Strategies to Simplify Word Problems Study Guide
Introductino to Strategies to Simplify Word Problems
Leaders are problem solvers by talent and temperament, and by choice.
—HARLAN CLEVELAND (1918–2008)
You have tackled some challenging problems so far, each one made easier by using various strategies. In this lesson, the strategies of solving a simpler problem and guess and check will be two more to add to your list. Each strategy will be explained and examples given to help guide you. Remember, there are many ways to solve most problems. Having a variety of strategies to choose from can only help you on this road to word-problem solving success!
Solving a Simpler Problem
With some word problems, the numbers used within the problem may be difficult to use. They may be too large for one of the previously mentioned strategies. Or, the numbers given in the question may be complicated, and should be simplified to make the question easier to handle. One way to manage this situation is to make the problem easier to solve by using simpler values than the ones given. Take, for example, the question that follows.
In a certain school district, there are 294 students who are bused to school each day. If each bus can fit 52 students, how many buses are needed?
Read and understand the question. This question is looking for the number of buses needed for a certain number of students.
Make a plan. Divide the total number of students by the number of students that can fit on a bus. Because the numbers are not easily divided, make the numbers simpler by rounding. Then, a reasonable solution can be found much more easily.
Carry out the plan. Instead of using 294 students, use a value of 300. Since each bus can fit 52 students, round this value to 50. Divide 300 by 50 to get 6 buses.
Check your answer. Check the solution by multiplying 6 buses by 50, which is 300. Since there are only 294 students who need to ride the bus and each bus can actually fit 52 students, there will be extra seats left. The solution is checking.
Be careful when using rounding to make simpler, more compatible numbers. As in the question, the number of students was rounded up slightly and the number of students who would fit on each bus was rounded down. This way, the number of buses needed was not underestimated. Always check a solution to make sure it is reasonable.
Here is another example of making a problem simpler. In the question that follows, you are asked to find the sum of many numbers. Notice how finding the sum of a few numbers can lead to an easier way to find a solution.
What is the sum of the first 19 natural numbers?
Read and understand the question. This question is asking for the total when the first 19 whole numbers beginning with 1 are added together.
Make a plan. This problem seems difficult when you are trying to add all 19 values. Begin by making the problem simpler by adding just a few numbers, and then look for a pattern.
Carry out the plan. You need to add the natural numbers from 1 to 19. This would appear as 1 + 2 + 3 + 4 + … + 18 + 19. However, instead of adding the numbers in order, begin by adding the first and last numbers: 1 + 19 = 20. Continue this pattern using the next numbers: 2 + 18 = 20, 3 + 17 = 20, 4 + 16 = 20, and so on until you reach 9 + 11 = 20. The value 10 in the list will not have a paired value. Therefore, there are nine sums of 20, plus the number 10: 9 × 20 + 10 = 180 + 10 = 190. The sum is 190.
Check your work. One way to check your work is to add the numbers in the list by hand or with a calculator. Each of these methods results in a sum of 190. The solution is checking.
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