We finish this 4-part i-Math Investigation on rotational symmetry by putting
things together. You will have the opportunity to think about the ideas you have
discovered in this i-Math as a whole by answering some review questions.
Learning Objectives
Students will
have the opportunity to think about the ideas they have discovered in this i-Math as a whole
Materials
Computer and Internet connection
Instructional Plan
Taking Stock...Rotational Symmetry
1. What is necessary to describe a rotation?
2. Draw a shape, a center of rotation, and the image of the shape rotated 90°.
3. Draw a shape with a center of rotation that has the property that the shape looks exactly the same after rotation through 120°. What kind of symmetry does your shape have?
4. Draw shapes with (a) point symmetry, (b) 3-fold cyclic symmetry, and (c) 4-fold cyclic symmetry.
5. If you see a cyclic shape, how do you determine where the center of rotation is?
6. If you see a cyclic shape, how do you determine what order the center of rotation has?
7. What rotations about the center of a circle are symmetries of the circle?
Use various representations to help understand the effects of simple transformations and their compositions.
Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.
Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools.
References
For All Practical Purposes: Introduction to Contemporary Mathematics,
W.H. Freeman and Company, New York, 1997
Understanding Congruence, Similarity, and Symmetry Using Transformations and
Interactive Figures: Visualizing Transformations, NCTM Principles and Standards
for School Mathematics: E-example 6.4. http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm<
The National Council of Teachers
of Mathematics is a public voice of mathematics education, providing
vision, leadership, and professional development to support teachers
in ensuring mathematics learning of the highest quality for all
students. The views expressed or implied, unless otherwise noted,
should not be interpreted as official positions of the Council.
