## Reflection: Staircase of Complexity Standard Form to Vertex Form Day 1 of 2 - Section 2: Investigation

For my students, the progression of this lesson helps them to understand the "why" behind completing the square.  Even though they have previously multiplied binomials in another lesson, I like starting from this point so students get a quick review (or spiraling) of the content and then move on first to finding the "c" term when completing the square.  From here, students look at  and graph a quadratic that does factor to a perfect square, followed closely by one that is close, but isn't quite there.  This is the key moment for my students where they realize they can get the first two terms of the expression, but will need to do some adjusting to get to the third.  I like to let them tackle this on their own, or with limited help here, because I think it builds their conceptual understanding about the structure of the expression.  In the next lesson, we will look at some examples and examine more "step based" approaches to completing the square.

Staircase of Complexity: The Lesson Progression

# Standard Form to Vertex Form Day 1 of 2

Lesson 8 of 18

## Big Idea: Using a quadratic quilting analogy, students learn how to “undo” the process of changing a quadratic function from vertex form to standard form.

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60 minutes

### Amanda Hathaway

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