Geometry

High School | Middle School | Elementary School | General

High School

Geometry Problem of the Week from the Math Forum features eight years' worth of geometry problems, with comments and student solutions.

Geometry 3D Shapes is an interactive lesson from the Annenberg Foundation that lets students explore shapes and their methematical properties.

Understanding Ratios of Areas of Inscribed Figures from the National Council of Teachers of Mathematics (NCTM) lets students explore the relationship between the areas of a polygon and an inscribed figure formed by joining the midpoints of the polygon's consecutive sides. (Linked to grades 9-12 geometry standards; teacher materials provided.)

The Mathematics of Rainbows from the University of Minnesota is on online lab that helps students understand geometric properties of rainbows by exploring the laws of reflection and refraction. It also enables students to experimentally determine the angle at which rainbows appear in the sky.

Euclid's Elements is an online version of the classic text from Professor David Joyce at Clark University. All figures are illustrated using Joyce's Geometry Aplet, an interactive program that lets users manipulate them by dragging points in the figure diagrams.

Interactive Mathematics Online is a student-created Web site with sections on geometry, algebra, trigonometry, and chaos theory.

The Fractory provides an explanation of what fractals are and how they are created. Developed by students, the site also allows users to create fractals of their own.

Fractals: An Introductory Lesson explores fractal mathematics with several small, interactive programs for hands-on construction of and interaction with simple fractals. Teachers using the site can request a password that allows students to open "answer boxes" only after they have worked the solutions themselves.

Geometry from the Land of the Incas is a Peruvian site which uses proofs, animation and sound to explore Euclidean geometry problems involving circles and triangles. Students can also investigate how geometric principles were used at ancient cities such as Cuzco, Machu Picchu, or the Nazca Lines.

Middle School

Fun Mathematics Lessons from Cynthia Lanius include Rectangle Pattern Challenges, Geometry Online, Fractals, Dueling Pinwheels, Polyominoes, and more.

Learning about Length, Perimeter, Area, and Volume from NCTM uses interactive figures and dynamically generated graphs to help students learn about geometric relationships among similar objects. (Linked to grades 6-8 geometry standards; teacher materials provided.)

Understanding Congruence, Similarity, and Symmetry Using Transformations from NCTM lets students manipulate a shape and observe its behavior under a single transformation or a combination of transformations. (Linked to grades 6-8 geometry standards; teacher materials provided.)

Understanding the Pythagorean Relationship from NCTM features an interactive figure that helps students understand this relationship and gain experience with transformations that preserve area but not shape. (Linked to grades 6-8 geometry standards; teacher materials provided.)

Native American Geometry describes a system of proportional geometry that has been used for at least 2,000 years. The site includes rules and methods for constructing different shapes, explores design variations that a particular polygon family can generate, and shows how familiar symbols and logos were generated from the primary polygons. It includes many drawings and activities for middle school students, as well as archaeological information.

Geometry in Hawaiian History and Culture from Kamehameha Schools presents photographs illustrating geometry concepts in the natural and built environment.

Origami presents photographs and instructions for mathematical origami.

The Mysterious Tangram Game provides several interactive tangrams for students to solve online.

Different Views of Solids from Harcourt e-Lab presents a visual exercise in which students can slice solids to make congruent plane figures.

The Pythagorean Theorem offers hints that help students discover the theorem on their own as they go through the online lesson.

Geometer's Sketchpad Classroom Resources from the Math Forum provides lessons, ideas, problems, and downloads for Sketchpad users.

Figure This! from NCTM presents mathematics challenges for families. Click on Math Index to find geometry challenges.

Math in Daily Life: Home Decorating from the Annenberg/CPB Project illustrates practical uses of geometry.

BrainBinders are puzzles that can be printed out and folded to create a particular shape.

Elementary School

Fraction Shapes from Rice University includes colorful visual exercises with pattern blocks that help students understand fractions.

Shape and Space in Geometry from the Annenberg/CPB Math and Science Project provides information and activities kindergarten-grade 8 (K-8) teachers can use to show students that geometry is fun, colorful, instructive, and practical.

Making Triangles and Creating Polygons from NCTM has an interactive geoboard where PK-2 can make shapes. It offers tips on helping students describe their properties and develop spatial sense. (Linked to prekindergarten-grade 2 (PK-2) geometry standards; teacher materials provided.)

Learning Geometry and Measurement Concepts by Creating Paths and Navigating Mazes from NCTM lets PK-2 students create paths to manipulate a ladybug and then encourages them observe the shapes or paths they have made. (Linked to PK-2 geometry standards; teacher materials provided.)

Developing Geometry Understandings and Spatial Skills with Tangrams from NCTM lets students use virtual manipulatives to solve tangrams, and use tangram pieces to form given polygons. (Linked to PK-2 geometry standards; teacher materials provided.)

Exploring Properties of Rectangles and Parallelograms from NCTM asks students to manipulate the corners and sides of a dynamic rectangle and a parallelogram in order to discover the properties of these shapes. (Linked to grades 3-5 geometry standards; teacher materials provided.)

A Fractals Unit from Cynthia Lanius explores the mathematics of fractals for elementary and middle school students. Teacher notes and lesson plans are included.

Pattern Blocks: Exploring Fractions with Shapes is an online program that lets students arrange colored shapes on a grid to create patterns or rotate shapes to see their names and definitions.

Shape Walk from the Minnesota Science Museum includes an activity suggestion for K-2 teachers.

Pattern Builder from Harcourt allows students to make and play a musical pattern.

Fun with Shapes is a simple shape-based puzzle for K-1 students.

Mathsurf Shapes from Scott Foresman is a simple online activity that invites kindergartners to click to identify different shapes in a picture.

General

K-12 Internet Geometry Resources from the Math Forum are provided here.

Shape and Space in Geometry from the Annenberg/CPB Math and Science Project, a resource for K-8 teachers, is described under "Elementary," above.

Principles and Standards for School Mathematics from NCTM provides the complete text of the national standards and includes extensive resources, such as Internet-based lesson plans and electronic examples that students can use online.

The Text-only menu provides accessible and printer-friendly access to the Surf Report Archives.

Please contact us if you have questions or suggestions for the Surf Report!