7.8: Problem-Solving Strategy: Choose an Operation
Introduction
The Beetles
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 \begin{align*}\frac{1}{2}''\end{align*} to 1” 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 \begin{align*}4 \frac{1}{2}\end{align*} 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 \begin{align*}\frac{1}{2}''\end{align*} and 1” long and the Goliath beetle is \begin{align*}4 \frac{1}{2}''\end{align*} 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 lesson, you will use this strategy to solve the problem.
What You Will Learn
In this lesson, you will learn the following skills:
- Read and understand given problem situations.
- Develop and use the strategy: Choose an operation.
- Plan and compare alternative approaches to solving problems.
- Solve real-world problems using selected strategies as part of a plan.
Teaching Time
I. Read and Understand Given Problem Situations
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.
Example
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.
Example
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.
Example
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.
Example
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.
- In all
- Left over
- Split up
Take a few minutes to check your work with a partner.
II. Develop and Use the Strategy: Choose an Operation
Now that you understand the key words associated with each operation, you will work to apply this information when reading a problem. The first thing that you would do is to underline the key words in a problem. Then you can choose an operation and solve for an answer.
Example
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?
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 \begin{align*}\times\end{align*} 5 \begin{align*}=\end{align*} 90
Kyle has 18 nickels, which is equal to 90 cents.
III. Plan and Compare Alternative Approaches to Solving Problems
This last example is a perfect one for thinking about alternative approaches to solving a problem. When figuring out the amount of money that Kyle has, we could have easily used repeated addition.
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = ____
Yes. It is a lot of fives. This is why using multiplication is a much faster, easier, simpler strategy than repeated addition.
In many problems, you will have to choose a strategy and then apply it. Often there will be more than one choice, you will have to select the best one; just as we did with Kyle.
Real Life Example Completed
The Beetles
Use the problem solving strategy: Choose an operation to solve this problem. Start by underlining key words. Then decide on an operation and solve for the answer.
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 \begin{align*}\frac{1}{2}''\end{align*} to 1” 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 \begin{align*}4 \frac{1}{2}\end{align*} 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 \begin{align*}\frac{1}{2}''\end{align*} and 1” long and the Goliath beetle is \begin{align*}4 \frac{1}{2}''\end{align*} long, what is the difference between their lengths?
The key word is “difference.”
The operation is subtraction.
\begin{align*}4 \frac{1}{2} = \frac{1}{2} = 4\end{align*} inches differences for a small dung beetle
\begin{align*}4 \frac{1}{2} - 1 = 3 \frac{1}{2}\end{align*} inches difference for a large dung beetle
The difference in size ranges from \begin{align*}3 \frac{1}{2}\end{align*} inches to 4 inches.
Vocabulary
Here are the vocabulary words that you can find in this lesson.
- Key words
- words that let you know which operation to use to solve a problem.
- Operations
- addition, subtraction, multiplication and division
Resources
Here are a few websites where you can read more about beetles.
http://rainforests.mongabay.com/amazon/insects.html
http://www.extremescience.com/zoom/index.php/creepy-crawlies/6-biggest-insect
http://en.wikipedia.org/wiki/Dung_beetle
Technology Integration
- http://www.thefutureschannel.com/dockets/hands-on_math/dell/ – A great video about how Dell, Inc uses problem solving in serving customers and making computers
Time to 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. In 5 weeks, Bo made 300 dollars. What was the average amount Bo made per week?
3. Bob has 45 dollars. Clara has 23 dollars. What is the difference between the amount of money Bo and Clara have?
4. Lakshmi reads 20 pages per hour. At this rate, how many pages will she read in 7 hours?
5. Bonnie has 85 hair barrettes. Clara has 43 hair barrettes. What is the total number of hair barrettes?
6. If Bonnie decided to give 5 of her hair barrettes away to Joanne, how many would Bonnie and Clara have left?
7. Each box has 12 bottles. How many bottles are in 15 boxes?
8. Five equal-sized boxes weigh 40 pounds. How much does each box weigh?
9. Magda had 42 fish. She gave 16 of them to Peter. How many fish did Magda have left?
10. Yusef has a \begin{align*}37 \frac{2}{3}\end{align*} inch long board. If he cuts it into 9 equal sized pieces, how long will each piece be?
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