Algebraic Properties Lesson

I'm sorry to realize that I haven't blogged in 6 weeks.  It's been busy and I guess nothing's seemed fabulous.  (Yes, we should blog the mundane, but there's no time for that at the moment.)

Today's Algebra lesson was actually one that I really liked, so I thought I would blog it so I could remember it in the future. 

It started Monday during a short class period.  I had my students (who had some prior experience with Associative, Commutative, and Distributive properties from 7th grade) arrange themselves in lines of about 4 students standing side by side.  I then asked them to form two groups without changing the order of the line to demonstrate Associative Property.  I asked them to reorder to show Commutative Property.  We did several examples, including some where I asked them to show Commutative Property within a single group.  They had fun and we got some wiggles out before an assembly.

This seems like a good time to mention that my school district has adopted EngageNY modules, so this lesson takes some inspiration and notation from Module 1, Lesson 6.  Students were off school yesterday (teacher inservice!) so I picked up today with a "flow diagram."  I gave the class an expression to write in the center of their papers.  I think I used 3x + 18y + 12z.  I asked for a property.  In both classes, they selected Distributive Property first.  I branched off with a double-sided arrow and labeled the arrow with "D."  I asked the class to generate an equivalent expression using Distributive Property.  The volunteer wrote it down.  We continued with new properties and new expressions, adding about 5 more to our papers.  Then, in table groups each team wrote three new expressions using a colored pencil to show what was different from the class diagram.  The groups then jigsawed, shared their expressions, and got feedback.  The entire thing took about 20 minutes (10 for whole-group, 5 for small group, and 5 for jigsaw).

Then, students completed a set of stations.  I took poster paper and wrote a series of 7 equivalent expressions on each.  Students had to determine the property used with their group.  They recorded their answers.  When they reached the last station and completed it, they used post-its to display their answers.  Then, we jigsawed again to have students put checks or Xs to show if they agreed or disagreed with the answers suggested.  I used the checks and Xs as a check for understanding and to see where I need to reinforce things.  I found the difference between Distributive Property and Associative Property to be our largest area of confusion.  (I did 5 stations for 3-4 minutes each, 2 minutes to Post-it answers, and 3 minutes to check those answers for 25 minutes in stations.  My summary based on their feedback on Post-its took another 5-10). 

Why I liked this lesson: students spent lots of time debating and discussing.  The difficulty level of the problems was about right for my students, as they were able to be successful about 80% of the time based on my observations. 

For homework, I gave students a new expression and asked them to make 5 equivalencies.   I hope to be able to share some of these in the future! 

How do you make properties a bit more challenging than 3•5 = 5•3?

Mathematically yours,
Miss B