Monday, July 02, 2007

Algebra Scale Balance

In learning algebraic manipulation of linear equations, it is important for students to try and grasp the basic concepts of balancing the equation on both sides. For instance, in the equation 2x+1=7. Students must understand why "bringing over the 1" to the other side turns it into -1. ie 2x=7-1. Students need to understand there is balancing process here so terms like "bringing over" and "cross-multiplying" should not be used first until they get the concept right. There are 4 basic balancing methods for an algebraic equation. They are as follows:

  1. Subtracting both sides by the same number, Eg: 2x+1-1=7-1
  2. Adding both sides by the same number, Eg: 2x+1+(-1)=7+(-1)
  3. Multiplying both sides by the same number
  4. Dividing both sides by the same number
I would recommend not lumping 1 and 2 as some students may not see when and what to add or subtract on both sides. An example should be given for each case.

Ample practice should be given for students to try out manipulating algebraic equations, with a mixed variety and ultimately questions that require all 4 techniques to be used successively. For 4, it should be emphasized early that dividing both sides can only be done for non-zero numbers. This can be done by the fallacy given in previous post.

A very good manipulative for this topic is the algebraic balance. A virtual one can be found here, by Utah State University.

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