Methods to Teach Multi-Step Linear Equations

Linear equations are the most basic form of variable equation. Linear equations present students with variables and numbers on either side of an equal sign. Linear equations can use addition, subtraction, multiplication and division within the problem. Additionally, multi-step linear equations will typically involve fractions to add an extra challenge to the problem. The equations may require several types of simplification to solve.
  1. Box Method

    • When first introducing multi-step linear equations, a student may have a hard time wrapping his mind around the idea of letters instead of numbers. In his mind, the letter may be a form of code that requires a special form of cracking when, in actuality, the number is simply a space filler. Help this type of student solve his problems by placing an empty box in place of the "x." So, for example, the problem may be x - 2/3 = 6. Change the "x" to a box and see if the student is then able to work through the problem.

    Overhead Assistance

    • Repetition is the key when learning new mathematical processes. Take the intimidation out of math for your students by working out a generous amount of math problems together on an overhead projector. Go over each problem slowly and never skip any steps. For even more reinforcement, make each student write down the steps in her notes.

    Party Method

    • Another common hurdle for many students is the use of fractions in linear equations. Help the student work through the fractions with the "party" method of teaching. To explain the party method tell the class, "The numbers are at a party and the denominator of the fraction wants to dance with all of the other numbers. To do this, the denominator must multiply each number." From the previous example, the denominator is 3, so this would turn the problem into 3x - 2 = 18. Then the problem is solved using the standard steps.

    Water and Oil

    • Another challenge in multi-step equations is when the problem presents the same variable multiple times in the problem. The simplest trick for helping students understand the rule of combining like terms is the water and oil trick. Tell the students that anything with a variable is like oil; it can be combined with other oil. Anything without a variable is like water; it can also be combined with other water drops but not oil. So if the students are evaluating 3x - 7 + 6x = 2 + 5, the students simply combine the x's and the numbers to turn the problem into 9x - 7=7.

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