TEACHER'S ACTIVITIES                                                                              STUDENTS' ACTIVITIES

INTO:
-pair up students as they enter the classroom                                                       -sit with assigned partner
tip: students will later be grouped into fours, so it may help to
        group them into fours at this point depending on how focused
        the students are in larger groups
-pass out angle worksheet and read instru                                                            -students complete worksheet
-get class back together after a few minutes of discussion                                    -refocus attention to teacher
-ask students about what they discussed
tip:   encourage students to pay careful attention to ratios

THROUGH:    Lesson
-Definition of Similarity:
    Triangle ABC ~ Triangle DEF iff AB/DE=BC/EF=CA/FD and                       -take notes and answer questions
    m<A=m<D, m<B=m<E, m<C=m<F
tip:    it is a good idea to make a list of new and uncommon symbols
           such as similar(~), measure(m), and angle(<)
-found that AAA results in similarity, what about AA?
AA Similarity Postulate:
    If two angles of one triangle are equal to two angles of another
    triangle, the triangles are similar
tip:    illustrate each postulate/theorem with examples
-are all congruent triangles similar?
SSS Similarity Theorem:
    If the lengths fo the sides of one triangle are proportional to the
    lengths of the sides of a second triangle, then the triangles are
    similar.
SAS Similarity Theorem:
    If an angle of one trianlge is equal to an angle of a second
    triangle, and if the lengths of the sides including these angles
    are proportional, then the triangles are similar.
-if 2 triangles are similar to the same triangle are they similar
  to one another?
tip:    at this point, it is beneficial to make a list of
            the ways to prove triangles are similar

                        Activity
-take students outside to side of the building where the sun is
  casting its shadow                                                                                               -participate in and think about group activity
-group students into fours
-ask one student in each pair to stand so that the end of his or
  her shadow ends where the building's does
-another student will measure the length of the student's
  shadow and height
-a third student will measure the length of the building's shadow
-the fourth student will record the data
-ask students to determine what the height of the building is

BEYOND:
-journal entry:  What have you learned today?
                        What concepts were the most difficult for you? Do you need more practice with them?
                        When will you use or have you used these concepts (outside of the class)?
-homework sheet

Accommodations:
    Different types of learner may need certain adjustments throughout this lesson.  For auditory learners, a teacher should read through the instructions with the entire group first.  Also, during the lecture portion of this lesson, notes should be both written on the overhead/chalkboard and spoken.  Kinesthetic learners may benefit from having pipe cleaners to maneuver during the lecture on the theorems.
    Students with disabilities should also be considered.  If a student is unable to work with a pencil to trace the angles, it is possible for the students to create the triangle using Geometer's Sketch Pad.  The student can also be teamed up with another student and share a triangle within a group of three.
    Given the various roles for the outside activity, there will most likely not be a problem get all students involved.  However, there is the possibility of poor weather.  If this is the case, simply do the activity with a strong flashlight or floodlight inside.

Standards:
    This lesson was written in accordance with both the NCTM and ISBE Standards.  Topics of geometry and measurement are explored through hands-on activities in which students engage in problem-solving.  Students are also required to make connection between the theorems that have been introduced to and facts that they have.  Finally, students are asked to communicate their reasoningboth in writing and orally.