Teachers 
Mastery of Geometric Concepts and Relationships
Through the GeoLeg Program, a five-step method has been developed that leads to mastery of
geometric concepts. We recommend that you use this five-step process to fully engage students
in the learning process. Learning becomes deeper and more lasting.
The goal of this five-step method is to take students from the exploration stage to describing the
concepts and relationships using albebraic expressions or equations.
1) Explore by building with GeoLegs
Use one or more GeoLegs as a hands-on circle or to build lines and polygons for visual
and spatial exploration of relationships and concepts. Students how have the complete
polygon with all interior and exterior angles. Or they can work with intersecting lines to see vertical
and supplementary angle relationships. Encourage exploration with tasks such as "Can a triangle
have more than one right angle?".
2) Observe measures and relationships
Skills are developed as students observe measures of sides and angles and their relationships.
Students can compare the change in angle measures in a triangle as the opposite side is
increased and decreased. They can observe angle differences and similarities between isosceles
and general trapezoids. Encourage predictions.
3) Draw figure and record measures
By drawing the shapes and recording lengths and angle measures of the built figures, students
have the opportunity to determine definitively angle-side relationships, perimeters, properties
and other relationships. Drawing and recording increases observation skills.
4) Form conclusions about concepts
After figures have been built, observed and drawn ask students to draw conclusions about
relationships. This step gives them the opportunity to anticipate theorems and concepts. Remind
them that any one exception is an incorrection conclusion.
5) Write expressions or equations
Take your students through this final stage that demonstrates their understanding of
relationships and equalities. By writing the expression or equation, students have bridged the
concrete measures to an abstract concept.
The GeoLeg Program offers three levels of instruction:
Elementary,
Middle, and
Secondary
Each level is based on the National Standards. The primary goal of the GeoLeg program is to
help students develop geometry relationships and measurement connections between circles,
angles, polygons and solids and to apply these concepts to everyday life.
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