Common Core Algebra Planning (Part 2)

Wow!

It's truly amazing that we have the technology to connect with so many people so very quickly!  Thank you for visiting my blog, and for the positive feedback from all of my fellow teachers and professionals in Twitter and the MTBoS!  As promised, I will continue my musings of how I envision the first couple weeks of school.

Outline

Distributive Property

I plan on continuing my work with the real numbers as Topic B outlines, but rather than the exact lessons I hope to talk about the distributive property first.  What I love about this approach is that it ties in a lot of what the elementary grades are currently doing with the properties.  Essentially, it is "filling in the gaps" of my students, since the work we do in Algebra assumes this understanding, but based on where my students are in the education system, they have not had the instruction.  I absolutely LOVE the pictorial references of distributive property to area.  Using the below picture, instead of having my little arcs connecting the 4 to each of the addends to show distribution, it is easy for any student to grasp since they can count the squares and relate it to the expression.  The picture below that, where I show distributive property with subtraction, shows the natural progression of the area model, which gets more abstract with area.

Math Progressions

This brings up a good point about the mathematical progressions.  If you have not looked at these, and you teach Common Core math, I highly suggest that you check it out.  Though the reading is at times dense, it completely puts things in perspective when it comes to the progression of mathematics with coherence across grade levels.  I am a secondary teacher and I thought I knew elementary math (what they teach in elementary school).  I was wrong.  Digging into common core math at the most basic level makes things so much easier for me to tackle the Algebra curriculum, which looks so different than the Algebra we are used to.  One suggestion: read these progressions a little at a time before bed; if you're having trouble sleeping, it'll put you right to sleep!

Commutative Property

I love the idea of having the students interact with the operations here rather than telling them there is a commutative property of addition and one for multiplication.  Have them explore all four since we have already dug into the operations earlier in the unit.  Most likely they will recognize that they have seen the properties before, and that is okay.  I doubt they have done much more than mention the properties and not use them again except perhaps on a quiz or in passing.  I love having cutouts representing length for addition and area for multiplication.  This way they can see the commutativity!

Associative Property

I like the explanation I use in the picture for associative property.  When I was learning these properties in school, I never really saw a need to mention associative since it was similar to commutative in my opinion.  I think that having visuals really made the distinction for me, and perhaps for my students it will as welll.  I plan on making the analogy of driving down the street: the number of houses is the same, but depending on which direction you are traveling, the grouping of houses is perhaps different.  In the picture above, it would be easy to have concrete blocks for students to build numerical expressions.  Again, going back to the concrete-->pictorial-->abstract flow of mathematical progression.

In looking at module 1, there is a flowchart in Lesson 7 of the properties that kind of confused me.  I tried to make it my own, by adding color to distinguish the variables.  However, it was still very cumbersome.  At first I thought I liked it, but I am rethinking that now.  Anyone who has taught this lesson: what did you do to tie in the properties?  Did you teach lesson 7?  How did you adapt it?

What other lessons do people have for the properties that really gets students engaged and thinking about structure?