## Exploring Geometry Concepts

This collection of resources helps students develop geometric thinking about shape and space in mathematical and real-world contexts. Students will gain knowledge and rich conceptual understandings of two- and three-dimensional shapes, patterns, transformations, symmetry, and visualization. Learning resources include interactive media, videos and games for both primary and upper elementary grades.

## Collection Discussion

Replies: 3
Created:10-14-2012 by Uncle Bob
Last Post01-07-2013by Uncle Bob

This interactive Flash activity asks the user to sort shapes into a 2 by 2 chart, known as a Carroll Diagram, based on their properties. Properties used to sort include "quadrilateral" or "not quadrilateral" and "regular polygon" or "not regular polygon."
2, 3, 4, 5, 6+

This interactive Java applet simulates the traditional Chinese tangrams puzzle that allows users to develop spatial reasoning skills. Users may explore freely, solve any of the 14 puzzles included, or work through four other sets of challenges. Users can rotate and flip pieces and change their colors. Some background, instructional uses and instructions are provided.

This interactive Flash lesson helps students to distinguish squares and triangles and be creative in the context of Navajo rug design. The animated pages give printed and voiced instructions in English. A teacher guide (pdf) is available - see #30 at MathActive Lessons for Grades K-2, cataloged separately. Navajo, Spanish, and non-spoken versions of the lesson are available also at the Lessons page.

This interactive Flash applet gives students the opportunity to copy, create and extend repeating patterns utilizing two different triangles. Many patterns are possible since the angles in both are multiples of 30 degrees and the shorter sides are equal in length. The Teachers' Notes page includes suggestions for implementation, ideas for extension and support, and printable sheets (pdf).

This activity has learners working with shapes and visualizing composite shapes. Learners solve a series of 13 tessellation problems, ending with two Escher designs. Learners slide geometric and irregular pieces to make the tessellations.
1, 2, 3

This activity has students experiment with turning through angles in a conceptual, qualitative way. It can be used prior to studying angles quantitatively. Students are given descriptions of physical phenomena to emulate on either the included Flash applet or a hands-on manipulative. They rotate colored disks in a circle to mimic turns and angles. The Teachers' Notes page includes suggestions for implementation, discussion questions and instructions for making the manipulative.

This interactive applet reinforces students' knowledge of the properties of rectangles and gives them a game in which to form and test hypotheses. In a 5x5 grid in which a rectangle has been hidden, students try to fix the location with the fewest number of probes (Note: press 'Start' to hide a different rectangle). Ideas for implementation, extension and support are included along with printable sheets and video clips of classroom testing.

This activity provides an opportunity for students to work on spatial visualization and number sense together. Learners are presented with a hundred grid and told there is another printed on the reverse side. They must work out the unseen numbers for several positions on the grid. Ideas for implementation, extension and support are included along with a printable sheet of grids.
Pre-K, K, 1

This interactive game challenges learners to create shadow shapes utilizing the two-dimensional shapes provided. Players use their knowledge of shapes and spatial sense to determine what individual pieces fit together to match the image. The activity is part of the PBS Kids series "Sid, the Science Kid."

This interactive application helps learners develop visualization skills in relation to 3-dimensional figures. In this Cyberchase activity, each member of the CyberSquad is standing in a different place, but they are all looking at the same arrangement of blocks. The challenge is to figure out exactly what each member sees from his or her point of view and make a 2- dimensional diagram of the solid figure's projection. A commentary and discussion questions are provided.

This activity gives students a chance to visualize a two-dimensional net of a three-dimensional object. Students are shown three views of a decorated cube and a net of six plain squares. They must decorate the net so that it folds to a cube consistent with the views. An interactive applet is provided. Ideas for implementation, extension and support are included along with three printable sheets (pdf).

In this game students use the isometric transformations (sliding, flipping and turning) to sink a golf ball into a cup. There are nine holes in the course and learners are challenged to meet or break a par score.
3, 4, 5, 6+

In this game students use basic transformations (sliding, flipping and turning) to make one or more shapes coincide with a congruent shape on a Cartesian plane. Players are challenged to complete the matching in the fewest possible moves.
3, 4, 5, 6+

This set of seven interactive Java puzzles and three inquiry tasks requires students to use spatial visualization to construct and complete a motion along a path. A marble must travel through a maze of right-angle mirror reflections and return to its origin. A practice session and a utility for designing an original maze are provided.

This three-part interactive lesson has students use spatial sense and analytical skills to investigate the parts of three-dimensional polyhedra. Students view and control animations of the solids and their nets, which help them to count faces, edges and vertices, and to establish Euler's relation among those counts. Teachers notes, worksheets and printable nets are provided.