Students think about the linear measurements and the corresponding area and volume measurements of the cube and rectangular prism. Ideas of scaling are investigated using both a manipulative and technology. Visiting the problem using both techniques addresses a variety of learning styles, brings the abstract into the concrete, and offers interaction with the computer as students investigate, discover, form hypotheses, draw conclusions, and benefit from the quick feedback, the interest and the increased visualization of scaling that a computer provides. Once students have had these experiences it is important to arrive at a synthesis by spending the time necessary to internalize the concepts. Manipulatives can provide space for group work, computers can afford individual explorations, and a synthesis can take place during a full-class discussion.
Students can then demonstrate their individual understandings through the writing process.
Have them fold on the lines and tape. Pass out one sheet of isometric dot paper to each student and instruct them to draw a unit cube. Discuss the idea of why it is called a unit cube. Introduce the idea of a scaling factor for the sides of the cube. Draw another cube using a scaling factor of 2.