The CA SOLVE Approach to Word Problems for CBEST Exam Study Guide (page 2)
Of course, it helps to know the formula or method needed to solve a problem. But there are always those problems on the test that you don't recognize or can't remember how to do, and this may cause you a little anxiety. Even experienced math teachers experience that paralyzing feeling at times. But you shouldn't allow anxiety to conquer you. Nor should you jump into a problem and start figuring madly without a careful reading and analysis of the problem.
The CA SOLVE Approach
When approaching a word problem, you need the skills of a detective. Follow the CA SOLVE method to uncover the mystery behind a problem that is unfamiliar to you.
C Stands for Conquer
Conquer that queasy feeling—don't let it conquer you. To squelch it, try step A.
A Stands for Answer
Look at the answers and see if there are any similarities among them. Notice the form in which the answers are written. Are they all in cubic inches? Do they all contain pi? Are they all formulas?
S Stands for Subject Experience
Many problems are taken from real-life situations or are based on methods you already know. Ask: "Do I have any experience with this subject or with this type of problem? What might a problem about the subject be asking me? Can I remember anything that might relate to this problem?"
Eliminate experiences or methods of solving that don't seem to work. But be careful; sometimes sorting through your memory for experiences and methods takes a long time.
O Stands for Organize the Facts
Here are some ways to organize your data:
- Look for clue words in the problem that tell you to add, subtract, multiply, or divide.
- Try out each answer to see which one works. Look for answers to eliminate.
- Think of formulas or methods that have worked for you in solving problems like this in the past. Write them down. There should be plenty of room on your test booklet for this.
Don't try to keep a formula in your head as you solve the problem. Although writing does take time and effort, jotting down a formula is well worth it for three reasons: 1) A formula on paper will clear your head to work with the numbers; 2) You will have a visual image of the formula you can refer to and plug numbers into; 3) The formula will help you see exactly what operations you will need to perform to solve the problem.
L Stands for Live
Living the problem means pretending you're actually in the situation described in the word problem. To do this effectively, make up details concerning the events and the people in the problem as if you were part of the picture. This process can be done as you are reading the problem and should take only a few seconds.
V Stands for View
View the problem with different numbers to help you get a better sense of the steps you will need to take in order to solve it. This tactic is especially helpful when the sight of a large or complex number is so overwhelming that you just don't know where to start. For example, you might be intimidated by being asked to calculate how long it would take a rocket traveling 650 miles per hour to go 1,300,000 miles. To view the problem differently, you might think of how long it would take a car traveling 10 miles per hour to go 50 miles. Write down the steps you will take to solve the simpler problem, and then apply them to the more complex problem in just the same way.
E Stands for Eliminate
Eliminate answers you know are wrong. You may also spend a short time checking your answer if there is time.
Solve this problem using the CA SOLVE steps.
- There are 651 children in a school. The ratio of boys to girls is 4:3. How many boys are there in the school?
- Subject Experience: You know that 4 and 3 are only one apart and that 4 is greater. You can conclude from this that boys are a little over half the school population. Following up on that, you can cut 651 in half and eliminate any answers that are less than half. Furthermore, since there are three numbers in the problem and two are paired in a ratio, you can conclude that this is a ratio problem. Then you can think about what methods you used for ratio problems in the past.
- Organize: The clue word total means to add. In the context in which it is used, it must mean girls plus boys equals 651. Also, since boys is written before girls, the ratio should be written Boys: Girls.
- Live: Picture a group of three girls and four boys. Now picture more of these groups, so many more that the total would equal 651.
- View: If there were only 4 boys and 3 girls in the school, there would still be a ratio of 4 to 3. Think of other numbers that have a ratio of 4:3, like 40 and 30. If there were 40 boys and 30 girls, there would be 70 students in total, so the answer has to be more than 40 boys. Move on to 400 boys and 300 girls—700 total students. Since the total in the problem is 651, 700 is too large, but it is close, so the answer has to be less than 400. This would narrow your choices to two.
- Eliminate: Since you know from the previous step that the number of students has to be less than 400, you can eliminate choices d and e. Since you know that the number of boys is more than half the school population, you can eliminate choices a and b. You are left with choice c, the correct answer.
Quick Tips and Tricks
Below is a miscellaneous list of quick tips to help you solve word problems.
Work from the Answers
On some problems, you can plug in given answers to see which one works in a problem. Start with choice c. Then if you need a larger number, go down, and if you need a smaller answer, go up. That way, you don't have to try them all. Consider the following problem:
- One-fifth of what number is 30?
Try c: of 50 is 10. A larger answer is needed.
Try d: of 120 is 24. Not yet, but getting closer.
Try e: of 150 is 30—Bingo!
Problems with Multiple Variables
If there are so many variables in a problem that your head is spinning, put in your own numbers. Make a chart of the numbers that go with each variable so there is less chance for you to get mixed up. Then write your answer next to the given answer choices. Work the answers using the numbers in your chart until one works out to match your original answer. In doing this, avoid the numbers 1 and 2 and using the same numbers twice. There may appear to be two or more right answers if you do.
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