Logo Transformations
The objective of this lesson is to analyze line and reflection symmetry and transformations in logos. The
activity has three different parts. The first explores the symmetry of the alphabet the second the
symmetry of existing logo and the third expects students to create their own logo and describe the
symmetry. A record sheet for students to record their responses to questions is also included.
A web source that was used to assist in the development is:
http://www.pbs.org/teachers/mathline/concepts/designandmath/activity2.shtm
Activity part 1:
Since many logos contain letters of the alphabet, analyzing the alphabet is a good place to start.
Distribute alphabet cards to each pair of students. Students separate the cards into 2 categories: letters
with line symmetry and letters without line symmetry. Use a dry erase marker and draw two large
circles on their desktop or on a white board. One circle will contain letters with horizontal symmetry
and one will contain letters with vertical symmetry. Discuss with students as to how to draw the circles,
overlapping or not overlapping. Take the letters with line symmetry and place them into the
appropriate area in the diagram. Students should record their answers on the handout. Draw each
letter and mark the line of symmetry on each.
Take the cards and separate into two categories: letters with rotational symmetry and letters without
rotational symmetry. Once again place the letters into two circles. Should the circles be separate or
overlap? List each letter note the center and degrees of rotation.
Activity part 2:
Distribute the logo cards. Ask students to draw two circles, one for line symmetry and one for rotational
symmetry. (Should the circles overlap?) Place the logos in the appropriate location in the diagram. Do
any of have translational symmetry?
Activity part 3:
Share a few for examples of logos to help students get some ideas or give students time to explore
different ideas for logos. Google images are a good source for examples. Discuss a few in class.
Each student creates their own logo and writes a description of the symmetry in their logo. The logo
must have at least 2 different symmetries: Two different lines, rotational or translational. Students may
not use one that already exists.
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Logo Transformations
Name__________________________Partner_____________________
This sheet is to record your responses as you explore different types of symmetry. For the first part of
this activity, you and your partner will need a set of alphabet cards, a dry erase marker and a white
board.
1.
Organize your alphabet cards into two piles: letters with line symmetry and letters without line
symmetry. Record:
Letters with line symmetry:
Letters without line symmetry:
2. Use a dry erase marker and draw two large circles on a white board. One circle will contain
letters with horizontal symmetry and one will contain letters with vertical symmetry. Be sure to
label your circles with the type of symmetry. Should your circles overlap or be separate?
Why?
3. Take the pile of letters with line symmetry from step one and organize them into the circles you
drew on your dry erase board. After your teacher checks your response, record your answer.
Draw your letters large enough so that you can draw in the lines of symmetry when you record
your answers on this paper.
4. Erase your dry erase board and draw two new circles. One for letters with rotational symmetry
and the other for letters without rotational symmetry. Be sure to label your circles with the
type of symmetry. Should your circles overlap or be separate?
Why?
5. Take all 26 cards and reorganize them into the circles you drew on your dry erase board. After
your teacher checks your response, record your answer.
6. Make a list of all letters with rotational symmetry. Write the letters large enough to be able to
draw in the center and angles of rotation on the letters. Beside each letter state the number of
degrees of rotation.
For this part of the activity you need the logo cards. Erase your dry erase board.
7.
Draw two circles on your dry erase board. Label one line symmetry and the other rotational
symmetry. Should your circles overlap or be separate?
Why?
8. Place your logos in the appropriate location on the diagram. After your teacher checks your
response, record your answer. (You may use the number to refer to the logo)
9. Do any of the logos have translational symmetry?
If so, which one(s)?
10. Individual assignment: Create your own logo and write a description of the symmetry in your
logo. It must have at least 2 different symmetries: Two different lines, rotational or
translational. You may not use one that already exists.