Equilateral Triangle � A trian-
gle with all three sides the
same length
Isosceles Triangle � A trian-
gle with two sides the same
length
Parallel Lines � Lines that
never meet no matter how
long they are extended. The
opposite sides of a square or
rectangle are parallel.
Vertex � Angles are formed by tw o rays that have the
same endpoint, this endpoint
is called the vertex.
Shapes and Designs
Glossary
Connected Mathematics
Project
Everett Public Schools
Mathematics Program
Proposed Time Frame:
Approximately 6 weeks
Shapes and Designs
Two-Dimensional Geometry
Unit Goals
Understand the relationships
between and among polygons
Learn im portant properties of
polygon
Create and determine
properties of shapes that tile a
surf ace
Explore symmetries in
squares, rectangles,
parallelograms, and equilateral
triang les.
Web Resources
You will find web resources
www.illuminations.nctm.org
Investigating Properties
of Triangles
Exploring Properties of Rectangles and Paral-lelograms
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 Bees and Polygons
Discover which regular polygons c an tile a
plane.
Discover combinations of regular polygons that
can be us ed to tile a plane
Discover that some irregular poly gons can be
used to tile a plane.
Invest igation 2 Building Polygons
Understand that triangle are st able figures that
keep their s hape under stress
Discover that the sum of the lengths of any two
sides of a tr iangle is greater than the length of
the third side.
Discover that quadrilaterals and ot her polygons
are not stable s hapes and become distorted
under stress
Discover that the sum of the lengths of any
three sides of a quadrilateral is greater than the
length of the fourth side.
Investigation 3 Polygons and Angles
Develop and understanding of what an angle is
and find examples in the real world
Understand the measure of an angle
360�, is a full circle, 180� is a half circle, 90� is a
quarte r circle
Use angles and angle measures in real-life ap-
plications
Investigation 4 Polygon Properties and
Tiling
Use information about angles to test potential
tiling patterns
Show how regular hexagons can be us ed to tile
Understand that most other polygons do not tile
Understand that circular shapes do not tile
Invest igation 5 Side-Angle-side Connec-
tions
Recognize and describe flips and tu rns that will
return a triangle, square, rectangle, or parallelo-
gram to its original orientation
Understand the properties of side s and an-
gels in isoscel es and equilateral triangles,
squares, rectangles, and parallelograms
Connected Mathematics Project
Mathematics in
Investigations
Phone: 425-385-4062
Fax: 425-385-4092
Email: mstine@everett.wednet.edu