Separate cardboard cutouts of geometric shapes by the desired criteria. You may choose to group together shapes that are similar in size or shape. As you do, point out the intrinsic characteristics of the shapes as well as lines that form the symmetrical aspects of the shapes.
Name the geometric shapes you will include in the game. Creating a geometry game requires a definition of the parameters that will be included and which limit the discussion to certain properties of the geometric shapes.
Begin the game by choosing one shape and encouraging your players to describe the properties. Beginners may use basic modes of description while those more advanced will undoubtedly refer to the shape by its correct name. Advanced players should be challenged to explore simple shape manipulations, such as separation of one rectangle into two equal pieces. Permit the players to use a ruler and pencil to draw a separating line on the cardboard cutout.
Offer the players scissors to actually separate the shapes along the lines they have drawn to get a feel for the newly designed shapes.
Encourage players to describe the shapes they now see. Once again, permit players to use their own words but now suggest the use of lines of symmetry in their descriptions. Review terminology that is associated with the newly created shapes.
Draw on the early success of the players be creating geometry games that build on the newly understood relationship between shapes. Ask the players now to use their understanding of the fractional relationship that exists between two squares and one rectangle to apply it further. While doing so, suggest that they describe the change of the patterns with respect to the changing attributes.
Include other shapes into the mix and in addition to rectangles and squares now permit the use of circles and triangles.
Offer brief interludes of free play with the newly created shapes to foster a further understanding of the relationships that exist between various two dimensional shapes. As you create geometry games, consider incorporating mini-games that pose the potential for showcasing different relationships. For example, you may offer a timed mini-game that challenges the players to create recognizable objects—such as houses, giraffes, or buses with the shapes which they currently possess.
Expand on the game as necessary to challenge the individual players according to their skill levels. Present advanced players with the opportunity to apply their knowledge of perimeter calculations and area measurements within the confines of another mini-game.