This project is an excellent introduction to 3-dimensional geometry, volume and surface area of solids. Some students say that they "can't draw, but practice with visualizing and drawing in 2 and 3 dimensions will help them in be able to draw "3D" drawings, and this will help them in Geometry, particularly in the chapter on volume and surface area of solids. Almost all students like games and puzzles, and this project is much like a puzzle.
If some students find it difficult to visualize which patterns make a cube, suggesting that students work in groups may be beneficial. After students have drawn as many patterns as they can think of, ask them to check and see if they have repeated any. This provides a good opportunity for the teacher to draw one pattern on an overhead transparency, and then flip the transparency over horizontally. The terminology of transformations can be introduced: "this pattern is a reflection of that pattern" etc. The concept of a "left-hand" and "right hand" pattern can also be discussed.
Practicing their ability to visualize and draw 2- and 3-dimensional objects will improve students understanding and abilities in working with volume and surface area of solids.
Can you draw any other patterns that will fold into a cube? Make copies of the grid below (or draw on tracing paper placed overy this grid) to draw your solutions.
You will find the answers on the next page:
8.9 Cube Answers