  The Topic:  Geometric 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 earlier. The Geometry Center
http://pittsford.monroe.edu/jefferson/calfieri/geometry/geoframe.html
Review the concepts of geometry and then take a quiz. Learn about space figures, polygons, symmetry, volume, area, perimeter, lines, rays, angles, and coordinate.

Geometry Online by C. Lanius (Grades 6-8)
http://math.rice.edu/~lanius/Geom/
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.

Lesson on Circumference of a Circle at Mrs. Glosser's Math Goodies (Grades 3-5)
http://www.mathgoodies.com/lessons/vol2/circumference.html
Learn about the circle and its properties of circumference, diameter, radius, and Pi.
Other Geometry Resources at Mrs. Glosser's Math Goodies:
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 http://www.mathgoodies.com/lessons/vol1/area_rectangle.html
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

Math Forum: Geometry
http://mathforum.org/geometry/k12.geometry.html
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 geometry.
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 to Shape 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 knowledge?   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 Geometry Flash Cards from APlus Math and see how many shapes they can identify.   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 Find the Area of the Shape! (Grades 7-10) and explore the meaning of the area of geometric shapes!   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 Amy's Gallery and look at the artwork submitted by students. Submit your own geometric animal.   Create Some Bubble Geometry. Get started by visiting Bubble Geometry at Thinking Fountain. You can find lots of information about Bubbles including a recipe formula for bubble soap.   Write a Shape Story. Write a story that includes geometric shapes that you see every day. Share your shape with an epal.   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 sites:  1) Greybeards' Ghost (Grades 8-12) http://www.bioc.rice.edu/precollege/galbay/galbay99/teachers/fibonacci/index.html 2) What in the World is a Shape? http://coe.west.asu.edu/students/cindelicato/intro.html 3) Geometry in the New World. http://www.campbell.k12.ky.us/links/webquest/gross/webquest_ss.html Websites By Kids For Kids
3D Look At 3D Geometry (1996 ThinkQuest Project)
http://library.thinkquest.org/2842/
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?

Geometry (A websection of a 1996 ThinkQuest Project)
http://library.thinkquest.org/2647/geometry/geometry.htm
Euclid have you stumped? Archimedes run rings around your head? This site can help you.

Geometry at Math for Morons Like Us
http://library.thinkquest.org/20991/geo/index.html
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.

Geometric Eagle (1997 ThinkQuest Project)
http://library.thinkquest.org/11482/
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.

Geometry for all (1999 ThinkQuest Junior Project)
http://www.thinkquest.org/library/lib/site_sum.html?lib_id=1827&team_id=28318
Here you will find activities to demonstrate geometry can be fun with hands-on information for real life.

Symmetry Around the World
http://www.schools.ash.org.au/stkierans-manly/Classes/Yr6/6B/Symmetry/index.htm
Click on the 'roofing' icon to get started learning more about symmetry.

More Websites on Geometric Shapes
Alfy Thematic Units: Patterns and Shapes (Preschool and Primary Grades)
http://www.alfy.com/teachers/teach/thematic_units/Patterns_Shapes/PS_1.asp
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 websites.

Areas at Dave's Math Tables
http://math2.org/math/geometry/areasvols.htm
Here you can find simple diagrams defining the area and volume of different shapes.

Erich's Packing Center
http://www.stetson.edu/~efriedma/packing.html
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

Flatland: A Romance of Many Dimensions
http://www.alcyone.com/max/lit/flatland/index.html
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/

Fractals at Eduscapes 42eXplore
http://www.42explore.com/fractal.htm
Learn about fractals, an endlessly repeating pattern that is a mixture of art and geometry.

Fractional Dimension by C. Lanius
http://math.rice.edu/~lanius/fractals/dim.html
This is a place to learn about lines, shapes and dimensions.

Geometry from Math League Help Topics (Grades 4-8)
http://www.mathleague.com/help/geometry/geometry.htm
This site defines the geometric terms; don't miss the 'Figures and polygons' section.

Geometry in Hawaiian History and Culture
http://kalama.doe.hawaii.edu/hern95/rt015/geo/index.html
Here you find a set of slides showing geometry in Hawaiian history and culture.

Symmetry and Pattern: The Art of Oriental Carpets
http://mathforum.org/geometry/rugs/index.html
This site is about the symmetry, asymmetry, and patterns that lie behind the art of Oriental rugs.

Tessellations at Eduscapes 42eXplore
http://www.42explore.com/teslatn.htm
Learn about tessellations at this site. A tessellation is a repeating pattern composed of interlocking shapes (usually polygons) that can be extended infinitely.

Websites For Teachers
Geometric Shapes in Architectyre
http://www.cis.yale.edu/ynhti/curriculum/units/1983/1/83.01.07.x.html
This lesson focuses on geometric shapes in architecture. It explores each shape and discusses how it is used.

Geometry and Measurement
http://www.iit.edu/~smile/mathinde.html#m1
Here you will find a large collection of lesson plans for various grade levels.

Geometry Everywhere by B. Allen at Kodak (Grade 10)
http://www.kodak.com/global/en/consumer/education/lessonPlans/lessonPlan076.shtml
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

I've Seen That Shape Before (Grades Pre-K - 2)
http://illuminations.nctm.org/lessonplans/prek-2/shape/index.html
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 K-1)
http://www.lessonplanspage.com/MathGeometricShapesIntroK1.htm

Shapes Cluster
http://www.smm.org/sln/tf/nav/tfclusters.html
Here are books, activities and experiments about shapes.

Tilings and Polygons in Nature (Grades 6-8)
http://coe.west.asu.edu/explorer/shapes/staffdevl/3.teacher.instructions.html
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. geometry shape point line plane space fractals dimension line angle circle conic section cylinder cone diameter circumference radius Pi area perimeter rectangle square equilateral triangle polygon pentagon square parallel perpendicular parallelogram trapezoid acute triangle obtuse triangle right triangle symmetry volume triangle octagon quadrilateral congruent equilateral isosceles triangle 'measure earth' sphere scalene triangle hexagon solid heptagon ratio hypotenuse mathematics measurement Pythagorus dimension tessellations Created by Annette Lamb and Larry Johnson, 2/01. Updated by King Family, 11/04.