Congruent Figures � Two figures are con-
gruent if one is an image of the other under
a translation
Kaleidoscope � A tube containing colored
beads or pieces of glass and carefully
placed mirrors. When the kaleidoscope is
held to the eye and rotated, the viewer
sees colorful, symmetric patterns.
Line Reflection � A transformation that
matches each point on a figure with its mir-
ror image over a line
Reflectional Symmetry � A figure or de-
sign has reflectional symmetry if you can
draw a line that divides the figure into
halves that are mirror images.
Rotational Symmetry � A figure or design
has rotational symmetry if it can be rotated
less than a full turn about a point to a psi-
tion in which it looks the same as the origi-
nal. Symmetry � An object or design has sym- metry if part of it is repeated to create a
balanced pattern. Tessellation � A design made from copies of a basic design element that cover a sur-
face without gaps or overlaps.
Transformation � A geometric operation that matches each point on a figure with an
image point. Translation � A Transformation that slides each point or a figure to an image point a
given distance and direction from the origi-
nal point.
Translational Symmetry � A design that can be created by copying and sliding a
basic shape in a regular pattern.
Kaleidoscopes, Hubcaps and Mirrors
Glossary
Connected Mathematics
Project
Everett Public Schools
Mathematics Program
Proposed Time Frame:
Approximately 6 weeks
Kaleidoscopes, Hubcaps, and
Mirrors
Geometry
Measurement
Unit Goals:
Recognizing symmetry in designs
Lookin g for patterns that can be
used to predict attributes of
designs
Relating rigid motions in words
and with coordinate rules Composing symmetry transformation Making tables of combin ations of symmetry
WWW.illu minations.nctm.org
Symmetry
http://math.rice.edu/~lanius/misc/r otat.
html
Tips for Helping at Home
Good questions and good listening w ill
help children make se nse of mathemat-
ics an d build self-confidence. A good
question opens up a problem and su p-
ports different ways of thinking about it.
Here are some questions you might try,
notice that none of them can be an-
swered with a simple �yes � or �no�.
Getting Started
What do you need to find ou t?
What do you need to know?
What terms do you understan d or
not understand?
While Working
How can you organize the inf orma-
tion?
Do you see any patterns or relation-
ships that w ill help solve this?
What would happen if�?
Reflecting about the Solution
How do you know your answer is
reasonable?
Has the question been answ ered?
Can you explain it another w ay?
At Home:
1 Talk with your child about
what�s going on in mathem atics
class.
2 Look for ways to link mathe-
matical learning to daily activi-
ties. Encourag e your child to
figu re out the amounts for halv-
ing a recipe, estimating gas
mileage, or figuring a restau-
rant tip.
3 Encourage y our child to sched-
ule a regular time for home-
work and provide a comfortable
place for their study , free from
distractions.
4 Monitor y our child�s home-
work on a regular basis by
looking at one problem or ask-
ing your child to briefly de-
scribe the focus of the home-
work. When your child asks
for help, work with them in-
stead of doing the problem for
them.
At School
1 Attend Open House, Back to
School Nigh t, and after school
ev ents.
2 Join the parent-teacher organi-
zation
Investigation 1: Three Types of Symmetry
Explore reflectional, rotational, and translational sym-
me try informally
Explore the use of tools, such as tr acing paper, to
analyze des igns to determine their symmetries
Design shapes that have specified sy mmetries
Identify basic design elements that c an be used to
replicat e a design
Investigation 2:
Examine reflections, translations and rota-
tions to determine how to specif y such trans-
formations precisel y
Use the properties of reflections, translat ions,
and roattins to perform tr ansformations
Find lines of reflection magnitudes and di rec-
tions of translation, and c enters and angles of
rotation
Examine the results of combining reflecti ons
over two intersecting lines or two parallel
lines, two trans lations, or two rotations to find
a single transformation that will produce t he
same result.
Investigation 3: Transforming Coordinates
Write directions for drawing figures com-
posed of line segments
Analyze the vertices of a figure under a tr ans-
formation and to specify tr anslations with
coordinate rules
Connected Mathematics Project
Mathematics in
Investigations
Phone: 425-385-4062
Fax: 425-385-4092
Email: mstine@everett.wednet.edu