Shapes and Figures
- Easier -
Circles, triangles, and squares are shapes. Geometry
is the mathematical study of shapes, figures, and
positions in space. It is useful in many careers such
as architecture and carpentry.
- Harder -
Geometry is the study of measurement and comparison of
lines, angles, points, planes, and surfaces and of
plane figures and solids composed of combinations of
these. A shape is the outer form of an object or
figure such as a circle, triangle, square, rectangle,
parallelogram, trapezoid, rhombus, octagon, pentagon,
and hexagon. There are equilateral, isosceles, and
right triangles. A solid is a three-dimensional figure
such as a cube, cylinder, cone, prism, or pyramid.
Other solid shapes include the tetrahedron,
octahedron, and dodescadhedron. Positions in space are
things like points, lines, and angles.
- Formulas can be used to figure out the dimensions
of shapes and figures. Instruments such as rulers,
triangles, compasses, and protractors are used in
geometry. Today, many people also use graphing
calculators and computers in geometry.
- The Greeks made many contributions to our
understanding of geometry. For example, Archimedes is
credited as the first to calculate the ratio between a
circle's diameter and its circumference now known as
pi. Pythagoras is famous for his theorem which states
that in any right-angled triangle the sum of the
squares on the two shorter sides equals the square of
the hypotenuse. However, many people think the
Egyptians and Babylonians knew this math much
- Review the concepts of geometry and then take a
quiz. Learn about space figures, polygons, symmetry,
volume, area, perimeter, lines, rays, angles, and
Online by C. Lanius (Grades 6-8)
- Here you find activities for middle or high school
geometry. Topics include the history of geometry,
hidden irrationals, hidden polygons, isosceles
triangle puzzler, impossible triangles, circles around
Pythagoras, SAT quiz, Golden Ration, volume, school
bus geometry, and a glossary.
on Circumference of a Circle at Mrs. Glosser's
Math Goodies (Grades 3-5)
- Learn about the circle and its properties of
circumference, diameter, radius, and Pi.
- Other Geometry Resources at Mrs. Glosser's Math
- 2) Lesson on Area of a Circle http://www.mathgoodies.com/lessons/vol2/circle_area.html
- 3) Lesson on Area of Parallelograms http://www.mathgoodies.com/lessons/vol1/area_parallelogram.html
- 4) Lesson on Area of Squares and Rectangles
- 5) Lesson on Perimeter of Polygons http://www.mathgoodies.com/lessons/vol1/perimeter.html
- 6) Lesson on Area of Trapezoids http://www.mathgoodies.com/lessons/vol1/area_trapezoid.html
- 7) Lesson on Area of Triangles http://www.mathgoodies.com/lessons/vol1/area_triangle.html
- Related Website for Older Learners:
- 8) Circles at Dave's Math Tables http://www.sisweb.com/math/geometry/circles.htm
- Although this site provides information about more
than just shapes and figures, you'll find it's a very
useful starting point. Explore resources for children
and teachers related to geometry. Topics include
classroom materials, software for geometry,
interactive geometry classroom activities, links to
other websites, and a public forum related to
- Other Resources at Math Forum:
- 2) Geometry Software http://mathforum.org/dynamic/classroom.html
- 3) Internet Geometry Projects http://mathforum.org/geometry/geom.projects.html
- After visiting several of the
websites, complete some of the activities
or projects below:
- Discover Shapes in Nature. Our
world is filled with many different
shapes. Take your digital camera outside
and take pictures of shapes in nature and
in the city. How many shapes can you find?
Can you find symmetry in nature? Create a
PowerPoint presentation sharing your
shapes. Create an online epal activity
sharing your photographs with another
class over the Internet.
- Learn About Geometry Online. Go
and Space in Geometry and complete two
lab activites; one about shape and the
other about space.
- Create a Geometry Timeline.
Geometry has an interesting history. Many
students have explored this topic. Check
out some of their ThinkQuest projects from
the "websites by kids for kids" below.
Create a timeline showing some of the
major events. Choose a person or an event
and learn about its importance. How would
math be different without this
- Play Some Shape Games. You'll
find many fun games at Alfy
Thematic Units: Patterns and Shapes.
Keep in mind that some of the games
require plugs-ins such as ShockWave. Young
learners (K-2) may want to start with the
game of Oddball
at FunBrain. Older kids can go to
Flash Cards from APlus Math and
see how many shapes they can
- Explore Shapes in Software.
Many software packages such as
AppleWorks, PowerPoint and
HyperStudio contain fun options for
creating shapes and figures. Use these to
create a geometry poster or presentation.
The presentation should convince people
that geometry is fun!
- Solve a Geometry Problem.
Complete the Challenge
Exercises: Circumference & Area of a
Circle and Challenge
Exercises: Perimeter & Area of
Polygons at Mrs. Glosser's Math
Goodies. Another challenge can be
found at Geometry
Problem of the Week from Math
Forum. Older learners should visit
the Area of the Shape! (Grades 7-10)
and explore the meaning of the area of
- Create Imaginary Polygon
Animals. You can get started by
looking at examples found at Geometry
Gallery of Imaginary Animals Project
(Grades 3-5). Be sure to visit the
Gallery and look at the artwork
submitted by students. Submit your own
- Create Some Bubble Geometry.
