When I say, “Show your work!” I mean…..
Mr. Rutledge’s Guide to Solving Math Problems
(And lots of other problems, too!)
1. Identify (or restate) the problem or question. You can’t start moving if you
don’t know where you’re headed. This is sometimes called the “Question
Presented.” Look for clues that may help you out, such as the units stated in the
question or in the space provided for an answer. (Life, unfortunately, doesn’t always
give hints like a test in school does…)
2. Organize the information you know. Pull facts and comparisons from the text
of a word problem or the description of a scenario. E.g., if the problem says, “Pat is
selling lemonade to raise money for a school trip. They’re charging $2.50 for a 12 oz.
glass.” You know that:



Two lines starting with the same words might suggest
One glass = (contains) 12 oz.
some sort of equivalency, but what do I know?
One glass = (sells for) $2.50
You might also note that Pat is raising funds with a goal, which hints
that there’s going to be a target number you need to find or match.
3. Identify what you think is missing. Are there facts or formulae that you believe
you’d need to solve the problem?
a. List them out in case you have an opportunity to ask for them or look them up.
b. If possible, make a best-guess estimate that will allow you to proceed with the
calculation, or create a variable for which you can plug in a value later when you
get the missing information.
c. If there are facts you need to assume, document them.
4. Illustrate the situation, if possible. Whether you draw a number line to
illustrate a mathematical process, draw a picture of a ladder against a wall, or show
a cannon firing a cannonball, illustrating the situation and attaching values to the
image (distances, heights, velocities, etc.) can help you visualize how numbers
relate, as well as which numbers may be missing.
5. Write out the equations you will need to solve. If some depend on the outcome
of others, list them in the order you will need to solve them.
6. Substitute the values you know for variables in your equations. This may
help you identify dependencies you missed in step 5.
7. Perform your calculations.
a. If they require multiple steps (e.g., if you have trigonometric ratios in the
formulae, or named constants such as π or e), work as far as you can before
substituting values for those functions, as it will make cancellation and
substitution of inverse functions easier along the way.
b. Carry fractions for as long as possible before computing decimal values (if at all),
as this will retain precision otherwise lost to rounding. Make sure you follow
instructions like “to the nearest one hundredth” or “in terms of π.”