Grades 6-8: Geometry
10-day unit—80 pages

Effects of Changing Lengths is part of the AIMS Essential Math Series that uses real-world investigations, comics, and animation to engage students and help them discover and make sense of key mathematical concepts. The units in this series are narrowly focused, conceptually developed, and carefully sequenced to provide a continuum of introduction, development, and reinforcement of the essential ideas.

In Effects of Changing Lengths, students will develop fundamental understanding of key measurement and geometry concepts.

Enlarging images on a copier, comparing values in a pizza purchase and evaluating the points in an arcade game provide contexts for studying how changing the lengths of figures affects their surface area and/or volumes. Cutting paper and wrapping arrangements of interlocking cubes provide the opportunity to reinforce and practice measurement skills while recognizing that area grows as the square of the scale factor and volume growth is represented by the scale factor cubed.

The “big ideas” expressed through creative activities in this book are:

• Changes to Perimeter and Area: The perimeter of scaled figures changes by a factor the same as the scale factor, while the area changes by the square scale factor.
• Changes to Surface Area and Volume: The surface are of scaled solids grows by the square of the scale factor while the volume changes by the cube of the scale factor.

The book includes a CD with interactive PDF instructions. Interactive links in the digital format enrich the learning experience with videos, animation and Flash® applications. Using a projector or interactive whiteboard allows the materials to display for the class and supplements the teacher’s instruction.