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Technology

Appropriate uses of technology can enhance learning and motivate students. This section includes brief descriptions of software and Web sites that can be used to improve geometry and measurement instruction in grades K-5. This list will continue to be updated. Your comments and suggestions are welcome.

For additional information about technology, see Introduce and Implement Technology and Use Technology as a Tool.

• Software
• Web Sites

Software

The best software is open-ended and allows students to explore, look for patterns, and make and test conjectures. What appears here is a selection of programs that exemplify this approach. Main criteria for choosing software were whether the program: (1) actively engages students; and (2) facilitates learning new concepts in the context of a problem situation.

Nearly all of the software listed here focuses on geometry and/or measurement and is designed for use by students under the guidance of a teacher. One exception is the Cognitive Tutor, which is designed to increase teachers’ content knowledge. Exemplars Math also provides a wealth of examples of student work and associated rubrics that will help teachers become better at assessing student work.

Cabri Geometry™ II
This dynamic, visual geometry software product allows you to check conjectures using Euclid’s five postulates. Along with Geometer’s Sketchpad®, Cabri is one of the best known of the dynamic geometry software packages.
Texas Instruments http://www.education.ti.com
[grades 3-16]

Cognitive Tutor®: Geometry
This is a secondary mathematics program by the same organization that developed Cognitive Tutor®: Algebra, one of the programs designated as exemplary by the U.S. Department of Education’s Mathematics and Science Expert Panel. It is included here as a resource for teachers wanting to improve their content knowledge. This program uses a combination of technology and a text to provide the instruction.
Carnegie Learning, Inc. http://www.carnegielearning.com
[grades 6-12]

Exemplars Math
This series includes two CD-ROMs. Best of MATH I contains 180 K-8 assessment and instruction tasks. Best of MATH II contains over 100 K-8 assessment and instruction tasks, uses a Web-based platform, and can be networked. All tasks are grouped grades K-2, 3-5, and 6-8. Both CDs include scoring rubrics and benchmark student papers and can be searched by standard or content area. Both allow you to edit tasks to meet specific needs. Exemplarshttp://www.exemplars.com
[grades K-8]

The Factory Deluxe
As students design, build, and ship products, they learn about shapes, rotations, angle measurement, and formulas.
Sunburst http://www.sunburst.com
[grades 4-8]

Geometry Inventor™
This dynamic, visual software is similar to the Geometer’s Sketchpad® (see below). You can graph relationships between two measures to show, for example, that the ratio of the circumference of a circle to its diameter is a constant.
LOGAL Tangible MATH http://www.riverdeep.net
[grades 3-16]

The Geometer’s Sketchpad®
This software is open-ended in the best sense, since it is limited only by the imagination of the teacher. Students can plot points in the plane or in a coordinate system. The software knows what constructions are possible based on what objects have been selected. Students select constructions from a menu and can measure length and perimeter, area, and angles. Students can also test conjectures by altering their construction to determine if a certain property holds for many shapes of the same type.
Key Curriculum Press http://www.keypress.com
[grades 3-16]

Microworlds™
This is the Logo program (also called turtle graphics), with many add-ons. In addition to being able to program the turtle to create geometric shapes, students can create a multi-media environment using sound and video. The software can be used for a multidisciplinary unit that integrates math and art or math and music.
Logo Computer Systems, Inc. http://www.lcsi.com
[grades 3-8]

Pythagoras™
This dynamic, visual software is similar to Geometer’s Sketchpad® in its design and use. The software has many built-in shapes to make it easier to create polygons or circles, explore their properties, and easily scale (dilate) figures.
Dalin, Inc., Educational Software http://www.interactivemathworld.com
[grades 3-16]

Shape Up!
This program allows students to create and explore two- and three-dimensional shapes and learn names and properties of shapes. Other concepts include similarity, congruence, and transformations. Students can write about their work.
Sunburst http://www.sunburst.com
[grades K-8]

SPEX+
Students develop spatial reasoning abilities as they create a room in two dimensions and then view a three-dimensional version of the room. The program requires students to measure and rotate objects.
The Knowledge Tree, Inc. http://www.theknowledgetreeinc.com
[grades 5-9]

TABS+
Using basic shapes, students can create and manipulate three-dimensional shapes. Models can be wire frames or solids, which can be dilated, rotated, and viewed from the front, side, or top. Shapes can be animated. Nets can be created from three-dimensional models, printed, and used to create the three-dimensional model.
The Knowledge Tree, Inc. http://www.theknowledgetreeinc.com
[grades 3-12]

