## Reflection: Developing a Conceptual Understanding Rearranging and Graphing Quadratics - Section 4: Creating Equations from Graphs and Matching Graphs

When reflecting on this section, I kept coming back to how technology helped support my efforts to develop a deeper conceptual understanding and connection between various representations of functions. As an overview, students worked on creating a function to match each of the graphs in the Creating equations matching graphs assignment.

The first graph is relatively straight forward, while the second example switches the concavity - students tend to struggle with the second example. Teachers can give reminders about concavity and ask guiding questions to help students make the connection that the value of a must be negative to create the correct graph.

Example 3 has roots that are not whole numbers - I put this problem in purposively so that students understand roots are not always integers and to continue to push their thinking to interpret graphs and create equation using the factored form of quadratic functions. For extra credit, I ask students to not only provide the factored form, but to provide the standard form of this quadratic - this is a great way to assess how well students can apply their knowledge of different forms of quadratics and is a good review of distributing polynomials.

I typically assign the fourth graph as an exit ticket and as a way to provide an easier problem for students who struggle on the more difficult problems. Whenever possible, I try to create problem sets/assignments so that the problems do not follow a linear progression of easy to hard. I want students to struggle with problems, but for students who cannot do the hardest problems, I want them to be able to move on and build confidence with some easier problems.

Developing a Conceptual Understanding: Making Connections Between Different Representations of Functions Using Technology

Unit 7: Interpret and Build Quadratic Functions and Equations
Lesson 4 of 13

## Big Idea: This jigsaw lessons lets students dive deep into one connection between quadratic equations and graphs, and then learn from each other in mixed groups!

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Standards:
Subject(s):
Math, Algebra, Quadratic Equations, quadratic models, modeling, completing the square, Geometry, Common Core, master teacher project, factoring, Jigsaw, HSA, HSF, 9th grade
90 minutes

### Jason Colombino

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