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Inequality Time Again

My colleagues and I choose to to teach inequalities (simple, compound, absolute value, linear, systems and quadratic) all in one clump after solving quadratic equations. March 20th, I got started with solving simple inequalities and unions and intersections. Since solving inequalities always goes so quickly as by March everyone is comfortable with solving, I like launching into unions and intersections on the same day.
As is most of what I teach, the party analogy for teaching unions and intersections was borrowed from a colleague. I tell them this story: I want to throw a party that includes the union of all kids who do ________ with all kids who went to ___________ elementary school. I change the blanks dependent upon who is in the room. Then I change it to the intersection, making my party a lot smaller, meaning a lot fewer sodas to purchase. 

Big Party vs Little Party
Once we get into trickier problems, like the union of x's greater than -1 with x's greater than 5, having this analogy to draw upon is super helpful.

The week of March 23 was spent doing more with compound inequalities, formative assessments, correcting quadratics Test, absolute value equations and closed with a favorite - white board stamp game. 

On a whim though last Sunday (3/22... sheesh I am behind on this blog), I threw out a quick tweet to the #mtbos asking if there is a better way to teach absolute value inequalities. Before sending said tweet, I had been sure that my question would be a dead end. How could there be any other way, other than telling them to set it equal to the number and then the opposite of the number?

I am always over-confident/wrong, pleasantly surprised bow how awesome the #mtbos is. Almost immediately, @samjshah, @danburf, and several others chimed in with ideas like this and this and this and this. Love it!

I went with @fawnpnguyen's script because if there is anything I have learned since participating in the #Mtbos, that would to always try what Fawn says. 

Once again, I was not disappointed. This approach led to excellent conversation and an overall engaging class. 

How does it match up to my (ever evolving) inventory of what makes a good an engaging lesson:
  • fun and interesting
  • it's a game with prizes
  • problem based
  • inquiry based
  • connected to an application
  • doesn't water down the mathematics or resort to tricks
  • gets kids collaborating,talking, teaching, writing, using technology in a meaningful way
Definitely meets at least two of the requirements. 


  1. >How could there be any other way, other than telling them to set it equal to the number and then the opposite of the number?

    Those methods may not work for an absolute value inequality like this:

    1. Oh snap! Boundary Algorithm FTW. I am hopeful that since I started with the "distance" model with absolute value equations that boundary algorithm for absolute value inequalities will make more sense. Thank you for reading!


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