Tools for Simplifying and Solving Equations

We don't just want our students to solve equations, we want them to understand the processes used in solving and justify their equation solving steps. This can be tricky for kids because it's pretty abstract to consider all this structural stuff that drives algebra. But doing this creates a really great depth of understanding. So it's a challenge to teach but if you can get it through to the kids, wow - it's great to know the "whys" of what we are doing.

Each of these headings will link to a foldable document if it's available.

We start with the basic properties of equality:

Then show how it is used in solving an equation:

But then there are additional tools for equation solving:

And more properties for simplifying 

(this one I'm tweaking for this coming school year - will add zero product property and put the number examples on the right hand page with only word descriptions in the foldable? ).

then we practice using them with problems where they justify each step in the solving process. Here are a number of worksheets. ( 1  2  3  4  5  6  ) The general format looks like this:

And then in action with multi-step equation solving (need to have them do this with justify steps on each line this coming school year).

That colorful one above is fun for the students but was a real pain to assemble! Found this foldable concept that I will probably use instead this coming school year. It's got more space so I can have them fill in reasons for justifying perhaps - will see what I come up with when the time comes!