Math can be difficult to visualize and can seem pointless without context. Pictures are a great way to give students a frame of reference for visualizing a scenario or give them a real world application. Take for example this picture of the Golden Gate bridge in San Francisco, CA. A teacher could use this picture to introduce a section of applications of quadratics in story problems. They could use the Golden Gate Bridge to introduce or remind students what a suspension bridge looks like. The teacher would then go on to ask the class how math is used to create and design these bridges. Regardless of the suggestions, the teacher should hint at the idea of how it is necessary to know the heights of the suspension cables if you are cutting the cables to length. Student would then work to develop a quadratic function that determines the height of the suspension cables based on the distance away from the center of the bridge. In order to do a story type problem, there would need to be an additional picture with number. The problem could be written as follows:

 

“The height of the suspension cables from the deck of the bridge form a parabola, as you can see in the picture. When I stand in the middle of the bridge, the suspension cables are 15 ft tall. If I walk 30 ft in either direction they are 35 ft tall. How tall are the suspensions cables if I walk 400 ft? How far would I need to walk to find cables that are 100 ft tall? Write a quadratic function to model the suspension cables on this bridge.”

This question targets the following Common Core State Standard:

CCSS.MATH.CONTENT.HSA.CED.A.1
“Create equations and inequalities in one variable and use them to solve problems.Include equations arising from linear and quadratic functions, and simple rational and exponential functions.”

This type of lesson would engage a variety of students. The lower achieving student and students who are most likely to be going into trades instead of looking at a four year degree would be interested in construction perspective. They can see how a person who is having to install the bridge and assemble or manufacture pieces needs math to do a good job. These students can develop a appreciation for math that is based on necessity for the work place. The higher achieving students and those students who are looking at four year degrees would be interested in the less hands on aspects. The students who might want to be architects, engineers, or analysts can see the applications of math in the planning and supervision of the project.

Additionally, all students have family or know someone who works in a job in either construction, engineering, or another job related to building. In this way the teacher will be using the community and personal assets of the students to engage students and make math relevant.