Multi-Step Equations with No Solution and Infinite Solutions

I’ll bet if we took a survey of the topics math teachers enjoy teaching most, solving equations would top the list. 

Actually, let’s find out how YOU feel about this.  Participate in the survey here: Create your survey with SurveyMonkey  

When I introduce equations with no solution and infinite solutions, I use these notes.  I’ve found them to be a quick way for students to compare these equations to those with one solution.  The interactive nature of the foldable notes helps to keep students focused.  Incorporating the checking of answers into the notes helps to make the rather abstract concept more concrete.  Students especially need to test multiple solutions to the infinite solution equation to help them grasp the idea, so I've included an area for that.

What next? ... Students need practice! 

Many textbooks and worksheets include very few problems with no solution or infinite solutions.  My belief is that students need a problem set that makes them think carefully about each problem.  If there is a good mix of equations having one solution, no solution, and infinite solutions, they must analyze each problem carefully.  I’ve found that textbook materials may contain only two or three special case equations in a problem set of 20-30 questions.  I want my students to have a problem set in which there are frequent examples of no solution and infinite solution.  That way, they must pause often to carefully analyze their solutions.  This increases the chances that they will actually remember what I am teaching them!  To provide more targeted practice, I created my own materials to use to teach this topic.  If you are interested, you can find them here along with the notes.

Typically, it doesn’t take very long for students to catch on to solving these sorts of equations.  However, it is very important that your students continue to see examples of no solution and infinite solution equations regularly throughout the year.  Bell work is an easy way to provide that review.