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Five Step Plan For Solving Math Word Problems
One of the most dreaded tasks for math students is solving word problems. If a student ever misses a question on an exam, you can be sure it would 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.
Regardless of 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 they graded homework or marked an exam, I would assign five points for a word problem. If students just give me the correct answer without following the Five Step Plan, they would only get one point for their answer. Students who followed the Five-Step Plan could get up to four out of five points, even if they got the answer wrong on the problem.
What is this plan for solving math word problems? Here is a chart that I would put on the board when teaching this strategy to my students.
a)? b) X = c) Equation d) Find x. e) Answer part a).
Part a): Students must write what they ask you to find in the word problem. This can usually be found in the sentence containing the question mark. If the question was phrased as a command, for example, “Find the number.” This would become the question to write in part a).
Part b): In part b) students had to list what information they were given and assign a variable to the unknown items. Included in this section would be 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 hardest part of this exercise, but with practice, students got better at identifying the equation to use. It often only required the student to translate an English sentence into a mathematical sentence. The verb in an English sentence is equivalent to the equal sign in an equation. The left side of the equation comes from all the words in the sentence that come before the verb. I would instruct students to write this information 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 side of the equation.
Part d): Students would then use the equation they constructed in part c) and solve the equation for x. This part of the plan requires students to know how to solve different types of equations.
Part e): Using the value of x they found in part d), students used this information to answer the question 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 xi meant 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 that uses 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 the 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 given and what they need to find in order to answer a word problem 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.
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