Probsolvwebquest

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A great problem solving webquest I found online

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Probsolvwebquest

  1. 1. Searching for Solutions Steps for Successful Problem Solving An Introduction to the Searching for Solutions WebQuest http://gouchercenter.edu/jcampf/searching_for_solutions.htm
  2. 2. Problem Solving <ul><li>Are you ready to tackle a math problem with confidence? </li></ul><ul><li>Do you have a briefcase filled with problem-solving strategies that help when you encounter a new problem? </li></ul><ul><li>Do you get confused about how to solve problems? </li></ul>
  3. 3. Strategies for Solving Problems <ul><li>making a table, chart or graph </li></ul><ul><li>using estimation </li></ul><ul><li>making a list </li></ul><ul><li>acting out the problem </li></ul><ul><li>guess and check </li></ul><ul><li>working backward </li></ul><ul><li>finding a pattern </li></ul><ul><li>solving multi-step problems </li></ul><ul><li>drawing pictures or diagrams </li></ul><ul><li>interpreting remainders </li></ul><ul><li>making and using models </li></ul><ul><li>using formulas </li></ul><ul><li>choosing an operation </li></ul><ul><li>solving a simpler problem </li></ul><ul><li>writing a number sentence or equation </li></ul>
  4. 4. Problem Solving Steps <ul><li>UNDERSTAND the problem </li></ul><ul><li>PLAN a solution </li></ul><ul><li>SOLVE the problem </li></ul><ul><li>LOOK BACK and check your solution </li></ul>
  5. 5. UNDERSTAND <ul><li>Restate the problem </li></ul><ul><li>Highlight or identify important facts </li></ul><ul><li>Determine the question or problem to be solved </li></ul>
  6. 6. PLAN <ul><li>Choose a strategy </li></ul><ul><li>Find a Pattern </li></ul><ul><li>Read a Table or Chart </li></ul><ul><li>Make an Organized List </li></ul><ul><li>Draw a Diagram </li></ul><ul><li>Choose a strategy </li></ul><ul><li>Write an Equation </li></ul><ul><li>Work Backward </li></ul><ul><li>Make a Simpler Problem </li></ul><ul><li>Guess and Check </li></ul>
  7. 7. SOLVE <ul><li>Identify Needed Facts </li></ul><ul><li>Choose an Appropriate Strategy </li></ul><ul><li>Pencil and Paper </li></ul><ul><li>Calculator </li></ul><ul><li>Addition, Subtraction, Multiplication, Division </li></ul><ul><li>Show ALL Work </li></ul>
  8. 8. LOOK BACK <ul><li>Restate the Question </li></ul><ul><li>Check the Answer </li></ul><ul><li>Does the Answer Make Sense? </li></ul><ul><li>Record the Answer </li></ul><ul><li>Add Necessary Units or Labels </li></ul>
  9. 9. Let’s Try Some Problems Finding a Pattern Making a Table or Chart Making an Organized List Drawing a Diagram Using an Equation #1 Using an Equation #2 Working Backward Make a Simpler Problem Application of Strategies
  10. 10. Finding a Pattern A penny bubble-gum machine contains four colors of gum balls. What is the maximum amount of money needed to get two gum balls of the same color? Explain your reasoning. Passport to Mathematics Book 1 - Chapter 1 - 1.1 Problem of the Day
  11. 11. UNDERSTAND the problem What are the most important facts in this problem? How many colors? What is the cost per gum ball? PLAN a solution / SOLVE the problem <ul><ul><li>What PATTERN can you create that is similar to this problem? Make the PATTERN and test it out. </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer 1¢ 1st color (red) 2¢ 2nd color (blue) 3¢ 3rd color (green)
  12. 12. Finding a Pattern - Answer 5 ¢ Consider only the worst case - the first four don’t match. The fifth gum ball will match one of the first four. Solve More Problems Finished Solving Problems
  13. 13. Making a Table or Chart Suppose you have 5 compact discs (CDs) and a CD player that holds 3 CDs at a time. How many different sets of 3 CDs can be chosen to load into the CD player? Passport to Mathematics Book 1 - Chapter 1 - 1.2 Problem of the Day
  14. 14. UNDERSTAND the problem What are the most important facts in this problem? How many CDs do you have? How many CDs will the player hold? PLAN a solution / SOLVE the problem <ul><ul><li>Make a TABLE and put the information into it. </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer A, B, C B, C, D C, D, E A, B, D A, B, E B, C, E Etc.
  15. 15. Making a Table or Chart - Answer 10 combinations ABC ABD ABE BCD BDE CDE ACD ACE CBE ADE Solve More Problems Finished Solving Problems
  16. 16. Making an Organized List A “palindromic” number is a number that reads the same forward as backward, such as 3223. Find the smallest palindromic number greater than 7456. Passport to Mathematics Book 1 - Chapter 1 - 1.3 Problem of the Day
  17. 17. UNDERSTAND the problem What are the most important facts in this problem? What is a “palindromic” number? PLAN a solution / SOLVE the problem <ul><ul><li>Make an ORGANIZED LIST of numbers greater than 7456. Check for palindromic numbers. </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer 7457 NO 7458 NO 7459 NO 7460 NO 7461 NO Etc. 7456 NO