The Tenth Planet™ Geometry Bundle
This series consists of six titles: Spatial Relationships and Introduction to Patterns (grades pre-K-1), Combining Shapes and Creating Patterns from Shapes (grades 1-2), Shapes within Shapes and Mirror Symmetry (grades 2-5). Sound, animation, and active engagement motivate students to explore geometric concepts.
Sunburst http://www.sunburst.com

Tessellation Exploration®
Students use transformations to create tessellations. Students are asked to predict and describe the results of transformations. Stamps included with the software allow students to create great-looking tessellations that can be printed or shown to the class using the Slide Show feature.
Tom Snyder Productions http://www.tomsnyder.com
[grades 4-8]

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Web Sites

Web sites are valuable resources for teachers and students in search of current ideas and activities in mathematics. Since the quality of Web sites varies widely, a teacher should explore a site thoroughly for its mathematical content before suggesting it to students. The selections presented here are only a sample of the high-quality sites that are available.

Some sites are commercial, while others are non-profit organizations offering free educational resources. Some of the following sites are targeted specifically to teachers, offering lesson plans and activities for use in the classroom. Others offer links to other sites that will assist teachers striving to improve measurement and geometry learning in their classroom. Some sites describe educational research in terms that will be most readily usable to teachers trying to incorporate the research in their classes.

Certain sites have activities for students as well as ideas for teachers. A few sites, such as the Research for Better Schools site, are resource sites. They provide software, Web site, video, and/or curriculum reviews, as well as links to professional development opportunities and other useful sites. We have provided brief descriptions to assist you in finding the type of site you are looking for.

All Web sites are current as of February 2004.

Sample State Mathematics Standards:

AIMS Education Foundation
http://www.aimsedu.org
AIMS (Activities Integrating Math and Science) offers an online database of hundreds of activities that can also be ordered through the Web site. Some sample activities are available for free, including measurement and geometry activities.

All about Geometry
http://www.aaamath.com/geo.html
These Web pages teach a wide variety of geometry facts and provide interactive practice.

Association for Supervision and Curriculum Development (ASCD)
http://www.ascd.org
ASCD is an international professional education association with more than 160,000 members. This site offers links to the many publications and professional development opportunities affiliated with ASCD, as well as the diverse products available through the online store.

Big Wind Kite Factory
http://www.aloha.net/~bigwind/20kidskites.html
The Big Wind Kite Factory in Moloka’i, Hawaii, shows how to make classroom kites.

Columbia Education Center
http://www.col-ed.org
This site includes over 600 lesson plans and Web activities contributed by classroom teachers, teacher resources with links to education Web sites, and information about educational grant opportunities.

Coolmath 4 Kids
http://www.coolmath4kids.com/geometrystuff.html
The Polyhedra Gallery has colorful pictures and diagrams of the platonic solids and semi-regular polyhedra. Lesson plan topics include tessellations, congruence, and interior angles of regular polygons.

Education World Math Center
http://www.educationworld.com/math
This site includes resources for mathematics educators including lesson plans, mathematics articles, professional development resources, and mathematics Web site reviews and links. Measurement and geometry problems are available in the Math Worksheet Library; there are teacher lessons plans in geometry and measurement.

The Educator’s Reference Desk (Formerly Ask ERIC - Educational Resources Information Center)
http://eduref.org/cgi-bin/lessons.cgi/Mathematics/Geometry
The Educator’s Reference Desk is a Web site from the U.S. Department of Education which includes lesson plans, links to online education materials, and all the archived questions that were previously available at askeric.org. This page offers geometry lesson plans that can be used at the elementary school level. Measurement lesson plans are available at http://eduref.org/cgi-bin/lessons.cgi/Mathematics/Measurement.

[Note: The ERIC Web site which featured a database with more than one million abstracts of documents and journal articles on education research and practice is being reengineered as of January 2004; during the transition period all materials should still be available at http://www.eric.ed.gov.]

Eisenhower National Clearinghouse (ENC)
http://www.enc.org/
ENC collects teaching materials for K-12 mathematics and science educators and disseminates information about federally funded programs. This site contains links to more than 100 sites related to geometry. See the Classroom Calendar (http://www.enc.org/features/calendar/?ls=ho) for weekly entries containing topic overviews, ready-to-go activities, and suggested curriculum materials.

M. C. Escher
http://www.iproject.com/escher/teaching/teaching.html
This site contains lesson plans for connecting the art of Escher to the teaching of geometry (and other topics). It also includes links to related articles in School Arts magazine.

