICE Use the strategy of draw a picture or diagram to solve this problem. Beth made a snack mix for the class party. She used 1 / 2 lb of peanuts, 4 / 6 lb of pretzels, and 5 / 8 lb of dried fruit. List the ingredients in order from greatest to least. Solve the problem and then click on the traffic light to check your answer. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

13. Solution Draw a picture using fraction bars and then compare the fractions. Then list the fractions in order from greatest to least. Answer: 4 /6, 5 /8, 1 / 2 1/2 1/81/8 1/ 6 1/81/8 1/81/8 1/81/8 1/81/8 Next Strategy Click on the arrow on the sign Next Strategy to go to Strategy # 2. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

14. Strategy #2 CONSTRUCT A TABLE This strategy is useful when problems include information that must be organized in a table so it is easy to read and understand. A table makes it easy to find the information needed to solve a problem. Example: Sadie took a survey of her classmates’ favorite subject at school. There are 24 students in the class. 1 / 2 of them like science the best. 1 / 8 of the class chose history. 1 / 4 of the class chose math. The rest of the class chose English. How many students chose English? Click on the traffic light to see the solution. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - - - - -- - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

15. Solution SubjectNumber of Students science12 history3 math6 English3 Total24 Make a table showing the favorite subjects. Figure out the number of students that chose each subject and put the number on the chart. Now the information is easy to read and understand. Add the numbers together and subtract from the total number of students. Answer: Three students chose English. Practice Problem Click on the arrow on the orange practice problem sign to solve another problem. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

16. Practice Juan took a survey of his classmates’ favorite cartoon. There are a total of 24 students in his class. 1 / 2 of the class likes Sponge Bob the best. 1 / 3 of the class likes Fairly Odd Parents, the rest chose Jimmy Neutron. How many students chose Jimmy Neutron? Solve the problem and then click on the traffic light to check your answer. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies Solve this problem using the strategy, Construct a Table.

17. Solution Next Strategy CartoonNumber of students Sponge Bob12 Fairly Odd Parents 8 Jimmy Neutron4 Total24 Make a table showing the favorite cartoons. Figure out the number of students that chose each cartoon and put that number on the chart. Now the information is easy to read and understand. Add the numbers together and subtract from the total number of students. Answer: Four students chose Jimmy Neutron. Click on the arrow on the sign Next Strategy to go to Strategy # 3. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

18. Strategy # 3 WRITE AN EQUATION Example: Mitsy and Jason made model airplanes. They decided to test their planes to see if they would fly. Misty’s plane flew 5 ¾ yards. Jason’s plane flew 2 ¼ yards less than Mitsy’s plane. How many yards did Jason’s plane fly? Solve the problem and click on the traffic light to see the solution. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

19. Solution The problem asks how far Jason’s plane flew. Jason’s plane did not fly as far as Misty’s so you need to subtract. Write an equation: 5 ¾ Misty’s plane - 2 ¼ less 3 2 / 4 or 3 ½ yards Answer: Jason’s plane flew 3 ½ yards. Click on the arrow on the orange practice problem sign to solve another problem. Practice Problem - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

20. PRACTICE Use the strategy Write an Equation to solve this problem. John ate 2 ½ donuts for breakfast. Julio ate 3 ½ donuts. How many donuts did the two boys eat? Solve the problem and click on the traffic light to check your answer. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

21. Solution The question asks how many donuts the two boys ate. Write an equation. Add together how many donuts each boy ate. 2 ½ donuts eaten by John + 3 ½ donuts eaten by Julio 6 Answer: John and Julio ate 6 donuts. Next Strategy Click on the arrow on the sign Next Strategy to go to Strategy # 4. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

22. Strategy # 4 Look for a Pattern Identify the pattern and then predict what will come next and what will happen again and again in the same way. Using this strategy you can sometimes solve the problem just by recognizing the pattern, but sometimes you have to extend the pattern. Making a table often reveals patterns, so it is frequently used with this strategy. Click on the traffic light to see an example of a problem using this strategy. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

23. Example Problem Laura was given an ant farm for her birthday. The farm could hold a total of 12,000 ants. Laura’s farm had ½ as many ants the first day as it did the second day and ½ as many the second day as the third day. If the number of ants in the ant farm on the fourth day is 12,000, how many ants were in the farm on the first day? Click on the traffic light to see the solution. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

24. Solution Look for a pattern: the number of ants doubles each day. Since you know how many ants there are on the fourth day, take half of that number and continue that pattern until you get to the first day. Make a table: DAYS 1 2 3 4 ANTS 1,500 3,000 6,000 12,000 ANSWER: The ant farm had 1,500 ants on the first day. Practice Problem Click on the arrow on the orange practice problem sign to solve another problem. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

25. PRACTICE Use the strategy Look for a Pattern to solve this problem. Ravi needed to earn $270. He earned 1 / 3 of what he needed each day. How many days did it take him to earn the money? Solve the problem and click on the traffic light to check your answer. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

26. Solution Take 1 / 3 of $270. The pattern is that he earned $90 a day. Make a table: Days 1 2 3 Money $90 $90 $90 Answer: It took Ravi 3 days to earn the money. Next Strategy Click on the arrow on the sign Next Strategy to go to Strategy # 5. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

27. Strategy # 5 WORK BACKWARD This strategy is useful in finding a starting amount or missing step when a total number or amount and the steps to reach that amount are given. Work backward is often used with problems that involve inverse operations. Write the steps of the problem in order from left to right using numbers and operations. Then reverse the order and use the opposite operation to find the answer. Click on the traffic light to see an example of a problem using this strategy. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

28. Example Problem Bruce collected some sand dollars. He gave 1 / 10 of 100 to his younger sister. His friend Mike gave him 1 / 5 of 35 sand dollars. He put 1 / 4 of 16 back in the water. He had 14 sand dollars left. How many did he collect? Click on the traffic light to see the solution. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

29. Solution First, solve the fractional equations and write the steps of the problem in order from left to right. Number of He gave Mike He put Number sand dollars 1 / 10 of 100 gave him 4 back left collected to his sister 1 / 5 of 35 ? -10 + 7 - 4 14 Then, reverse the order and use the opposite operations to find the answer. 21 + 10 - 7 + 4 14 Answer: Bruce collected 21 sand dollars. Practice Problem Click on the arrow on the orange practice problem sign to solve another problem. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

30. PRACTICE Use the strategy of Work Backward to solve this problem. Sasha and Chuck played a number game. Sasha chose a number and then subtracted 1 / 3 of 9. Next she added 1 / 2 of 24. Then she subtracted 1 / 2 of 40. Last she added 1 / 11 of 121. The result was 30. What number did Sasha begin with? Solve the problem and then click on the traffic light to check your answer. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies

31. Solution First solve the fractional equations and write the steps of the problem in order from left to right. Then reverse the order and use the opposite operations to solve. __?__ __- 3__ __+ 12__ __- 20__ __+ 11__ __ 30__ __30__ __+ 3__ __- 12__ __+ 20__ __ - 11__ __ 30__ Answer: The number Sasha chose was 30. Click on Fraction Freeway to play the game or go back and review steps and strategies if you need to. - - - - - - - - - STOP Main Menu Problem Solving Steps - - - - - - - - - Fraction Freeway Home Navigation Road Problem Solving Strategies