Before you can write equations from a problem situation, you will need to think about which operations are being used in a problem. To do that, consider the actions being performed in the problem.

In this section, you will practice interpreting operations from problem situations. You will apply that skill in the next section of the lesson to write equations that represent the problem.

To begin with, think about how you have used strip diagrams in previous grades to represent addition and subtraction problems. For example, consider the problem below.

In this problem, Lauren spent money on a movie ticket, and she also spent money on concessions. You know how much money Lauren spent on concessions, and you also know the total amount of money she spent. This is a part-part-whole problem, where Part 1 + Part 2 = Whole. The strip diagram is a visual model of the relationship.

Create a strip diagram to model the problem shown below. Drag the strips from the bank to the appropriate place to construct your strip diagram.

Wesley ran 37 over 8 7 8 miles last week. His goal is to have run a total of 7 miles by the end of this week. How many miles does Wesley need to run in order to meet his goal?

Sort the problems below into problems that represent each operation. Use your completed sort to answer the questions that follow.

Use the interactive to answer the questions that follow.

• What types of verbs or actions represented addition situations?

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  Problems with joining or combining represented addition.

• What types of verbs or actions represented subtraction situations?

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  Problems with removing or separating unevenly represented addition.

• How could you use a strip diagram to represent addition or subtraction situations?

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  A strip diagram is a visual representation of quantities that are being combined or separated.
  
  

• What types of verbs or actions represented multiplication situations?

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  Problems with an area or rows of equal numbers of objects represented multiplication.

• What types of verbs or actions represented division situations?

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  Problems with grouping into equal-size groups or partitioning evenly represented division.

Practice

Identify the operation that each problem situation below represents.

1. Mr. Jacobs purchased three items: a hammer that cost $14.95, a roll of tape that cost $2.45, and a bucket of paint that cost $21.39. Excluding sales tax, how much money did Mr. Jacobs spend?

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   If you were to make a strip diagram representing the problem, it would look like this.
   
   

   What action is being performed with the prices of the three items?

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   Addition
2. Anu earns $11.30 per hour as a forklift operator. If she works 120 hours in one month, how much money will Anu earn?

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   You are given a rate and the number of hours worked. What is the question asking you to determine? What do you need to do with the two numbers in order to answer the question?
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   Multiplication
3. Sylvia lives 3 3 over 8 3 8 miles from the museum. Her cousin, Shane, lives 51 over 2 1 2 miles from the museum. How much farther does Shane live from the museum than Sylvia?

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   If you were to make a strip diagram representing the problem, it would look like this.
   
   

   What action is being performed with the prices of the two distances?

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   Subtraction
4. One bag of oranges weighs 4.25 pounds. How much will 8 bags of oranges weigh?

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   You are given the weight of one bag and the number of bags. What is the question asking you to determine? What do you need to do with the two numbers in order to answer the question?
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   Multiplication