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

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=?)

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=?)

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)

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)

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

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

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

WRITE AN EQUATION 3 drinks (John + 2 friends = 3) = 3d 1 pizza = 14.00 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

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

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

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 to 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) ?

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!

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.

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.