Expressions, Equations & Inequalities

This is a really starting unit in Algebra One and often is what people think of when they think of Algebra. An internet search of “what is algebra” gave this as a response

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

This is pretty fundamental to the study of Algebra – it gives us a symbolic way to work with numbers and to generalize. So this unit gets us started in how to do that. Students really need to understand what they are doing and not just memorize.

Sadly the symbolic nature of Algebra gets a bad rep and people can get very frustrated and joke about their frustration.

We are just going to move on from this and try to shed some light on how to teach this unit using ISNs.

Just to give some context, where is what we are working with from our curriculum:

Essential Questions:

·         How does one create an equation/inequality using symbolic algebra, specifically how are operations used in building? 

·         How are inverse operations used to deconstruct an equation/inequality by creating a series of equivalent equations/inequalities ultimately resulting in a solution?

·         How and in what ways do you use symbolic algebra to represent and explain mathematical relationships and real world situations? 

·         What is a solution set for a linear equation or linear inequality?

·         How do we utilize technology to justify a solution method?

Corresponding Big Ideas:

·        Obtaining the solution to an equation or inequality, no matter how complex, always involves the process of undoing the operations.

This is a long unit, so here is my TOC listing - I'm going to have to break down my foldables into a few blog posts (thus this is part 1). just remember my handwriting disclaimer...

I started the unit with the students being given a variety of mathematical items - numerical expressions, algebraic expressions, equations and inequalities. Check out my sorting cards HERE.  They had to sort them into 4 groups any way they saw fit (they weren't given those category names) - then we discussed and played around with what they came up with (at one point I gave them the category names and asked them to adjust their sorting into those groups). This was to warm them up to the vocabulary of these symbolic representations. From their we did little frayer diagrams of each in our notebooks:

For a structured right hand side sample, check this out. 

equation solving "practice" on the right side (my students should know these without instruction from last year's class). You can also find more equation solving ISN samples here. 

I added the "backwards inequalities" from the foldables I found on line. Here is what I started with...

and corresponding practice on the right hand side opposite each frayer diagram. Some of the "practice" was somewhat informational as you can see (I included those that were).  What's a frayer diagram? Learn more HERE.