Problem solving strategies story problems
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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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Problem solving strategies story problems

Problem Solving Strategies: Story Problems


Step one

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

STEP TWO

  • Identifying what type of arithmetic you will need to do (based on key words)

    • Addition

    • Subtraction

    • Multiplication

    • Division


Addition

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

  • 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

  • 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

  • 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

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

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

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

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


Make a table

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

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

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) ?


Guess and check

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

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

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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