One of the most dreaded tasks students have in math is solving word problems. If a student ever leaves out a question on a test, he can be sure it will be a word problem. Part of the reason for this is that the student often has difficulty deciding what steps to take to analyze and understand what the problem is about.
No matter the math level, I have found the following method to be very successful in solving word problems. I call it the Five Step Plan. As a high school math teacher, I insisted that my students use this five-step plan to solve word problems. When grading your homework or correcting a test, you would assign five points for a word problem. If students gave me the correct answer without following the Five Step Plan, they would only receive one point for their answer. Students who followed the Five Step Plan could earn up to four points out of five, even if they gave the wrong answer to the problem.
What is this plan for solving math problems? Here is a chart that I would put on the board when teaching this strategy to my students.
five step plan
TO)? b) X = c) Equation d) Find x. e) Answer part a).
Part a): Students have to write what they ask you to find in the word problem. This can usually be found in the sentence that contains the question mark. If the question was posed as a command, for example, “Find the number.” That would be the question to write in part a).
Part b): In part b) the students had to list what information they were given and assign a variable to the unknown items. This section would contain a list of elements and one of them would be equal to x.
Part c): Part c) is the algebraic equation needed to solve for x. Writing the correct equation was often the most difficult part of this exercise, but with practice, students became better at identifying the equation to use. Often it only required the student to translate an English sentence into a mathematical sentence. The verb in an English sentence is equivalent to the equals sign in an equation. The left side of the equation comes from all the words in the sentence that appear before the verb. I would instruct students to write that information first and then put the equals sign. All the words in the sentence after the verb were transcribed into an algebraic expression and placed on the right hand side of the equation.
Part d): Students would then use the equation they built in part c) and solve the equation for x. This part of the plan requires students to know how to solve various types of equations.
Part e): Using the value of x they found in part d), the students then used that information to answer the question asked in part a). Often finding the value of x is not the answer to the word problem. Students should check with part b) to see what the x represented and then use it to answer the question. Students had to write part e) in a complete sentence.
Here is an example of a pre-algebra level word problem using the Five Step Plan.
Example: A number multiplied by six is four more than four times the number. Find the number.
Answer: a) Find the number. b) Let x = the number c) 6x = 4x + 4 d) 2x = 4
x = 2 e) The number is 2.
Here is another example.
The sum of three consecutive even numbers is 36. What is the second number?
Answer: a) What is the second consecutive even number? b) 1st number = x
2nd number = x + 2
3rd number = x + 4 c) x + x + 2 + x + 4 = 36 d) 3x + 6 = 36
3x = 30
x = 10 e) The second number is 12.
Regardless of math level—pre-algebra, algebra I, algebra II, precalculus, calculus, trigonometry, or statistics—using the five-step plan helps students discover exactly what information is being provided and what they need to find in order to answer a problem. verbal. Often using a diagram can help identify the variables needed in part b). Once part b) is on paper, writing the equation becomes much easier and students can use their equation solving skills to find the answer to the word problem.
