While you might not want to foster a competitive atmosphere in your classroom, a creative racing game can reinforce your students' knowledge of two-dimensional shapes. Call two students to the front of the room, and give each a pipe cleaner. Call out a geometrical shape you have studied. Students must race to form the shape out of the pipe cleaner. You can hold a tournament where the winner stays on to face a new challenger until defeated. Crown a geometry king or queen at the end of the game.
Students at the sixth-grade level have tons of energy. Take advantage of this fact to teach a geometry lesson. Break the class into groups of two students. When you call out a shape, each group must make the two-dimensional shape physically with their bodies. For the next round, groups must merge into groups of four and repeat the exercise with a new shape. Double the size of the group at the end of each round until the entire class must work together to make one giant shape.
Make your students into city planners, and teach a geometry lesson at the same time. Have each student design a city or neighborhood on a piece of paper. Specify that each city plan must contain a certain number of shapes, such as a trapezoid, two circles, a rhombus and three different kinds of triangles. Let students have fun and be creative as they use two-dimensional shapes to make roads, houses, movie theaters and restaurants. If you have time, ask students to come to the front of the room and explain their designs to the rest of the class.
A number of online games teach two-dimensional shapes at the sixth-grade level. The website Apples 4 the Teacher (see the link in the References section) allows students to make Chinese tangram designs by rearranging a variety of two-dimensional shapes. At Math is Fun (see the link in the References section), students can play with an interactive quadrilateral, dragging the four points of a four-sided shape to make any new shape they want. For a more advanced game, students can use the online Triangle Explorer to calculate the area of a triangle. The game keeps score for students so they can compete against one another.