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My Struggles With Completing the Square

This year I have been struggling with this quadratics unit. I feel as if there are no cohesive elements tying one concept from one to the other. The outline from this unit has been as follows:


11/63-11Graphing Quadratic Functions
11/73-11Graphing Quadratic Functions
11/83-21Solving Quadratic Equations by Graphing
11/93-41Solving Quadratic Equations by Factoring
11/121Review
11/131Quiz
11/143-31Complex Numbers
11/151Complex Numbers
11/161Complex Numbers
11/193-51Solving Quadratic Equations by Completing the Square
11/201Solving Quadratic Equations by Completing the Square
11/263-61The Quadratic Formula and the Discriminant
11/273-61The Quadratic Formula and the Discriminant

With 35 minute periods I have been trying to include different strategies, but overall I want them to know that by completing the square we are finding vertex form of a standard form of a parabola. 

I had students use a visual model of completing the square with algebra tiles from Bob Lochel's site: https://mathcoachblog.com/2017/06/05/area-models-and-completing-the-square/

They came away from this with the idea that they are actually trying to fill out a square. The next day I borrowed Julie Morgan's ideas and used this tweet.




I felt like it tied it more directly to properties of a parabola, but I feel like I need a better way to assess what they really know about parabolas.

I think I am going to use Nat Banting's post about writing everything they know about a specific parabola and print out each one for groups or partners to discuss.


I need to find a better way to teach this where I am developing conceptual and procedural understanding evenly. If you have any thoughts let me know.
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