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Title of Lesson: Electronic Geometry Notebook
Math and Geometry
Students create a geometry notebook throughout their study of geometry. Entries will be added weekly.
Mark Heeg &Trudy Driskell
If students can apply their geometry knowledge to real applications they can have a more realistic understanding about the study of spatial objects.
Students will describe relationships among the two and three dimensional shapes and their connections to the real world.
Students learn to solve problems by using their drawings and technology.
Students will make a hypertext notebook of the formulas and ideas in their geometry unit which will include real applications to that formulas or ideas.
At the beginning of the unit of study in geometry the teacher explains that the students will create a "Geometry Notebook" using HyperCard or HyperStudio. After each new concept learned, the class will be adding to their notebook. This notebook will become part of their final grade in the geometry unit of study.
After the teacher explains each new geometry formula or idea and gives the class examples of practical use of the formula/idea the class will add it to their geometry notebook. Each concept should be explained in two to five cards and should include: 1.) the name of the geometric formula or idea, 2.) an example drawing to show the concept along with the formula, 3.) examples of how the formula/idea relates to shapes in nature*, 4.) two real -world applications of that formula or idea and 5.) at least one sample real world problem for someone in the class to work at a later date. The HyperCard or HyperStudio tools can be used for drawing and design of the cards in the stack.
* All snowflakes, when crystallized, are built around some form, the regular hexagon. A honeycomb built by bees where each hexagon in the honeycomb is a cell in which the bees store their honey. The cells fit together like the tiles on a bathroom floor. The spiral of the nautilus shell or the seeds of the sunflower that are arranged in a pattern forming spirals winding from its center, the cone of a volcano or the spheres of the planets are all geometric and can relate to the formulas and ideas that are to be placed in the electronic geometric notebook.
The volume of a solid or of a three-dimensional figure is the amount of space it occupies. Volumes of regular figures are obtained by simple formulas. the volumes are expressed as cubic units, whatever the unit of measurement being used.
L x W x H = Volume
Students would draw a box, book, cabinet, book or any object that has length, width and height.
Real World Application:
The student would measure it and them record the measurements in their HyperCard Notebook. Bricks could be an example.
Books about mathematics from the library, CD ROM encyclopedias, video: The Birth of Modern Geometry
Rulers, tapes, micrometers if possible.
Computer Hardware and Software Required:
Macintosh computer, HyperCard or HyperStudio software. Students may have access to Geometric's Sketchpad software from Key Curriculum Press or Cabri Geometry II available from Texas Instruments (Refer to article: Bridging the Gap Between Algebra and Geometry by Phillip E. Duren, Learning and Leading With Technology, February 1997, pp. 34-38).
Geo World by Tom Snyder Productions, Inc http://www.EDnet.ns.ca/educ/program/lrt/eval/recomm.htm#Geo World
Books about mathematics, objects to draw like globes, boxes, cabinets and things that would be "real" to draw and measure that are in the classroom.
Related WWW Sites
Gallery of Interactive Geometry
Lots of fun things to do with geometry.
Math Forum - K-12 Geometry
Classroom materials for students and teachers for geometry, free software, archives for Geometer's Sketchpad, Internet projects and a public forum for discussing geometry.
The Geometry Center
Great resources for teachers who teach geometry.
Geometry Forum Newsgroups
The Forum administers eight newsgroups, an online electronic community for all those interested in geometry.
Math Forum - Internet Geometry Hunt
A monthly interactive project consisting of questions about math and mathematicians.
Dynamic Geometry Software
Tools such as Sketchpad and Cabri to be used in creating an exciting, discovery-oriented geometry environment.
Any real-life math that requires critical thinking skills, problem solving and logical reasoning is great to use in the classroom. Students working in groups to solve each other's geometry problems makes the lesson active and fun. This lesson with it's "record keeping" concept will allow the students to review the formulas and ideas learned many times. The students will get creative with their examples for the particular formula or idea in the example or problems to solve sections of the HyperCard stack. After all, what is geometry without spatial visualizations? HyperCard is the perfect software for this project and one that so many schools are teaching students to use for projects.
Prerequisite Student Skills:
The students need to be able to create a HyperCard or HyperStudio stack.
Six weeks or the entire unit on geometry.
Students divided into groups will show their stacks and have the group work the problems in the stacks together.
Did the students complete the stack? Were the student's concepts correct and examples applicable?
Students will evaluate their own work as well as their peers as they work the problems in each of the group's geometry project.
Set New Challenge:
A geometry exercise that is both challenging and enlightening is to have students relate (derive) area formulas for rectangles, triangles, and trapezoids.
Give the students the area formula for a rectangle, length x width, and have students draw a rectangle.
Have students draw a triangle and see if they can derive the area formula using the drawing of a rectangle. The students should be able to explain their results.
You can do the same with trapezoids.
Math Forum - Internet Geometry Hunt
Post this project for student's extra credit or challenge: Monthly interactive project consisting of questions about math and mathematicians.
Just for Fun!
Tangrams - Introduction
The origins of the tangram puzzle are not known with any certainty, but the idea is thought to have originated in China about 250 years ago. Students create designs using geometric shapes.
Bamdad's Math Comics
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