# How Tall is the Flagpole- Using mirrors to find Proportions CAMT 2019

Introduction
We ask our students to imagine a huge variety of scenarios in math class:  trains approaching each other, roller coasters, boats sailing into the wind, buying ice cream, baking cakes, filling vases, sharing pizzas and on.  But our students come from a wide variety of backgrounds, with very different life experiences and may not be able to relate to these scenarios. With this lesson we have an opportunity to provide an activity that is physical, and interactive but also closely related to concepts and math we expect them to master and demonstrate on paper.

Ms. Mardi introduced the session sharing with the group the variety of courses she teaches at Austin High and the ways she has used this mirror activity in Algebra, Geometry, Pre-cal.

Today’s engagement/investigation:
Look into each other’s eyes (in the mirror on the floor)!

Paola Garcia explains to participants that they will be looking at each others eyes in the mirror on the floor. With her volunteer she demonstrates a couple of variations and encourages the group to try as well.

By looking at another person instead of an object we reinforce the concept of rays of light going from one person’s eyes to the mirror to the other person’s eyes.   By taking a picture with the iPad, and then using the Markup function, we can draw these rays, and show the similar triangles.

Partners move closer, farther, up and down.  Observations included:  if one partner moves away from the mirror, the other person has to step backwards.  If one partner stands on a chair, the other partner has to go closer to the mirror.

If iPads are available, students will be able to do the geometric analysis on their own pictures.  Even with the variety of set ups,  the two triangles will always be similar.  We can confirm this with a protractor.  Once these relationships and angles are found we can talk about using the AAA Theorem to prove the triangles are similar, and also use SOHCAHTOA to set up proportions.

Participants shared ideas like placing pictures of monuments like the Eiffel Tower on the classroom walls or creating a scavenger hunt, or asking students to position themselves so that they create similar triangles with a certain attributes like degree angle measure.  If you put a picture of eyes on the wall say 6 ft from the ground and a mirror 3 ft away, then a student could measure the height of his/her eyes by looking at the eyes in the mirror, then measuring and doubling his or her distance to the mirror.

Thanks for a great experience at CAMT.  Here’s the Handout based on Mardi’s lesson plans. page 1   and page 2

Presenters: Mardi Nott, Austin High Teacher, Paola Garcia UTeach Graduate, MathHappens Intern and new Teacher, Lauren Siegel, Director MathHappens.