How to teach the properties of equality through problem solving

I like to teach mathematical concepts via problem solving. It right away engages students mind. It creates a need for learning a more systematic way of doing things and hence a reason for learning the concept. It provides a context for making connections. Most important of all, it gives students opportunity to learn before they are taught.

One of the ways of creating a problem solving task for this kind of lesson is to start by giving the solution.  For example, a standard textbook task is to solve for x in an equation.  Why not do it the other way and ask students to find the equation given the solution?  I found this kind of task a very powerful context for introducing a concept.

Here is my favorite problem for introducing the properties of equality:

Write three equations in x with solution x = 5.

Students will generate equations by trial and adjust. That is, they think of an equation then check if it gives x = 5 by substituting the value of x to the equation.  This is something very tedious. Read more of this post

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