Measuring with Mirrors

Present the warm-up problem (10 minutes).  The warm-up problem for this lesson (found in the slide show) asks students to write as many equations as they can about the angles in a diagram.  The warm-up problem helps them to understand one part of the proof they will write later.  Using student work or demonstration, extend the warm-up problem to show that the complements of congruent angles are themselves congruent.

The Lesson Opener follows our Team Warm-up routine.

Motivate the lesson (2 minutes).   Tell students that today they will apply what they have learned about similar triangles to measure the flag pole in front of the school (or a suitable substitute).  First, they will learn why the method works.  Tell students that up to now they have used flow charts to organize fairly simple proofs.  Today, they will see how a flow chart can be used to organize the argument behind a more complicated proof.  Challenge the students to do their best and complete the proof in the time limit, so that the class can go outside.

Review learning targets and the agenda for the lesson (2 minutes).   Display the agenda and learning goals for the lesson as you distribute materials for the activity.  Ask students to read them over and invite questions. 

Have students complete the cooperative learning activity (20 minutes).  Before class, print the Measuring with Mirrors Activity handout.  You may want to make a few extra copies, in order to allow students to start over with a fresh sheet if they go down the wrong path.  Distribute the half-sheets to the teams.
 
Tell the class that they will have to divide up the work amongst the members of the team in order to complete all the tasks in the time limit.  Every student must complete one part of the problem.  Tell students that you expect them to ask for or offer help, but no student may let another have his or her part of the problem. 

Have the students go outside to measure the flag pole (10-15 minutes).  Have the teams stand in a semicircle about 40 feet from the base of the flag pole.  With a large tape measure (the track coach has one), measure 480 inches out to the points where each team will place a mirror on the ground.  Have students refer to the diagrams in their previous work as you explain the method for measuring the flag pole.  Time permitting, you can use the instructions in the lesson presentation to go over the procedure before you leave the classroom.