ETA/Cuisenaire
http://www.etacuisenaire.com
This company sells more than 150 manipulative-based and supplemental educational materials related to geometry and measurement.

The Geometry Center
http://www.scienceu.com/geometry
This Web site is part of the Science U Web site. Some of the elementary geometry activities include triangle tilings and polyhedra, symmetry and tiling, and tetrahedral puzzles.

The Geometry Junkyard
http://www.ics.uci.edu/~eppstein/junkyard
This resource site for teachers includes various topics in geometry with links to other sites. The origami page of this site (http://www.ics.uci.edu/~eppstein/junkyard/origami.html) has links to other sites with colorful photos of origami foldings.

Geometry Step-by-Step from the Land of the Incas
http://Agutie.homestead.com/files/index.html
This colorful, interactive site includes a mix of sound, science, and Incan history related to the study of geometry. Although the site is more appropriate for high school students, elementary school teachers can learn about concepts that upper elementary students could explore in historical and multicultural contexts.

Goudreau Museum of Mathematics in Art and Science
http://www.mathmuseum.org/
Visit the Web site of this museum (in New Hyde Park, NY) for information about their annual Pi Day Contest.

Helping Your Child Learn Math
http://www.ed.gov/pubs/parents/Math/index.html
The online version of this booklet (published in 1999 by the U.S. Department of Education) provides activities for families with elementary school-aged children. It is designed to help parents to have fun with their children while reinforcing mathematical skills. Many activities are related to measurement and estimation.

Interactive Games
http://www.oswego.org/staff/cchamber/techno/games.htm
This site includes interactive mathematics games and allows the user to create games and quizzes. Two of the pre-made games involve graphing points on the coordinate plane and numerous games involve time.

Investigating Patterns: Symmetry and Tessellations
http://www.camosun.bc.ca/~jbritton/jbsymteslk.htm
Educational consultant and textbook author Jill Britton is the author of this site, listing Web resources for grade 5-8 mathematics. It includes tutorials and fun activities for students and printable activity sheets and lesson plans for teachers. It contains topics such as soap bubbles and honeycombs, Islamic tessellations, M. C. Escher, symmetry by paper folding, and more.

The Joy of Pi
http://www.joyofpi.com/
Find out about the book published by Davis Blatner and discover links to other places on the Web to have fun with pi.

Juvenile Literature Related to Math
http://www.coastal.edu/library/mathlit.htm
The Kimbel Library at Coastal Carolina University has correlated many children’s books with mathematics topics, including measurement, shapes, symmetry, and tangrams.

Cynthia Lanius
http://math.rice.edu/~lanius/Lessons/index.html
Cynthia Lanius, Executive Director of the Center for Excellence and Equity in Education (CEEE) at Rice University, authored these lessons in geometry and other areas of mathematics.

The Lesson Plans Page
http://www.lessonplanspage.com/Math.htm
This site includes free lesson plans for grades pre-K-1, 2-3, and 4-5 in the areas of geometry, measurement, and shapes and architecture.

Literature for Science and Mathematics: Kindergarten through Grade Twelve
http://www.cde.ca.gov/ci/scimathlit/
Sponsored by the California Department of Education, this site includes science and math related literature for children. Titles are listed for both geometry and measurement.

Making Tracks Towards Area
http://library.thinkquest.org/TQ0311000/
Students from South Decatur Junior-Senior High School were the winners of the ThinkQuest USA 2003 contest for the state of Indiana. On this site children can learn about finding area of circles, triangles, squares, rectangles, and other polygons.

Math Central
http://MathCentral.uregina.ca/index.html
This site is an Internet service for mathematics teachers and students. Use the search feature in the “Resource Room” section to find geometry and measurement activities and resources.

The Math Forum at Drexel University
http://www.mathforum.org
The Math Forum offers mathematics resources by subject and problems of the week.

In particular, see these activities:

• Chameleon Graphing
  http://mathforum.org/cgraph
• Varnelle Moore’s Primary Math Activities
  http://mathforum.org/varnelle
• Tom Scavo’s Tangrams
  http://www.mathforum.org/trscavo/tangrams.html

Math Fun Facts
http://www.math.hmc.edu/funfacts/
These “Math Fun Facts” from the Harvey Mudd College Mathematics Department can be used to enrich mathematics lessons. Use the search feature at the easy level to find geometry fun facts. One of the activities you will find introduces Pick’s Theorem.

