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Problem Solving

Problem Solving. Steps and Strategies. The Problem Solving Plan. Step 1: Understand the Problem What are you asked to find? Reword the problem so it makes sense to you. What information is given? Identify the important facts in the problem. What information do you need?

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Problem Solving

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  1. Problem Solving Steps and Strategies

  2. The Problem Solving Plan Step 1: Understand the Problem • What are you asked to find? • Reword the problem so it makes sense to you. • What information is given? • Identify the important facts in the problem. • What information do you need? • Not all information is always needed. Sort out the important facts needed to solve. • Is all the information given? • Can you solve the problem with the information given?

  3. Step 2: Make a Plan • Have you ever solved a similar problem? • What strategy or strategies can you use? Step 3: Solve • Follow your plan – Show the steps in your solution. Write your answer as a complete sentence.

  4. Step 4: Look Back • Have you answered the question? • Is your answer reasonable? • Is there another strategy you could use? • Did you learn anything while solving this problem that could help you solve similar problems in the future?

  5. In Summary • When problem solving: • Understand the problem • Make a Plan (Know the strategies) • Solve (Show All Work and Write in Complete Sentences) • Check your Work

  6. Key Words Why is it important to understand key words when problem solving? They help you decide how to solve the problem - Key words will tell you whether to add, subtract, multiply, or divide. What key words do you already know? Discuss with your partner and be ready to share with the class.

  7. Let’s Practice Identifying Key Words

  8. Practice: Choose a key word from each operation (addition, subtraction, multiplication, and division) and create a story problem using your key words. Example: Key Word: Product What is the product of 3 and 5? Example: Key word: Difference Sally and Joe were competing in the 100 meter dash. Sally ran it in 9.5seconds. Joe ran it in 7.5 seconds. What is the difference between their times?

  9. Make sure your name is on your paper. Switch papers with your partner. Take a few minutes to read through your partners paper. Underline the key words in each story problem. Then decide which operation you would use (+,-, x, or ÷) and write it out next to each problem. You do not have to solve the problem. Now check with your partner. Do you both agree what the key words and operations are? If not, discuss why. Be ready to share one of your story problems with the class.

  10. Sometimes There is More Than just needing to know key words. There are lots of different ways to go about solving a problem – Knowing and understanding different strategies will help make problem solving much easier! What strategies do you already know?

  11. Know the Strategies • Draw a Picture A bald eagle has built a nest 18 feet below the top of a 105 foot tall oak tree. The eagle sits on a limb 72 feet above the ground. What is the vertical distance between the eagle and its nest? 18 feet ??? feet 105 feet 72 feet

  12. Make an Organized List A spinner has 4 different colors: red, blue, yellow, and white. If you spin the spinner 2 times, how many different color combinations could you get? Red, Blue Red, Yellow Red, White Red, Red Blue, Yellow Blue, White, Blue, Blue (Blue, Red is already used) Yellow, White Yellow, Yellow (Yellow, Red & Yellow, Blue are already used) White, White (White, Red & White, Blue & White, Yellow are already used) What makes this an organized list?

  13. Guess and Check Shannon used equal numbers of quarters and nickels to buy an embossing template that cost $1.50. How many of each coin did she use? Hmmm…does this work? 3 Q = $0.75 3 N = $0.15 $0.90 No Hmmm…does this work? 5 Q = $1.25 5 N = $0.25 $1.50 Yes

  14. Make a Table/Chart • A subway train left downtown with 121 passengers aboard. At the first stop, 1 person got off. At the second stop, 3 people got off. At the third stop, 5 people got off. At the fourth stop, 7 people got off. If the pattern continues, how many people will get off at the 7th stop? How many people will be left after the 7th stop?

  15. Use Logical Reasoning • All elephants are wrinkled. Ajax is an elephant. • A) Ajax is wrinkled • B) No conclusion possible • All squares have 4 sides. Susan drew a 4-sided figure. • A)Susan drew a square • B) No conclusion possible

  16. Work Backwards • Susan made a deposit of $74 to her bank account. She then had $192 in the account. How much money was in the account before the deposit? $192 - $74 = $118 (Deposit means add, but to find out how much she had BEFORE the deposit we need to subtract from the end result)

  17. Other Strategies… • Act it Out • Make a Model • Find a Pattern

  18. Review Problem Solving Process: • When problem solving: • Understand the problem • Make a Plan (Know the strategies) • Solve (Show All Work and Write in Complete Sentences) • Check your Work

  19. Now you try…. 1) Today is the teacher’s birthday. The teacher said: “If you multiply my age by 3, then subtract 20, the result is 100.” How old is the teacher? 2) The sum of two numbers = 15 The difference of the numbers is 3 Find the numbers Work Backwards: 100 + 20 = 120 120 ÷ 3 = 40 Guess and Check: 9 + 6 = 15 9 – 6 = 3 It Works!

  20. 3) The telephone operator has told Jed to deposit 60 cents. In how many ways can he do this using nickels, dimes, and quarters? Organized List: 0Q 12N 0D 2 Q 2N 0D 1Q 7N 0D 0Q 10N 1D 2Q 0N 1D 1Q 5N 1D 0Q 8N 2D 1Q 3N 2D 0Q 6N 3D 1Q 1N 3D 0Q 4N 4D 0Q 2N 5D 0Q 0N 6D

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