`Mirror Symmetry/Mirror ImagesAlan Tobecksen                 Henry Clay Elementary School                               13231 S. Burley                               Chicago IL 60633                               (312)535-5600Objectives: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 11. 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 studentOne block of wood per studentOne rubber band per studentOne rubber stopper and pencil per 2 studentsOne protractor per 2 studentsOne geometric figure sheet per studentOne mirror writing sheet per studentSeveral round mirrors plus pictures per classOne mirror mirage demoOne long closet mirrorOne "WHAT A COOKIE" mirror puzzleStrategy: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.     `