If you have a collection of Geoshapes, make your own 3D object, then unfold it to find its net. Is there more than one net for your shape? I,""Cube B--Bisecting II,""Cube C--Bisecting Horizontally,""Cube D--Bisecting on the Diagonal,""Cube E--Bisecting III,""Making a Cube from a Cube with a Single Cut," and "Module Cube." Origami

Show 1 x 6 rectangular arrangement of the squares. You may use different colors for the square faces to show how some of the faces coincide when folding them up. There are a total of 11 distinct nets for the cube (Turney 1984-85, Buekenhout and Parker 1998, Malkevitch), illustrated above, the same number Ways to use the book: Most important thing about: 3rd grade, a new friend I met, fractions, geometric shapes, etc. (Great idea when using attributes.) The rectangles are drawn next to each other, joined along the dimension that is the length of the prism.

Overview and Objective

Place the students in pairs or groups of three and share this canvas and let them work on which one of these sets fold up to a cube. Alternatively, consider simply asking each group to find all possible arrangements of 6 cubes that can make a net. If you select this approach, you don't need to share a starting canvas with them.

The maximal cross sectional area that can be obtained by cutting a unit cube with a plane passing through its center is , corresponding to a rectangular section intersecting When the students have found and recorded all 11 (perhaps in a way which shows the 'longest line families'), there are still several possible investigations.

Looking for something different

Today students will use their knowledge of attributes of cubes, work together in groups and find as many ways as possible to make a cube. A two-dimensional pattern for a three-dimensional shape is called a "net." Next, students work together in groups of four, using the two-inch squares, to come up with as many different nets for a cube as possible. Give each group two sets of 6 so that everyone in the group has a chance to try out their ideas. Once they think they have a net, have them prove that it works by copying the net onto the 2" grid paper, cutting it out and folding it into a cube. You may want to show the whole class the first few working nets that are discovered. You can make it into a competition to keep students focused. The group with the most different nets for a cube is the winner. Subtly too, she placed the gallery under the Working Mathematically Process display. This was the process guiding the investigation of finding the number of nets of a cube.

The illustrations above show the cross sections obtained by cutting a unit cube centered at the origin with various planes. The following table summarizesAs a class choose a two- or three-dimensional object in the classroom (for example: the globe or the flag). Have the students come up with attributes while the teacher lists the attributes on the board.