One of most dreaded assignments students have in math is solving word problems. If ever a student leaves out a question on an exam, you can be sure it would be a word problem. Part of the reason for this is the student often has difficulty in deciding what steps to take to analyze and understand what the problem is about.
No matter what level of math, I have found the following method to be very successful when solving word problems. I call it the Five Step Plan. As a teacher of high school math, I insisted my students use this Five Step Plan to solve word problems. When grading their homework or marking an exam paper, I would assign five marks for a word problem. If students just 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 get up to four points out of five, even if they got the wrong answer to the problem.
What is this plan for solving math word problems? Here is a chart I would put on the board when teaching this strategy to my students.
Five Step Plan
a)? b) X = c) Equation d) Find x. e) Answer part a).
Part a): The students have to write down what they are asking you to find in the word problem. Usually this could be found in the sentence containing the question mark. If the question was stated as a command, for example, 'Find the number.' That would become the question to be written in part a).
Part b): In part b) the students had to list what information they were given and assign a variable to the items that were unknown. Included in this section would be a list of items and one of them would be equal to x.
Part c): Part c) is the algebraic equation that is needed to solve for x. Writing the correct equation was often the hardest part of this exercise, but with practice, students became better at identifying the equation to be used. Often it only required the student to translate an English sentence into a math sentence. The verb in an English sentence is equivalent to the equal sign in an equation. The left hand side of the equation comes from all the words in the sentence that appear before the verb. I would instruct the students to write that information down first and then put the equal 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 that they constructed 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 for x that they found in part d), 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 need to check with part b) to see what the x stood for and then use it to answer the question. Students were required to write part e) in a full 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 even consecutive 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.
No matter what level of math - pre- algebra, algebra I, algebra II, pre-calculus, calculus, trigonometry, or statistics, using the Five Step Plan helps students to discover exactly what information is given and what they need to find in order to answer a word problem. Often using a diagram can help to identify the variables needed in part b). Once part b) is down on paper, then writing the equation becomes much easier and students can use their equation solving skills to find the answer to the word problem.Pre written Paper