What's the difference between word problems and stumpers or problem solving?
This is a question that I often get from parents. Most often, problem solving and stumper like problems are confused with word problems. However, there is a difference and sometimes the two will overlap. A word problem often involves the computational strategy or strategies that have been taught. Word problems determine if the child can apply the computational strategy. At a very young age the word problems will focus on addition, subtraction, multiplication and division. A basic word problem would be something like: A man had a bouquet of balloons. The wind blew away 4 and now he only has 6 left. How many balloons did the man have before the wind came along.
What I like about the baloon word problem is that the unknown value is at the beginning of the problem. It requires a tad more thinking than if the problem was stated: A man had 10 balloons, the wind blew away 4, how many does he have left?
Teachers and parents tend to turn computation into word problems where the unknown is at the end. However, students need practice with word problems when the unknown is at the beginning or at the middle. Word problems at a higher level may be based on Pythagorean's Theorem or perimeter, area, volume. Typically, a word problem requires the student to apply the knowledge of the concept to an authentic situation. There is usually one way to do the problem and a right answer.
Problem solving differs in that there may be 2 or 3 steps to solve the problem and there also may be a variety of approaches that can be done. The math stumpers found here tend to be problem solving questions. They are somewhat open ended and there are a few different strategies that students can use to solve the problem.
When you take the problem, if everyone in the room shook hands with everyone else, how many handshakes would there be? Students can act out the problem to solve it, use a diagram or a T-Chart to solve it, or some may even just come up with the formula or algorithm to solve the problem. There is one right answer but a variety of ways that the problem can be solved. Hence, this type of problem is called problem solving vs a word problem. Word problems and problem solving questions tend to find their way into standardized tests on a regular basis.