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7.20: Problem Solving Plan, Choose an Operation

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Have you ever studied the insects of the rainforest? Take a look at what Julie has learned.

Before Julie finishes her project she knows that she has to include something about insects. Julie is not a fan of bugs, so she has saved this piece of information for the end of the project. After looking at a lot of pictures of bugs, Julie decides to focus on two different types of beetles. The dung beetle is famous in the rainforest. There are different types of dung beetles and they are pretty common. The average dung beetle is \frac{1}{2} to 1 inch long. Julie works on including a drawing of a dung beetle in her project. The second type of beetle Julie studies is the Goliath beetle. This is a HUGE beetle at 4 \frac{1}{2} inches long. Julie begins drawing the Goliath beetle next to the dung beetle. She decides to show a comparison between the lengths of the two beetles.

If the dung beetle is between \frac{1}{2} and 1 inch long and the Goliath beetle is 4 \frac{1}{2} inches long, what is the difference between their lengths?

As Julie does her calculating, you can solve this by using the problem solving strategy: choose an operation. At the end of the Concept, you will use this strategy to solve the problem.

Guidance

When solving a problem, it is very important to read and understand the problem in order to figure out which operation you will need to use to find a correct answer. This is especially important with word or story problems because you will have to identify key words in the story or word problem that let you know which operation to use. Our four operations are addition, subtraction, multiplication and division. Here is a description of each and some key words that you can look for when reading a problem.

Addition – a problem where two quantities are being combined. Key words are sum, total, in all, combined, altogether.

John has 8 books and Mary has four books, how many books do they have in all ?

In all are the key words that help us identify that we need to use addition to solve this problem.

Subtraction – a problem where two quantities are being compared or one quantity is being removed from another quantity. Key words are left, left over, take away, difference, more, less, more than, less than, compare, greater than, increased or decreased by.

Karen had fifteen records, but she gave three to her friend Louise. How many does she have left ?

Left is a key word that clues us in that subtraction is the operation required.

Multiplication – word problems using repeated addition or groups. Key words are a lot like addition-pay attention to the repeating-that will help you know that you need to multiply. Key words are total, in all, each, every, per, how much, at this rate, and of.

What is one-half of 18?

Of means multiply. This is our key word.

Division – Division problems generally involve a situation in which a single quantity is split up into many equal-sized parts. Key words are split, divide, shared, equal size, average, groups, per.

Chris has fourteen marbles. He has divided them into two groups. How many marbles are in each group ?

Group is a key word that means division.

Identify which operation is indicated by each key word.

Example A

In all

Solution: Addition

Example B

Left Over

Solution: Subtraction

Example C

Split up

Solution: Division

Now back to Julie and the beetles. Here is the original problem once again.

Before Julie finishes her project she knows that she has to include something about insects. Julie is not a fan of bugs, so she has saved this piece of information for the end of the project. After looking at a lot of pictures of bugs, Julie decides to focus on two different types of beetles. The dung beetle is famous in the rainforest. There are different types of dung beetles and they are pretty common. The average dung beetle is \frac{1}{2} to 1 inch long. Julie works on including a drawing of a dung beetle in her project. The second type of beetle Julie studies is the Goliath beetle. This is a HUGE beetle at 4 \frac{1}{2} inches long. Julie begins drawing the Goliath beetle next to the dung beetle. She decides to show a comparison between the lengths of the two beetles.

If the dung beetle is between \frac{1}{2} and 1 inch long and the Goliath beetle is 4 \frac{1}{2} inches long, what is the difference between their lengths?

The key word is difference.

The operation is subtraction.

4 \frac{1}{2} = \frac{1}{2} = 4 inches differences for a small dung beetle

4 \frac{1}{2} - 1 = 3 \frac{1}{2} inches difference for a large dung beetle

The difference in size ranges from 3 \frac{1}{2} inches to 4 inches.

Vocabulary

Here are the vocabulary words in this Concept.

Key words
words that let you know which operation to use to solve a problem.
Operations
addition, subtraction, multiplication and division

Guided Practice

Here is one for you to try on your own.

Kyle has fourteen nickels. He found four more nickels in his pocket. How many nickels does he have? How much money are the nickels worth in all

Answer

Our key term is in all. This lets us know that we are going to need to add up the nickels. Then there is a second part of the problem where we will decipher how much money Kyle actually has.

14 nickels + 4 nickels = 18 nickels

Each nickel is worth 5 cents. Here is where you have to understand the problem. We could add 5 eighteen times for the amount of money, or we can multiply.

18 \times 5 = 90

Kyle has 18 nickels, which is equal to 90 cents.

Video Review

Here is a video for review.

Khan Academy: Word Problem Solving Strategies

Practice

Directions: Read each problem. Identify the key words, name the operation and solve each problem. Each problem will have three answers.

1. Clara has 30 dollars. If she splits it into 5 equal groups, how many dollars will each group have?

2. If Clara doubles this number and then splits it into 5 equal groups, how many dollars will each group have?

3. What if she starts with 24 dollars? How does this change the division?

4. In 5 weeks, Bo made 300 dollars. What was the average amount Bo made per week?

5. In 10 weeks, at this rate, how much money will Bo have made in all?

6. If Bo made 600 dollars in five weeks, what is the average amount made per week?

7. Bob has 45 dollars. Clara has 23 dollars. What is the difference between the amount of money Bo and Clara have?

8. Lakshmi reads 20 pages per hour. At this rate, how many pages will she read in 7 hours?

9. Bonnie has 85 hair barrettes. Clara has 43 hair barrettes. What is the total number of hair barrettes?

10. If Bonnie decided to give 5 of her hair barrettes away to Joanne, how many would Bonnie and Clara have left?

11. Each box has 12 bottles. How many bottles are in 15 boxes?

12. Five equal-sized boxes weigh 40 pounds. How much does each box weigh?

13. Magda had 42 fish. She gave 16 of them to Peter. How many fish did Magda have left?

14. Yusef has a 37 \frac{2}{3} inch long board. If he cuts it into 9 equal sized pieces, how long will each piece be?

15. If Yusef cuts the same board into 18 pieces, how long will each piece be?

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Oct 29, 2012

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Aug 18, 2014
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