A few years ago, I began to teach a noncredit science class at a local community college. One of the lessons was how to solve word problems. This is what the material gave us to teach the students.
1.Read questions carefully
2.Define terms, think about relationships
3.Identify key or clue words
4.Identify the problem to be answered
5.Analyze the problem
6.Plan a solution
7.Answer the question
8.Evaluate the solution
Over time I began to realize that this was too much info to give, so I began looking for better ways to explain the process. I finally stumbled on an acronym that was simple and yet explain the steps in a concise way.
The acronym was WORD which stood for:
W- What does the question give you and does it want for answer (covers points 1, 3, 4)
O- Organize the information. Most science questions have a distinct order to them that can either be organized or diagrammed to assist in ‘seeing the problem’...
When working with my math students, I find that they get intimidated very quickly by lots of words or lots of numbers. Also if it has a radical, they shut down very quickly. I try to help them by having them write down everything they already know about
the problem. When they realize how much information they already have, the problems don't seem as daunting to them. They can more easily start to plug in the numbers in the problem and are able to find the answers. Also, we do several of the same type of
problem, so they start to feel more comfortable with it. I will give them worked examples and extra practice problems to take home with them for independent working if they want more practice.
0. Many STEM problems involve manipulation of a set of constrained equations. Identify the set for the problem you are solving.
1. The numbers don't matter; so, ... plan on always deriving the formula or mathematical expression for your answer, first.
2. Never operate on or write dimensionless numbers in a derivation or problem solution.
3. VARIABLE = Quantity x [Units]. This is always true, even if its not presented this way in introductory courses.
4. Only variables with the same units can be added (or subtracted).
5. The result of multiplying two variables is has units that are the product of the multiplier and multiplicand:
VARIABLE_1 x VARIABLE_2 = Quantity_1 x Quantity_2 x [Units_1 x Units_2] .
Sometimes, units in the numerator(denominator) of one variable will cancel out units in the denominator(numerator) of the other.
6. For details, Google "Dimensional Analysis". That's what I'm talking about!
7. Corrects answers come from derivation...