Seeing Math Everywhere We Look

Exploring Quadratics in our World

GOALS:
1. Move from the “When am I ever going to use this?” to “I see it being used” stage in math class – specifically for quadratic equations
2. Begin to relate the parts of the quadratic equation to its implementation in real world applications. For example, see that for a negative leading co-efficient the parabola is shaped like an “n” (McDonald’s arches) versus for those with a positive leading co-efficient the parabola open upwards like a “u” (as in the curve of a fishing net).

RATIONALE:
Many 13-14 year old 9th grade high school students have struggled with math and find it totally unrelated to anything that is or maybe meaningful to their lives. And yet, as they begin to pursue their high school career, they are expected to grasp more and more abstract concepts. Such is the case with quadratic equations. Understanding the quadratic formula is now a requirement for all 13-14 year old 9th grade high school students and is a baseline for graduation as a critical component of Integrated Math I (or Algebra I). With this lesson, I will create an interest in a variety of real world applications (construction, marketing, rocketry, sports, landscape design, etc.) by having students search for and photograph parabolas in the world around them.

RELATIONSHIP TO SCHOOL MISSION:
Oxford Preparatory School , http://www.oxfordprephs.org , is focused on developing the leaders of tomorrow and helping students in our poor, rural area gain a better understanding of how what they are doing in school relates to what they can aspire to do for the remainder of their lives. In our area only about 17% of citizens have a college degree. We work to give our students insights into what is possible for them even though no one in their families has probably had the college or professional experience. We feel that a critical component of inspiring young people to look at their world in a different manner is through experiential learning. This lesson has students experience the use of the quadratic equation in many different aspects of the world around them.

COMMON CORE STANDARDS SUPPORTED:
High School: Functions » Linear, Quadratic, & Exponential Models* » Construct and compare linear, quadratic, and exponential models and solve problems. 1. Distinguish between situations that can be modeled with linear functions and with exponential functions.



LESSON:

INTRODUCTION:

1. Introduce pictures I have taken (eyebrow, water fountain, fishing net, McDonald’s arches) as examples of parabolas.
2. Overlay Cartesian plane plus associated quadratic equation over each picture.
3. Allow students to brainstorm WHO might use quadratic equations in the “real world”

MATH CONCEPTS - QUADRATIC EQUATIONS and the MEANING OF THEIR PARTS:
4. Using the Interactive Notebooks, students will document the meaning of the “size” of the leading co-efficient, the meaning of the sign of the leading co-efficient and discuss the relationship between the exponent and the symmetry of the resulting graph (parabola)
5. Explore a series of quadratics with changing numbers and signs using graphing calculators.
6. Demonstrate how to find the line of symmetry and the roots and then graph the related quadratic on a coordinate plane.

HOW TO USE YOUR CAMERA
7. Demonstrate camera basics - ON, OFF, flash, focus
8. Provide examples of bad and good pictures that can be "presentation ready"
9. Have each student select object in the room and capture its image
10. In pairs, students are to critique their partner's photograph.

ASSIGNMENT:
11. Using your digital camera, capture as many examples of a quadratic equation in the world around you.
12. Choose three of your pictures to have printed.
13. Using the Cartesian Plane overlays you have been provided, copy your parabola and identify the following:
a. Vertex (indicate whether the leading co-efficient is to be positive or negative)
b. Line of symmetry (include the equation for this line)
c. Roots (approximate as near to 0.1 as possible)
d. The domain and range for the graphed representation of your picture.
14. Choose one of your pictures for presentation.
a. Research and write a full paragraph on the job that would be related to it.
b. Incorporate your picture and the information you learn into a digital presentation using Powerpoint, Glogster or Prezi.
c. Be ready to provide a 2-5 minute overview of what you have learned about the use of quadratics within the context of the picture you captured.

EQUIPMENT NEEDED:
15. Class set of 20 Wi-Fi Digital Cameras
16. Transparency overlays for creating parabolas
17. Access to laptop and printer
18. Graphing Calculators