Return to Physics IndexMirror Symmetry/Mirror Images

Alan 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 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 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.