  18. 18. Making an Organized List - Answer 7557 is the smallest palindromic number greater than 7456 Solve More Problems Finished Solving Problems
  19. 19. Drawing a Diagram If each edge measures 3.7 inches, what is the sum of the measure of the edges of a cube? Passport to Mathematics Book 1 - Chapter 1 - 1.4 Problem of the Day
  20. 20. UNDERSTAND the problem What are the most important facts in this problem? What measurements are given? What is a cube? How many edges will be measured? PLAN a solution / SOLVE the problem <ul><ul><li>What DIAGRAM can you draw to solve this problem? </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer 3.7 inches per edge x ? edges = ???
  21. 21. Drawing a Diagram - Answer 44.4 inches 3.7 inches x 12 edges on a cube = 44.4 inches Solve More Problems Finished Solving Problems
  22. 22. Using an Equation #1 “ Echoing” a one-digit number to make it a two-digit number (e.g., making 3 into 33) is the same as multiplying by 11. When a two-digit number is “echoed” in the same way, making it a four-digit number, by what number is it being multiplied? Passport to Mathematics Book 1 - Chapter 1 - 1.5 Problem of the Day
  23. 23. UNDERSTAND the problem What are the most important facts in this problem? What is echoing? Can you find examples? PLAN a solution / SOLVE the problem <ul><ul><li>What EQUATION can you create that is similar to this problem? Write other EQUATIONS and look for a pattern. </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer 22 2222 57 5757 93 9393
  24. 24. Using an Equation #1 - Answer 101 Using the prior examples: 2222 ÷ 22 = 101 5757 ÷ 57 = 101 9393 ÷ 93 = 101 Solve More Problems Finished Solving Problems
  25. 25. Using an Equation #2 Three times a certain number is between 380 and 390. Four times the same number is between 500 and 510. What is the number? Passport to Mathematics Book 1 - Chapter 1 - 1.6 Problem of the Day
  26. 26. UNDERSTAND the problem What are the most important facts in this problem? What equations are given? What can you predict? PLAN a solution / SOLVE the problem <ul><ul><li>What EQUATION can you create that is similar to this problem? Write other EQUATIONS and look for a pattern. </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer 390 ÷ 3 510 ÷ 4 500 ÷ 4 380 ÷ 3
  27. 27. Using an Equation #2 - Answer 127 Dividing 380 and 390 by 3 showed the answer was between 126 and 130. Dividing 500 and 510 by 4 showed the answer was between 125 and 128. Solve More Problems Finished Solving Problems
  28. 28. Working Backward The average of five numbers is 78. Three of the numbers are 65, 83, and 92. The other two numbers are the same. What are the other numbers? Passport to Mathematics Book 1 - Chapter 1 - 1.7 Problem of the Day
  29. 29. UNDERSTAND the problem What are the most important facts in this problem? What is an average? What numbers are given? PLAN a solution / SOLVE the problem <ul><ul><li>WORK BACKWARD using the given numbers and the formula for finding an average. </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer Subtract 65, 83, and 92 Average of 5 numbers = 78 78 x 5
  30. 30. Working Backward - Answer 75 and 75 78 x 5 = 390 65 + 83 + 92 = 240 390 - 240 = 150 150 ÷ 2 = 75 Solve More Problems Finished Solving Problems
  31. 31. Make a Simpler Problem Use the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Find four numbers in a row whose sum is one half the sum of the other eight numbers. Passport to Mathematics Book 1 - Chapter 1 - 1.8 Problem of the Day
  32. 32. UNDERSTAND the problem What are the most important facts in this problem? What numbers must be used? What operations will be needed? PLAN a solution / SOLVE the problem <ul><ul><li>MAKE A SIMPLER PROBLEM by testing the process on easier numbers. </li></ul></ul>What is the question? LOOK BACK and check the solution Does it make sense? The Answer Sum of 5, 6, 7, 8, 9, 10, 11, 12 = 68 Sum of 1, 2, 3, 4 = 10
  33. 33. Make a Simpler Problem - Answer 5, 6, 7, 8 5 + 6 + 7 + 8 = 26 1 + 2 + 3 + 4 + 9 + 10 + 11 + 12 = 52 26 x 2 = 52 Solve More Problems Finished Solving Problems
  34. 34. Application of Strategies A large store plans to assign a three-letter inventory code to each kind of item it sells. How many different three-letter codes are possible? Passport to Mathematics Book 1 - Chapter 1 - 1.9 Problem of the Day The Answer
  35. 35. Application of Strategies - Answer 26 x 26 x 26 = 17,576 Solve More Problems Finished Solving Problems
  36. 36. Congratulations! You have lots of skills to add to your problem-solving suitcase. Now it is time to begin the Searching for Solutions WebQuest !

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