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Problem Solving Strategies: Story Problems

Problem Solving Strategies: Story Problems. STEP ONE. Read the story problem through. Read again to identify the important information (numbers & key words) you will need to solve the problem. Make sure you know the question you are answering. STEP TWO.

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Problem Solving Strategies: Story Problems

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  1. Problem Solving Strategies: Story Problems

  2. STEP ONE • Read the story problem through. • Read again to identify the important information (numbers & key words) you will need to solve the problem. • Make sure you know the question you are answering.

  3. STEP TWO • Identifying what type of arithmetic you will need to do (based on key words) • Addition • Subtraction • Multiplication • Division

  4. Addition • Addition story problems often use words like: • Sum • More than • Increased by • Combined • Together • Total of • EXAMPLE: • Jane has 10 Barbie's and for her birthday she gets 3 more. How many Barbie’s does Jane have now? (10+3=?)

  5. Subtraction • Subtraction story problems often use words like: • Difference • Less than • Fewer than • Decreased by • Reduced by • (how many) More • (how many) Left • Minus • Take away • EXAMPLE: • If there are 10 cars in one parking and 6 fewer cars in the second parking lot. How many more cars are there in the second parking lot? (10-6=?)

  6. Multiplication • Multiplication story problems often use words like: • Of • Times • Multiplied by • Product of • EXAMPLE: • If Mary has 3 pets and Annie has 2 times as many pets as Mary. How many pets does Annie have? (3x2=?) • {or “twice” as many} • 12 is 25% of what number? • (12 = 0.25x)

  7. Division • Division word problems often use words like: • Quotient • Per • Each • Out of • Ratio of • EXAMPLES: • If Bobbi had 15 cookies and ate the same amount each day for 5 days how many did she eat per day? (15 / 5=? ) • If Madison spent 3 hours doing homework the last 4 days, how much did she do each day? (3/4) • 4 out of 5 dentists recommend flossing daily. (4/5)

  8. STEP THREE • Put the information into a useful form: • Write a Verbal Model • Write an Algebraic Model • Create a Table • Draw a Diagram

  9. STEP FOUR • Solve the Problem • Does it fit a known type of Problem? • Interest : I =Prt • Distance: D=rt • Geometric: A = bh, C=2Π, V=1/3Bh • What type of solution is it? Numeric? Algebraic? • Are there answers you can eliminate? • Using one of the following strategies

  10. Choose a Strategy to Solve the Problem: • Write an Equation or Inequality • Make a Table • Drawings and illustrations • Working Backwards (try given answers) • Guess and Check

  11. WRITE AN EQUATION • John and 2 friends are going out for a pizza for lunch. They split one pizza and 3 large drinks. The pizza costs $14.00. After using a $7.00 gift certificate, the spend a total of $12.10. What is the cost of one large drink. • 3 drinks (John + 2 friends = 3) = 3d • 1 pizza = 14:00 • Discount = -7.00 • Total = 12.10 • 3d + 14.00 – 7.00 = 12.10

  12. MAKE A TABLE • Andy and his parents decided that for his allowance would go up one dollar and 50 cents every week for 3 consecutive weeks. If he starts out at getting 6 dollars how much would he make week 5? Week $ allowance 1 $6.00 2 $7.50 3 $9.00 4 $10.50 5 $12.00 $12.00

  13. DRAWINGS AND ILLUSTRATIONS • Drawing a picture is a great way to solve word problems. • Makes it is easy to see WHY you get the answer. EXAMPLE: The length of a rectangle is 3 more than twice the width. If the Perimeter is 36 feet, how wide id the rectangle? 2w + 3 2w+3+w+2w+3+w = 36 6w +6 =36 w w 2w + 3

  14. WORKING BACKWARDS This works well for Multiple Choice Questions A Camera manufacturer spends $2,100 a day plus $9 per camera. The cameras sell for $14 each. How many cameras must they sell top break even? a) 420 b) 480 c) 380 d) 150 2100 + 9( number of cameras) = 14(number of cameras) 2100 + 9(420) = 14(420) ? (hint start with the middle value) 2100 + 9(480) = 14(480) ? 2100 + 9(380) = 14(380) ? 2100 + 9(150) = 14(150) ?

  15. GUESS AND CHECK If two sisters ages add up to 22 years and one is 4 years older than the other what are there two ages? Plan: Select random numbers that add up to 22 until you find two that are 4 apart. • 10 and 12: 10+12=22 but 12-10=2 not 4; • 8 and 14: 8+14= 22 but 14-8=6; • 9 and 13: 9+13=22 and 13-9=4 so their ages are 9 and 13!

  16. STEP FIVE • Writing your answer to the story problem is the final step • When writing the answer there are a few things you have to remember • What are you trying to find • Your answer probably should be in units (mph, cups, or inches) • Answer should be in a complete sentence.

  17. Examples of Answers If Keri has 3 apples and 5 oranges how many more oranges does she have than apples? Answer: Keri has 2 more oranges than apples.

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