Goal:This lesson introduces students to how tessellations are formed and which type of polygons will tessellate the
plane.
Research!Have your students research M.C. Escher, an artist who has designed numerous pieces of artwork using
tessellations. Have each student choose a piece of artwork, outline its preimage figures and give a short presentation.
Create Your Own Escher Print!An activity many students love to do is designed an unique piece of art. Complete
the following steps:
a. Cut out a 2[U+0080][U+009D]square from a sheet of copy paper.
b. Draw a curve between two consecutive vertices. Be careful to not cut off a vertex!
c. Cut out the curve and slide the cutout to the opposite side of the square and tape it in place.
d. Repeat this process with the remaining two sides of the square.
e. This is your template, or preimage. Begin with an 11[U+0080][U+009D]× 14 [U+0080][U+009D]piece of
copy paper. Trace your preiamge and continue the pattern by rotating and translating until you cover the entire
sheet.
f. Color and post for a bulletin board.Did You Know?The first person to discover how to tessellate with a pentagon was....
Symmetry
Pacing:This lesson should take one class period
Goal: The purpose of this lesson is to introduce the concept of symmetry. Students have experienced symmetry
in previous lessons: isosceles triangles and various quadrilaterals. This lesson incorporates two-dimensional and
three-dimensional figures and their lines of symmetry.
Maximum Points!Have your students write the alphabet in uppercase letters. Using one colored pencil, show which
letters possess horizontal symmetry by drawing in the symmetry line. For example,Bhas a line of symmetry, as
doesEandK. Using a second color, draw in the vertical lines of symmetry. Have a contest to determine who can
write the longest word possessing one type of symmetry. For example, MAXIMUM is a word where all the letters
have vertical symmetry. KICKBOXED is another.
Project!Using a digital camera, have students (or groups thereof) take photographs of objects possessing symmetry,
either rotational or reflective. Give points for the most original, the most nature made, etc. Create a slide show
presentation in PowerPoint or Microsoft Movie Maker.
Vocabulary!When discussing rotational symmetry, some textbooks may refer to it asn−fold rotational symmetry.
This simply means that thenis the number of times the figure can rotate onto itself. For example, a regular pentagon
has 5−fold rotation symmetry, because it can be rotated 5 times of 108 degrees before returning to its original
position.
The Return of the Breadknife!The notion of cutting through a 3−dimensional object with a breadknife was used in
an earlier lesson to demonstrate cross sections. This concept can be used to illustrate planes of symmetry. The plane
of symmetry essentially “cuts” through the 3−dimensional solid so that each piece is identical.
Dilations
Pacing:This lesson should take one class period
Chapter 1. Geometry TE - Teaching Tips