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Mathematical Problem Solving

Mathematical Problem Solving. 7 White Math 10/26/2006. Why Use Problem Solving?. *Develop your PS Skills - the more practice you get, the better you get! *It positions you for future problem solving success. *It makes math meaningful!. Solutions .

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Mathematical Problem Solving

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  1. Mathematical Problem Solving 7 White Math 10/26/2006

  2. Why Use Problem Solving? *Develop your PS Skills - the more practice you get, the better you get! *It positions you for future problem solving success. *It makes math meaningful!

  3. Solutions • In problem solving, there are reliable methods of finding solutions, and there are unreliable methods. Look at the chart below, can you tell the difference? http://www.hawaii.edu/suremath/solutionPaths.html

  4. Multiple Ways • Just like the previous chart displayed, there are multiple ways to reach the same outcome. • This is the same for many problems we solve on daily basis. • Should I brush my teeth first or hair first? • Should I ride the bus or walk? Question: What other types of problems similar to these do you face daily?

  5. Here’s Some Options • Here are some options and examples of the different ways you can solve math problems. Say them with me… • Find a Pattern • Make a Table • Work Backwards • Guess and Check • Draw a Picture • Make a List

  6. Mike’s Decisions • On the next few slides, you will be given a few prompts. Write down on your paper what you feel would be the most appropriate strategy of the six on the previous slide to solve the real-life problems of a guy named Mike.

  7. Find a Pattern • Question: Mike has written a number pattern that begins with 1, 3, 6, 10, 15. If he continues this pattern, what are the next four numbers in her pattern? +What do you need to find? +How can you solve the problem? You can find a pattern. Look at the numbers. The new number depends upon the number before it.

  8. Find a Pattern (cont.) Look at the numbers in the pattern.3 = 1 + 2 (starting number is 1, add 2 to make 3)6 = 3 + 3 (starting number is 3, add 3 to make 6)10 = 6 + 4 (starting number is 6, add 4 to make 10)15 = 10 + 5 (starting number is 10, add 5 to make 15)Let’s do these together. The new numbers will be…15 + 6 = ?21 + 7 = ?28 + 8 = ?36 + 9 = ?

  9. Make a Table Question: Mike saves $3 on Monday. Each day after that, he saves twice as much as he saved the day before. If this pattern continues, how much would he save on Friday? +What do you need to find? +How can you solve the problem?You can make a table like the one on the next slide. List the amount of money you save each day. Remember to double the number each day.

  10. Make a Table (cont.) So, Mike saved $48.00 on Friday.

  11. Work Backwards Question: Mike walked from Glasgow to Hiseville. It took 1 hour 25 minutes to walk from Glasgow to Goodnight. Then, it took 25 minutes to walk from Goodnight to Hiseville. He arrived in Hiseville at 2:45 P.M. At what time did he leave Glasgow? +What do you need to find? +How can you solve the problem? You can work backwards from the time Mike reached Hiseville. Subtract the time it took to walk from Goodnight to Hiseville. Then, subtract the time it took to walk from Glasgow to Goodnight.

  12. Work Backwards (cont.) Start at 2:45. This is the time Jack reached Hiseville. Subtract 25 minutes. This is the time it took to get from Goodnight to Hiseville.What is the time?Subtract: 1 hour 25 minutes. This is the time it took to get from Glasgow to Goodnight.So, what time did Mike leave Glasgow?

  13. Guess and Check Question: Mike and Jill sold 12 coupon books altogether. Mike sold 2 more tickets than Jill. How many tickets did each girl sell? +What do you need to find? +How can you solve the problem? You can guess and check to find two numbers with a sum of 12 and a difference of 2. If your first guess does not work, try two different numbers.

  14. Guess and Check (cont.) First Guess:Mike = 8 books Jill = 4 booksCheck8 + 4 = 128 - 4 = 4 ( Mike sold 4 more books)These numbers do not work! Second Guess:Mike = 7 booksJill = 5 booksCheck7 + 5 = 127- 5 = 2 ( Mike sold 2 more books)These numbers do work!Mike sold 7 books and Jill sold 5 books.

  15. Draw a Picture Question: Mike has 3 green chips, 4 blue chips and 1 red chip in his bag. What fractional part of the bag of chips is green? +What do you need to find? +How can you solve the problem?You can draw a picture to show the information. Then you can use the picture to find the answer.

  16. Draw a Picture (cont.) Draw 8 chips on your own paper. Now, what fraction of the chips are green? 3/8 of the chips are green.

  17. Make a List Question: Mike is taking pictures of Jill, Aiden, and Jon. He asks them, " How many different ways could you three stand in a line?" +What do you need to know? +How can you solve the problem? You can make a list to help you find all the different ways. Choose one person to be first and another to be second. The last one will be third.

  18. Make a List (cont.) When you make your list, you will notice that there are 2 ways for Jill to be first, 2 ways for Aiden to be first and 2 ways for Jon to be first. So, there are 6 ways that they could stand in line.

  19. Conclusion So, as well all can see, there are many different ways to solve many different problems. The goal, however, is always the same – getting the correct answer.

  20. Helpful Links If you would like some more information on different problem solving techniques, feel free to visit any of the following cites as well as any other reliable sources on the web. http://math.about.com/library/weekly/aa041503a.htm http://www.mathcounts.org/webarticles/articlefiles/155-Problem_Solving.pdf http://www.abcteach.com/

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