Prove to yourself that the area of a parallelogram is the base times the height.
Here's an overview video:
Three puzzle sets are provided. Each set can be arranged to form the same rectangle and rearranged to form different parallelograms with the same area.
Teachers: Have students follow the Exploration Guide (pdf file). It asks some good questions to get them thinking mathematically.
Here are the Common Core standards associated with this manipulative: 3.MD.5, 3MD.8 and 4.MD.3
I've included the source files (SketchUp) in a zip archive.
Print out the base container and the three puzzle sets and follow the exploration guide.
Here are the colors I used in the video:
BLACK: Base container (with white text, see below)
ORANGE: Puzzle Set A
YELLOW: Puzzle Set B
GREEN: Puzzle Set C
I don't have dual extrusion on my printer, so to get the white-on-black for the container, I started with black then paused the printing at 4mm and switched to white filament. Looking forward to learning how to make dual extrusion files soon.
Note: If puzzle set C doesn't fit right, try the alternate version.