Maths Thesaurus
http://thesaurus.maths.org/
This site provides an alphabetized listing of mathematics definitions; each definition also includes links to related and/or similar words.

Mathworld (Wolfram Research)
http://mathworld.wolfram.com/Cube.html
This page of Mathworld includes diagrams of all the possible nets for a cube. Explore this mathematics Web site for other polyhedra nets, mathematical art, and origami. Diagrams and photographs are colorful and some are animated.

NASA “Why?” Files
http://whyfiles.larc.nasa.gov
The “Why” files integrate mathematics, science, and technology with a distance learning format. Each episode includes online investigation, activities/worksheets, free educator’s guide, related resources, and implementation strategy.

National Council of Teachers of Mathematics (NCTM)
http://www.nctm.org
This site features professional development opportunities, Web resources, teaching resources, and classroom activities.

NCTM Illuminations
http://www.illuminations.nctm.org
NCTM provides ready-to-use, online interactive multimedia math investigations, mathematics education Web resources reviewed by an NCTM panel, and Internet-based lesson plans. Visit http://illuminations.nctm.org/imath/3-5/GeometricSolids/index.html for an interactive investigation, “Exploring Geometric Solids and Their Properties.”

National Library of Virtual Manipulatives for Interactive Mathematics
http://www.matti.usu.edu
Utah State University, working under a grant from the National Science Foundation, has made available online dozens of free pre-K-12 mathematics manipulatives. Every manipulative is correlated to NCTM standards. Geometry and measurement activities are appropriate for grades K-2 or 3-5. New online manipulatives are added each month.

National Metric Week
http://lamar.colostate.edu/~hillger/ideas.htm
This site includes ideas from the U.S. Metric Association for celebrating National Metric Week.

Native American Geometry
http://www.earthmeasure.com
Students can learn geometry through creating Native American designs. This site explores constructions of regular polygons and connects geometry, art, and history. The site is divided into four areas: foundations, anthropology, design, and education.

Origami Mathematics
http://merrimack.edu/~thull/OrigamiMath.html
This page was created by mathematics professor Thomas Hull. It contains a mathematics bibliography, models and tutorials, and links to other origami mathematics pages.

Origami USA
http://www.origami-usa.org/
This very complete site, run by a membership organization devoted to origami, has a model index, lists origami resources on the Internet, and features fun diagrams, quizzes, and puzzles.

Pattern Block Program
http://www.arcytech.org/java/patterns/patterns_i.shtml
On this interactive site students can easily manipulate pattern blocks to create shapes and designs.

PBS Teacher Source
http://www.pbs.org/teachersource/math.htm
This site includes activities for classroom use, including excellent geometry and measurement resources for preschool and grades K-2 and 3-5.

PBS’s “News Hour Extra” Teacher Resources
http://www.pbs.org/newshour/extra/teachers/math/
Each “News Hour Extra” story includes a lesson plan for teachers that connects school subjects to important news events around the world. Currently available on this page is a measurement lesson, “A Gigabyte of Music, How Much Is That?”

Pearson Learning Group
http://www.pearsonlearning.com/
The Pearson Learning Group, which includes the imprint Dale Seymour Publications, sells more than 100 programs in geometry, from kits to units. Search by subject and grade level.

Pop-up Art
http://www.robertsabuda.com
Robert Sabuda had created delightful pop-up versions of classic children’s books. His Web site includes patterns for pop-ups that can be printed and then made by children. Geometric concepts can be reinforced by making the pop-ups.

Practical Uses of Math and Science
http://pumas.jpl.nasa.gov
This site is an online journal of mathematics and science examples for pre-college students. Measurement and geometry activities for elementary school students are available.

Research for Better Schools
http://www.rbs.org
A special section is devoted to the mathematics and science state resources in the mid-Atlantic region (ENC access centers, informal mathematics and science education, professional development, and technology resources), as well as free publications.

Saskatchewan Education
http://www.sasked.gov.sk.ca/docs/elemath/
Saskatchewan Education created this site, “Mathematics 1-5: A Curriculum Guide for the Elementary Level.”

Thinking Fountain Shapes Cluster
http://www.smm.org/sln/tf/nav/shapescluster.html
The Science Museum of Minnesota presents books, activities, and hands-on experiments related to shapes.

Visual Geometry Dictionary for Kids and for Kids’ Teachers
http://www.math.okstate.edu/%7Erpsc/dict/Dictionary.html
Pre-service students at Oklahoma State University prepared an online, visual geometry dictionary for children and their teachers.

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