The study of two- and three-dimensional geometry is made much more
meaningful to students with the use of Geoshapes (Geofix).

They are an excellent, durable manipulative which provides students
with the necessary informal explorations of geometry in earlier grades
and more formal relationships between two- and three-dimensional
geometry in the upper grades.

Most of my work with students and teachers involves the use of
manipulatives. I have used Geoshapes with teachers and students
throughout the United States. They are a welcome addition to the chest of
manipulatives available for teachers to teach geometry at several grade
levels.

Below are only a few of the ideas and skills that can be developed.
Geoshapes allow students to:

-analyze characteristics and properties of two- and three-dimensional
geometric objects;

-explore the use of other representational systems, particularly networks;
use line and rotational symmetry to describe and classify polygons and
polyhedra;

-extend transformations to three-dimensions;

-develop fluency with two-dimensional representations of three-dimensional
objects;

-compose and decompose two-and three-dimensional objects in order to solve
problems;

-use geometric models to represent and explain numerical and algebraic
relationships;

-draw and interpret two- and three-dimensional objects;

-select appropriate units and scale to estimate and measure angles,
perimeter, area, surface area, and volume;

-analyze how changes in the measurement of one attribute of an object relates
to others.

In addition, they provide an opportunity for students to explore many ideas
in science, such as crystals, building structures, and bubbles.

Dr. Don S. Balka, Professor
Mathematics Department
Saint Mary¹s College
Notre Dame, Indiana
Ph.D., University of Missouri
M.S., Indiana University
M.S., Saint Francis College
B.S., Missouri Valley College

Publications:
Balka, D. Mathematics Activities for Home Schooling with Unifix Cubes.
Rowley,
MA: Didax Educational Resources, 1994.
Balka, D. Investigating Three-Dimensional Geometry. Rowley, MA:
Didax E
Educational Resources, 1994.
Balka, D. Exploring Pre-Algebra and Algebra with Manipulatives.
Rowley, MA:
Didax Educational Resources, 1995.
Balka, D. Show Me: Assessment with Unifix Cubes. Rowley, MA: Didax
Educational Resources, 1995.
Balka, D. Algebra: Using Number Tiles. Chicago: ETA, 1997.
Balka, D. et al. Math Steps (Level 7 California Edition). Boston:
Houghton Mifflin, 2000.
Balka, D. and Callan, R. Math, Literature and Unifix: Making the
Connection.
Rowley, MA: Didax Educational Resources, 2001.
Balka, D. and Callan, R. Math, Literature and Manipulatives. Rowley,
MA: Didax Educational
Resources, 2001.
Balka, D. Developing Algebraic Thinking: Problem Solving and Number
Tiles. Rowley, MA: Didax
Educational Resources (in press).