Problem Solving Strategies: Story Problems

STEP ONE Read the story problem and identify the important information you will need to solve the problem.

STEP TWO Identifying what type of arithmetic you will need to do Addition Subtraction Multiplication Division

Addition Addition story problems often use words like: Increased by More than Combined Together Total of Sum Added to 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: Decreased by Minus, less than Difference Less than Fewer than Away/loose EXAMPLE: If there are 10 cars in one parking and 6 less 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=?)

Division Division word problems often use words like: Per Out of Ratio of Quotient of “a” EXAMPLE: If Bobbi had 15 cookies and ate the same amount each day for 5 days how many did she eat per day? (15 / 5=? )

STEP THREE Solve the Problem Using one of the many problem solving strategies

Choose a Strategy to Solve the Problem: Working Backwards Drawings and illustrations Making an equation Visualizations Make a Table Guess and Check Or use your own strategy

WORKING BACKWARDS A problem you would use the working backward method on would be something like this: Mary Ann flew from Marquette, Mi to Los Angeles , CA . It took her 2 hours to get from Marquette to Chicago, Il and 4 hours to get from Chicago to Los Angeles. If she arrived at 4:00pm what time was it when she left? Figure out what you are trying to find. In this case it is the time in which she left Marquette. Make a plan of action. In this case you would take the time she arrived and work backwards by subtracting the hours she was in flight. 4:00 (when she arrived in LA) – 4 hours (it took to go from Chicago to LA) = 12:00 (time she left Chicago). You would then take that time and subtract the time it took to go from Chicago to Marquette. 12:00pm – 2 hours = 10:00 am (your answer)

DRAWINGS AND ILLUSTRATIONS Drawing a picture is a great way to solve word problems. You not only get the answer but it is easy to see WHY you get the answer. A good example of a problem you would want to make a drawing for would be a problem like: For Stacie's birthday she got a bag of marbles from her friend Amy. The bag has 6 red marbles, 10 blue marbles, 4 yellow marbles, and 1 green marble. How many marbles does she have in her bag? Figure out what you are trying to find: How many marbles there are in the bag. Make a plan: Draw out each set of marbles and count them up. there are a total of 21 marbles!

MAKE AN EQUATION Making an equation of story problems is also a great way to solve story problems. You just take the numbers from the problem and turn them into an equation. This problem would be a good example of when to use an equation: For a school bake sale 5 students each brought in something to sell. Keri brought 2 dozen cookies, Rachel brought 3 dozen brownies, Max brought 5 dozen muffins, Michelle brought 1 dozen cupcakes, and Sarah brought 4 dozen rice crispy bars. How many treats did they have to sell? Decide what you are trying to find in this case: How many treats they will have to sell. Make a plan or in this case an equation. We know that there are 12 treats in a dozen and we know how many dozen cookies we have so here are some sample equations you could use: 2(12)+3(12)+5(12)+1(12)+4(12)=180 (2+3+5+1+4)12=180 Then just simply solve the Problem Mathematically

VISUALIZATIONS/HANDS ON This problem solving strategy can be the most fun and it is very simple. You actually use visuals to do the problem much like when using drawings but instead of using pencil and paper you use the actual things. Say you have a problem like this: At the beginning and the end of every day Mrs. Smith collects and hands back papers. On Monday at the beginning of the day she hands back 25 and collects 18. At the end of the day she hands back 29 and collects 26. How many papers will the teach have collected on Monday and how many will the students have gotten back? To do this problem hands on is very simple. I would actually take the class and do exactly what the story problem says. Hand out some papers, collect some paper, and repeat the process. As if it were the beginning and end of the day. Then when you are finished count the papers the students have and how many the teacher has.

MAKE A TABLE Week $ allowance 1 $6.00 2 $7.50 3 $9.00 4 $10.50 5 Making a table is a very organized and simple way to solve some story problems. It is best used when dealing with problems like: 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? Find: What will his allowance be week 5? Plan: Make a chart of what his allowance will be each week  Week $ allowance 1 $6.00 2 $7.50 3 $9.00 4 $10.50 5 $12.00 $12.00

GUESS AND CHECK They guess and check method isn’t the fastest but it is very effective. You would usually use it on problems like this: If two sisters ages add up to 22 years and one is 4 years older than the other what are there two ages? You are trying to find what: Their 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 15: 8+15= 22 but 15-8=6; 9 and 13: 9+13=22 and 13-9=4 so there ages are 9 and 13!

STEP FOUR 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 If your answer should be in units such as (mph, cups, or inches) Your answer should be in complete sentences

Examples of Answers Wrong way to Answer this Story Problem: If Keri has 3 apples and 5 oranges how many more oranges does she have than apples? Wrong way to Answer this Story Problem: 2 (it is the right answer but when working with story problems you have to explain your answer) Right Way to Answer this Story Problem: Keri has 2 more oranges than apples. Now that you are familiar with Solving Story Problems lets test your memory with some worksheets and a quiz!