This interactive applet lets students create quilting type patterns and explore tessellation possibilities. The applet gives learners a choice of six polygons that can be turned or flipped and fitted together. Suggestions for exploration and five challenge patterns are provided. The tool supports a number of lessons and units including What's So Special About Triangles and Virtual Pattern Blocks (cataloged separately).

This five lesson Illuminations unit gives students an opportunity to create and analyze numeric and geometric patterns with particular emphasis on growing patterns. The lesson titles are respectively, What's Next?, Patterns On Charts, Growing Patterns, Exploring Other Number Patterns and Looking Back And Moving Forward. Each lesson includes learning objectives, material list, instructional plan, linked resources and assessment options.

This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).

"Each student creates parallelograms from square sheets of paper and connects them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square" (from NCTM's Illuminations).

In this math activity, learners classify polygons according to more than one property at a time. In the context of a game, learners move from a simple description of shapes to an analysis of how properties are related. This lesson guide includes sample steps in the game and extensions.

Learn about the dynamic relationships between a jet engine's heat loss, surface area, and volume in this video adapted from Annenberg Learner's Learning Math: Patterns, Functions, and Algebra.

This interactive activity adapted from the Wisconsin Online Resource Center challenges you to plan, measure, and calculate the correct amount of roofing material needed to reroof a house.

In this web-based application from Illuminations students must sort shapes based on the categories of the Venn diagram. Users can choose the categories from a drop down menu. The application includes instructions and exploration steps.

This interactive tool allows a user to create many geometric shapes. Squares, triangles, rhombi, trapezoids and hexagons can be created, colored, enlarged, shrunk, rotated, reflected, sliced, and glued together.

This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180_.

Students use this Flash tool to build tessellations, discovering which shapes tile the plane with copies of themselves or together with other shapes. Regular polygons with 3-12 sides of the same length are provided; students may arrange, rotate, group, ungroup, paint, copy, and erase them.

Students construct "a tetrahedron and describe the linear, area and volume using non-traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed." (from NCTM Illuminations)

In this activity, learners walk the sides and interior angles of various polygons drawn on the playground. As they do so, learners practice rotating clockwise 180 and 360 degrees. Learners discover there is a pattern to the sum of the interior angles of any polygon.

I use this activity to reinforce the vocabulary used when practicing with polygons.  Students are asked to describe a polygon by identifying what it is, but also what it is NOT. 

In these two geometry activities students explore the properties of triangles, discover what shapes triangles can form, and investigate what shapes can form triangles. Each activity includes a student recording sheet, extension ideas, and questions for students. Cataloged separateley within this site are the Patch Tool and the related How Many Triangles Can You Construct? activity.