Geometry and Spatial Sense, Grades 4 to 6 - EduGains

Ask students to work with a partner to see if they can find a way to mark the centre of rotation
for the equilateral triangle. Allow time for experimentation, and ask for volunteers to share
their findings. (The centre of rotation can be found by bisecting one angle of the triangle
through folding, repeating this process with a second angle, and finding where the two fold
lines meet. Bisecting a third angle will verify that the centre of rotation is correct. Demonstrate
with a large equilateral triangle if none of the students discover the strategy.)
Label the centre of rotation for each of the large equilateral triangles and place one triangle
exactly on top of the other, using a paper fastener to hold the triangles in place. Label the angles
A, B, and C. Slowly rotate the top copy until it lies exactly over the bottom triangle. Have the stu-
dents tell you when each overlying occurs. Keep rotating the triangle until it returns to its original
position. Ask, “How many times does one equilateral triangle lie exactly over the other?” (3)
Instruct the students to work in pairs or groups of three, repeating the process with the
square, the pentagon, and the regular hexagon. Students should record their findings and look
for patterns.
Have a discussion to see which patterns the students have found. You want them to recognize
that the number of rotations corresponds to the number of sides. However, the students might
discover other interesting ideas or patterns.
Ask if their patterns or ideas would be true for other regular polygons. What about irregular
polygons? Have the students cut out other shapes to test their conjectures.
Teachers with access to The Geometer’s Sketchpad might want to let their students test their
conjectures in that environment, exploring more complex regular polygons.
LEARNING CONNECTION 2
Alphabet Rotations
MATERIALS
• Mov6.BLM4: Rotating the Alphabet (1 per student)
• tracing paper (1 piece per student)
Students use Mov6.BLM4: Rotating the Alphabet to discover which of the capital letters of
the alphabet have rotational symmetry. Students work individually to decide on the letters that
they believe have rotational symmetry. At this time they are not permitted to use any aids and
must base their conjectures on perception.
Students then work in pairs, checking their conjectures with tracing paper to prove which of
the letters have rotational symmetry.
Students could also discover, and then check, which of the numbers and the lower case letters
of the alphabet have rotational symmetry.
Grade 6 Learning Activity: Movement – Logo Search and Design 22