The Fantastic Five-Step Problem Solving Process
Word problems can often intimidate students because there may be a lot of information. The important facts are embedded in the text; and, unlike a regular equation, it is not always clear exactly what you are supposed to do. No matter what type of problem students encounter, there are five steps that will help students organize their interpretation and thinking about the problem. This is the key to good problem solving-organizing for action.
Step 1: What are the FACTS? Write them down or draw a picture.
Step 2: What is the QUESTION? What are you trying to find out?
Step 3: What can you ELIMINATE? Is there any information that is not important? Often there is extra information that can cause us to get confused or overwhelmed. Set that aside and again focus on what is needed to solve the problem.
Step 4: Choose a STRATEGY and SOLVE. There are 7 “Super Strategies” to help you solve the problem. (See below.) Choose one and solve the problem.
Step 5: Does the answer MAKE SENSE? Once you come up with an answer, check to see if it makes sense. Is it a reasonable answer? If not, then go back to step 4 and choose a different strategy. Don’t forget to write the label with the answer. If the answer is 72, then it’s 72 of what units? 72 cats? 72 balloons?
The Super Seven Problem Solving Strategies
While children should be encouraged to use the Five-Step approach to any problem, Step 4 includes a wide range of choices. Some commonly helpful strategies are below. Students should have experience with all of the strategies. The more practice they have, the easier it will be for them to choose a strategy that fits the problem and helps deliver an answer.
#1 Guess and Check: If you’re not sure what to do, begin with a reasonable guess to get you started. Look for key words and phrases, like “altogether” or “more than”, that may help you choose an operation. Once a first attempt answer is arrived at, consider whether the answer is reasonable, too high, or too low. This is the “Check” part. After considering the answer, decide if you need to revise and how. Would a higher answer make sense? A lower answer? Continue until you have a reasonable answer.
#2 Draw a Picture: Drawing a picture can sometimes help make the problem clearer. You can then arrange and manipulate the facts more easily and discover relationships more quickly. This is not artwork! Leave out unnecessary details or coloring. Use simple symbols to represent elements of a word problem, such as stick figures for people and triangles for trees.
#3 Make an Organized List: This strategy helps us identify and organize what we know. Compiling a list can help to see all the possibilities. It also helps reveal patterns that may exist.
#4 Look for a Pattern: Our number system is organized as a set of patterns that repeat and grow. Number lines, hundred charts, and calculators can be useful tools in helping students recognize a pattern in a problem.
#5 Make a Table or Chart: Tables and Charts are a great way to organize groups of data. It helps make patterns and functions more apparent. As kids use tables, we caution them as to how far to extend the data. You only want to go as far as necessary. Going further will cause extra work and create more information than is needed.
#6 Use Logical Reasoning: Logical reasoning is an approach that organizes and analyzes information so that it ultimately leads to a conclusion. Ideas that help students think logically include using lists, pictures, tables, charts, and looking for patterns. A logic matrix is also a helpful tool in organizing information in a logical way and seeing possibilities.
A logic matrix can help organize facts and use the process of elimination to arrive at an answer. For example, “ Jim lives in a blue house and drinks milk. Bert does not live in a green house. The person in a white house drinks juice. Joan drinks water. Were does Bert live?
| Person | House | Drink |
| Burt | ? | Juice |
| Joan | Green | Water |
| Jim | Blue | Milk |
#7 Working Backward: When you know how a problem ends up, but don’t know how it started, this is a great strategy to use. For example, “I went to the store and bought a hammer for $2.50. The clerk gave me $2.50 in change. How much money did I give the clerk to begin with? We could think:
I gave the clerk X. Since I got back $2.50 and the hammer costs $2.50, then $2.50 + $2.50 = X. X must = $5.00
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