My Little Transversal: A multi-day project lesson

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SWBAT apply their knowledge of angles by creating transversal problems using photos they take in or out of school.

Big Idea

Looking for a direct or an abstract connection to a concept can bring math content to life.

Introducing the Project

10 minutes

I introduce the project at the end of a class session. I show the class a collection of photos of transversals and parallel lines that I have found and illustrated with geometric figures. Then, I encourage students to take a few photos of their own over the next couple of days. I ask students to email their photos to me. 

I typically give the class about a week to take photos. Then, the My Little Transversal Project usually takes about two class sessions. The goal is to get them excited about the notion of using photography in math class. I love this project because students are always shocked at how easy it is to find parallel lines and transversals. They see them every day, but are not necessarily aware of it. Once they start to look for them, they find them everywhere. 


Starting the Project

60 minutes

Once students have their photos (each member of the group has taken several photos and emailed them to me and their group members), we talk about the details of the project. I show them this Photoshoot Copy PowerPoint to review all the components of the project.

  1. The first step is to use google docs or powerpoint or some other program to edit the photos. The students begin by adding lines and text boxes over their photos to create a geometry problem for solving. 
  2. The second step is to make a reasonable estimate of the angle they want to focus on (are they acute, obtuse, right?)
  3. The third step is to create algebraic expressions for each angle in the photo.
  4. The fourth step is to solve the expression algebraically and confirm the correct angle values. 

I also introduce the rubric to the students: transversal project rubric.pptx. The rubric helps students keep track of all the expectations of the project. More importantly, it gives the students suggestions to improve their work. 

Today, each student will progress through all four steps of the project. Each will produce a draft version of their final project. The algebraic reasoning is challenging, but the students have fun working the "back end" of an equation. They learn so much by controlling the value of x and then decomposing the angle values to form an algebraic expression (all show in the powerpoint). 

Before concluding, I discuss the collaborative nature of the project. I make sure that students aren't simply "splitting" up the work, but working together on each section of the project. I try and avoid the situation where one student is working on photo editing and another is working on algebra. This might be fine in some circumstances, but I want both students to use this project as an opportunity for creativity, and, for mathematical review. I don't want a student spending all their time editing a photo and then missing the opportunity to practice the algebra used in the project. 

Bringing it all Together

60 minutes

For this part of the lesson, students finalize their project. I ask each group to assemble the original photo, the edited photo, the question and algebra work together in a google presentation, powerpoint or keynote presentation. However, if they want to write out their reasoning in a document and that is also accepted. Some students find it difficult to type out their reasoning in mathematics, so I am happy for them to practice in a format that makes it easiest for them to communicate effectively. 

The challenge of this revision lesson is for students to effectively write about "why" they know they are correct. In other words...

  • How do they know that their algebraic expressions will work?
  • How do they know that the angles should be equal or supplementary? 

To help them I put common math terms on the board and give them advice as I circulate. I ask them "why" whenever I can.  If students need more time to work on the project, they can bring the work home and submit the project the next day. 


Teaching Note: I will allow students to use google images if they are struggling with getting a suitable photo. I only ask that they correctly credit the source of the photo by telling the audience if the image is an original or photo from online.