A problem asks for something. This request often follows words such as how, when, where, show and find. What is asked for is frequently followed by a question mark.
The response to the request is commonly in the problem statement.
The starting equation then will make a request.
The response to the request by the equation is commonly in the problem statement.
Variations of problems result from changing the wording. This does not change the problem solving process. It provides exercise in different algebraic and arithmetic operations. This is illustrated in the following three presentations.
In textbook problems, particularly in the so-called real-life problems, distractors (irrelevant information) may be present. By identifying what is asked for, the request, you can quickly scan the problem, looking for a specific response to the request. You know what you are looking for in the jumble of words and can skip over distractors.
Students will frequently skip problems like the following one simply because of the number of words and conditions involved. They do not know what to pay attention to. By identifying the request and looking for the response this mental block is removed.
A simple problem can be reworded in a great variety of ways without changing the structure of the solution. This is illustrated by the following problem in which a slightly more complex description of the change in the number of the item involved has been used.
Have your students construct single-variable problems. These will have the same solution path as that shown in these examples. Also examine textbooks and other instructional materials for problems which have the solution structure shown here.
The words change and the numbers change but the problem-solving process remains the same.
Help your students become aware of the fact that the problem-solving process shown here is logically no different from what they do many times every day. For example, use the following exercise: