Story Problems & Key Words

Added to

More than

sum

increased

total

gain

plus

raise

together

difference

minus

decreased

fewer

How many more?

exceed

times

of

product

twice

triple

double

divided

quotient

average

ratio

per

distribute

left

In each

Problem Solving StrategiesStrategies:

Read the problem carefully.Underline the Key WordsBox the necessary information (numbers)Are units mentioned in the question? If so circle them.Cross out unnecessary information (size of paper, etc.)

Write a number sentence that relates to the above information.

Solve the problem – don’t forget units.

Does the answer make sense?

Example 1

Tripp and Charlotte are going on a 36 mile hike. Tripp's backpack weighs 25 pounds. Charlotte's back pack weighs 7 pounds less. They hiked 9 miles the first day. How many miles do they have left?

Example 1

Tripp and Charlotte are going on a 36 mile hike. Tripp's backpack weighs 25 pounds. Charlotte's back pack weighs 7 pounds less. They hiked 9 miles the first day. How many miles do they have left?What operation is indicated?

What is the math sentence?

36−927𝑚𝑖𝑙𝑒𝑠

Does the answer make sense?

Example 2The Sweet Shop gets a new candy shipment every 35 days. There are 25 cases of chocolate bars. There are 55 cases of lollipops. How many cases of candy altogether?

Example 2The Sweet Shop gets a new candy shipment every 35 days. There are 25 cases of chocolate bars. There are 55 cases of lollipops. How many cases of candy altogether?

What operation is indicated?

What is the math sentence?

25+558 0𝑐𝑎𝑠𝑒𝑠

Does the answer make sense?

Example 3In a month, a printer specializing in printing business cards sells 369 orders for a total of $4059. What is the average cost for each order?

Example 3In a month, a printer specializing in printing business cards sells 369 orders for a total of $4059. What is the average cost for each order?What operation is indicated?

What is the math sentence?

4059÷369

Does the answer make sense?

$11

Example 4

Each bushel of apples has 87 apples in it. How many apples are in 37 bushels?

Example 4

Each bushel of apples has 87 apples in it. Each bushel can make 12 apple pies. How many apples are in 37 bushels?

What is the math sentence?

87 ∙37 apples

Does the answer make sense?

Does thisALWAYS

work?

UnfortunatelyNO

Different Strategies Read the problem carefully. What do you know from the problem? Does it provide clues? What do you need to know? Eliminate unnecessary information. Draw a sketch or model Can you use a simple problem with the same conditions?

(buying 2 pair of jeans) Try to restate the problem in your own words. What are we trying to determine? Can you write it to contain a key word?

Make a plan. How will you try to solve the problem?

Does the answer make sense?

Example 5

Mr. John's new hybrid car gets him 50 miles per gallons. If Mr. John get a full tank with 14 gallons of gas, How far can Mr. John go?

What do we know?

The car gets 50 miles per gallon.

He purchases 14 gallons of gas.

What do we need to know?

How many miles can Mr. John drive on 14 gallons?

Is there any unnecessary information?

No.

Can you use a simpler example that will help you figure out what operation to use? Use something you are familiar with.

You earn $8 per hour. How much do you earn in 3 hours?

$24. What operation did you use to determine your pay?

Write the math sentence.

50 ∙14miles

Does the answer make sense?

Example 6

You are asked for a quote for business cards. The print shop tells you that they can cut 8 from every 8 ½ x 11 sheet. How many sheets are needed to print 1000 business cards?

What do we know?

We can get 8 cards per sheet.

We need to print 1000 cards.

Is there any unnecessary information?

At this point we don’t need to know the paper size.

Can you use a simpler example that will help you figure out what operation to use? Use something you are familiar with.

You can get 12 cookies on each baking sheet. How many sheets do you need to bake 24 cookies?

2 sheets. What operation did you use?

Can we rewrite the question?

How many equal sets of 8 do I need to produce 1000 cards?

Write the math sentence.

8

125 h𝑠 𝑒𝑒𝑡𝑠Does the answer make sense?

On Your Own

The print shop produces 15897 pamphlets in 3 days. What is the average production per day?

On Your Own

The print shop produces 15897 pamphlets in 3 days. What is the average production per day?

Write the math sentence.

35299 h𝑝𝑎𝑚𝑝 𝑙𝑒𝑡𝑠𝑝𝑒𝑟 𝑑𝑎𝑦

Does the answer make sense?