Mirror Symmetry/Mirror Images

Alan Tobecksen                 Henry Clay Elementary School
                               13231 S. Burley
                               Chicago IL 60633
                               (312)535-5600

Objectives:

The intended grade level is sixth grade, but much of this is easily adapted to 
any grade.  This would be at least a two day lesson.

Day 1

1. The learners will understand that different geometric figures will have 
   different lines of symmetry, in different locations and in varying numbers.
2. The learners will develop a definition for symmetry.
3. The learners will use their developed definition of symmetry to predict where
   lines of symmetry will be located in some other geometric figures.
4. The learners will understand that some figures do not have a line of 
   symmetry.

Day 2
                                                                            
5. The learners will use two mirrors to produce multiple images, eventually 
developing a mathematical concept to predict what angle will produce what number 
of images. 

Materials Needed:

One mirror per student
One block of wood per student
One rubber band per student
One rubber stopper and pencil per 2 students
One protractor per 2 students
One geometric figure sheet per student
One mirror writing sheet per student
Several round mirrors plus pictures per class
One mirror mirage demo
One long closet mirror
One "WHAT A COOKIE" mirror puzzle

Strategy:

Day 1

   Invite a few students to pick up a few coins from the mirror mirage.  When 
they can not do it, ask them why they can not.  Next, point out that regular 
mirrors, such as those found throughout the house, seem to reverse the images 
that are seen in them.  Pass out mirrors.  Ask the students if they can read the 
phrases that are printed on the mirror writing sheet; ask a few students to read 
a phrase out loud.  Try and get the class to agree that a mirror always reverses 
the images. 
   Once your students agree that a mirror reverses images, you are ready to fool 
them yet one more time with the "WHAT A COOKIE" mirror puzzle (words done in red 
MAGIC marker do not reverse - of course, it is a trick).  Do not give them time 
to think about it or they will figure it out.
   Ask the students to hold the mirror in front of them at arms length and look 
at their nose.  Then have them turn the mirror (not their head) so they can see 
the person next to them, then turn the mirror so they can see the ceiling, then 
their shoes, then a poster on the wall, etc.
   Ask the students to look at the geometric figure sheet.  Direct their 
attention to the rectangle; ask them where they could cut the rectangle into two 
parts where the one part was a mirror image of the other part.  After they tell 
you, ask them to check their answers with the mirror.  Some student will always 
suggest that you can cut a rectangle on a diagonal; ask the students to check 
the diagonal.  At this point, ask the students to find all of the lines of 
symmetry (the cut where one part of the figure is the mirror image of the other 
part) of all of the figures on the sheet.

Day 2

   Have the students attach the block to the mirror with the rubberband.  
Students pair up an make an angle with two mirrors and place a rubber stopper 
with a pencil stuck in it in front of the mirrors inside the angle.  Students 
arrange the mirrors so they see exactly three images.  Point out to the students 
that this should be a 90 degree angle.  Pass out protractors; have the students 
check the angle.  Have the students arrange the mirrors so they can see exactly 
four images, and check the angle, then five images, and check the angle, then 
six images, and check the angle, then eight images, and check the angle, then 
ten images, and check the angle.  If you keep doing this and doing it in reverse 
- that is have the students set the mirrors at a sixty degree angle and count 
the number of images, then set a fifty degree angle and count images - 
eventually the students will see a very simple mathematical relationship.

Performance Assessments:

Day 1

   Have the students list all the figures on the geometric figure sheet that 
have no lines of symmetry, all the figures that have exactly one line of 
symmetry, exactly two lines of symmetry, exactly three lines of symmetry, etc.  
A suggested grading rubric is 10-11 correct answers is a 4 (meets or exceeds 
learning expectations), 8-9 is a 3 (satisfactorily meets learning expectations),
5-7 is a 2 (needs improvement), 4 or less is a 1 (does not meet learning 
expectations.)

Day 2

   All students should copy the chart that lists the angles of the mirrors and 
the number of images that are produced.  Ask the students to memorize the chart 
and be able to reproduce it from memory the next day.  The next day the students 
reproduce the chart from memory.  The grade is either 100% or 0%; on the grading 
rubric the 100% receives a 4 and a 0% receives a 0.