This document provides examples of word problems and strategies for solving them. It discusses key words to look for in problems and shows the steps of understanding the information given, identifying the relevant numbers, choosing the correct mathematical operation, writing a number sentence, and checking if the answer makes sense. Several story problems are worked through as examples, such as calculating total distance traveled given miles hiked per day, finding the total number of candy cases from quantities of different types, and determining average cost from total price and number of orders.

1. Story Problems & Key Words

2. doubleplusdividedraiseMore thanexceedHow many more?In eachincreasedtimesdistributegainleftsumdifferenceratioAdded tominuspertripleaveragetotalofquotientproductdecreasedtogethertwicefewer

3. 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?

4. Example 1Tripp 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?

5. 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 1What operation is indicated?

6. What is the math sentence?36 −9 27 𝑚𝑖𝑙𝑒𝑠 Does the answer make sense?

7. 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?

8. The 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 2What operation is indicated?

9. What is the math sentence?25+55 80 𝑐𝑎𝑠𝑒𝑠 Does the answer make sense?

10. 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?

11. In 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 3What operation is indicated?

12. What is the math sentence?4059÷369 $11 Does the answer make sense?

13. Example 4Each bushel of apples has 87 apples in it. How many apples are in 37 bushels?

14. Each bushel of apples has 87 apples in it. Each bushel can make 12 apple pies. How many apples are in 37 bushels?Example 4

15. What is the math sentence?87 ∙37 3,219 apples Does the answer make sense?

16. Does thisALWAYSwork?

17. UnfortunatelyNO

18. Different StrategiesRead 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 modelCan 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?

19. Example 5Mr. 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?

20. What do we know?The car gets 50 miles per gallon.He purchases 14 gallons of gas.

21. What do we need to know?How many miles can Mr. John drive on 14 gallons?

22. Is there any unnecessary information?No.

23. 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?

24. Write the math sentence.50 ∙14 700 miles Does the answer make sense?

25. Example 6You 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?

26. What do we know?We can get 8 cards per sheet.We need to print 1000 cards.

27. Is there any unnecessary information?At this point we don’t need to know the paper size.

28. 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?

29. Can we rewrite the question?How many equal sets of 8 do I need to produce 1000 cards?

30. Write the math sentence.1000÷ 8 125 𝑠h𝑒𝑒𝑡𝑠 Does the answer make sense?

31. On Your OwnThe print shop produces 15897 pamphlets in 3 days. What is the average production per day?

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

33. Write the math sentence.15897÷ 3 5299 𝑝𝑎𝑚𝑝h𝑙𝑒𝑡𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦 Does the answer make sense?