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Problem Solving Strategies: Story Problems

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Problem Solving Strategies: Story Problems

- 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.

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

- 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 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 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 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)

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

- 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

- Does it fit a known type of Problem?

- Write an Equation or Inequality
- Make a Table
- Drawings and illustrations
- Working Backwards (try given answers)
- Guess and Check

- 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

- 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

- 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

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) ?

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!

- 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.

- When writing the answer there are a few things you have to remember

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.