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Math Tourist: Artistic Parabolas in Phoenix

**Essential Questions for students (objectives):** How is graphing parabolas related to ratios?

**Supplies:** video (length -0:52), note-maker

**CCSS:** A-SSE-3, A-CED-2,Math Modeling, Selecting Tools, **TEKS** Algebra II: 2A.2A and 2A.4

**Time needed:** 30 minutes

**Instructional Format:** Video, student problem-solving, group work

**Vocabulary for a Word Wall:** ratio, proportion, parabola, axis of symmetry

**Lesson Description:** There are many ways to use this video in your math class. First of all, I did film it for an advanced algebra class, but you can use it any time that you are working with graphing quadratic equations. The upshot of this lesson is the connection between ratios and quadratics as well as the effect of the multiplier when you write quadratic equations. A great classroom conversation would be for students to show the different methods they used to solve this problem as well as the tools they used to check the reasonableness of their answer. I have included a note-maker to assist students in problem-solving. You can use this video in a couple of ways:

1) You can show this video (0:52) at the beginning of a unit on graphing quadratics as a hook that will keep the students interested in learning about the skill. You can have them work on the problem at the end of daily lessons (or once a week) armed with new knowledge that they are exploring in class. Or you could revisit the video at the end of the unit as a formative check to see what the students have learned about applying graphing quadratics and whether they can apply that knowledge.

2) You could show this video as a warm-up activity after the students have learned how to graph quadratics. It is an unexpected way to show context to a quadratic equation. However, the strength really lies in the multiple ways that students can attack this problem and they define undefined variables.

**Extensions:** (These questions appear on the notemaker) How do artists use mathematics to create their artwork on a large scale?