Get started by visiting Bubble
Geometry at Thinking Fountain.
You can find lots of information about
including a recipe formula for bubble
- Write a Shape Story. Write a
story that includes geometric shapes that
you see every day. Share your shape with
- Become an Architect. Many
shapes and figures are used in
architecture. Learn more about architecture
at another thematic project from
eduScapes 42eXplore. Then, design a
unique building using interesting shapes.
How do they fit together? Why?
- Tell a Tale with Tessellations.
After learning about shapes, visit
eduScapes 42eXplore's tessellations.
Create a visual story by creating
tessellations from interesting shapes.
Write about how you created the
tessellation and the shapes you used.
- Complete a Geometric Shapes
Webquest. Follow or adapt the
procedures found at the following webquest
- 1) Greybeards' Ghost (Grades 8-12)
- 2) What in the World is a Shape?
- 3) Geometry in the New World.
- Websites By Kids For Kids
Look At 3D Geometry (1996 ThinkQuest
- Why stick with boring old 2-dimensional geometric
figures, like squares and triangles, when you can add
a third dimension and get cubes and pyramids?
(A websection of a 1996 ThinkQuest Project)
- Euclid have you stumped? Archimedes run rings
around your head? This site can help you.
at Math for Morons Like Us
- This site tries to clear up some of the common
problems people have with geometry; everything from
parallel lines to volumes of prisms and a couple of
word problems. covered.
Eagle (1997 ThinkQuest Project)
- Need to know the difference between an isosceles
trapezoid and a kite? Take a look at this site, which
leads you from beginning to intermediate geometry.
Organized in chapter-by-chapter format, topics
includes angles, direct and indirect proofs, the
Pythagorean and other theorems, properties of
polygons, and lots to know about circles.
for all (1999 ThinkQuest Junior
- Here you will find activities to demonstrate
geometry can be fun with hands-on information for real
Around the World
- Click on the 'roofing' icon to get started
learning more about symmetry.
- More Websites on Geometric Shapes
Thematic Units: Patterns and Shapes (Preschool and
- This website provides links to great resources and
games for young children. Unfortunately many of these
websites require shockwave and java. Be sure to check
the resources on your computer before you try these
at Dave's Math Tables
- Here you can find simple diagrams defining the
area and volume of different shapes.
- This site provides interesting views and
discussions of geometric packing of shapes.
- Related Page:
- 2) Erich's Combinatorial Geometry Page http://www.stetson.edu/~efriedma/comb.html
A Romance of Many Dimensions
- Here online is Edwin A. Abbott's 1884 classic tale
of interdimensional experience.
- Related Websites:
- 2) Beyond Flatland: Geometry for the 21st Century
by K. Urner http://www.inetarena.com/~pdx4d/ocn/urner.html
- 3) Fourth Dimension http://www.geocities.com/CapeCanaveral/7997/
- 4) Speculations on the 4th Dimension http://www.alkaline.org/4thdim/
at Eduscapes 42eXplore
- Learn about fractals, an endlessly repeating
pattern that is a mixture of art and geometry.
Dimension by C. Lanius
- This is a place to learn about lines, shapes and
from Math League Help Topics (Grades
- This site defines the geometric terms; don't miss
the 'Figures and polygons' section.
in Hawaiian History and Culture
- Here you find a set of slides showing geometry in
Hawaiian history and culture.
and Pattern: The Art of Oriental Carpets
- This site is about the symmetry, asymmetry, and
patterns that lie behind the art of Oriental
at Eduscapes 42eXplore
- Learn about tessellations at this site. A
tessellation is a repeating pattern composed of
interlocking shapes (usually polygons) that can be
- Websites For Teachers
Shapes in Architectyre
- This lesson focuses on geometric shapes in
architecture. It explores each shape and discusses how
it is used.
- Here you will find a large collection of lesson
plans for various grade levels.
Everywhere by B. Allen at Kodak (Grade
- The purpose of this activity is to help students
become more aware of geometric shapes and lines in
objects around them.
- Other Related Kodak Lesson Plans:
- 2) Re-Inventing Fourth-Grade Mathematics by J.
Lopez (Grades 1-6) http://www.kodak.com/global/en/consumer/education/lessonPlans/lessonPlan151.shtml
Seen That Shape Before (Grades Pre-K -
- Students learn the names and explore properties of
solid geometric shapes. They identify these shapes in
the real-world and in pictures found on web sites. In
the pre-activities and the extensions, students use
physical models of simple solid shapes.
- Related Lesson:
- 2) Geometric Shapes by A. Geurkink (Grades
- Here are books, activities and experiments about
and Polygons in Nature (Grades 6-8)
- The student will investigate geometric shapes in
nature by examining the patterns of tilings seen in
nature. Students will learn how to divide triangles an
parallelograms into rep-4 tiles and rep-9 tiles.
- Created by
2/01. Updated by King