The Parallelogram Machine is meant to illustrate why rectangles are also parallelograms. I have an activity entitled Quadrilateral Sorting, or How can a square be a Rectangle? that uses 3 models of these. As you can see, the machine makes only parallelograms. How does that work?
Well, the opposite sides are equal. In the drawing above, the two short sides hold the two longer sides exactly the same distance apart, so those two long sides are parallel. And vice-versa. You can let your students try to make a quadrilateral that has equal opposite sides into a shape that doesn’t have parallel opposite sides.
Any shape you can make with these is a parallelogram. Including these.
Here’s a .pdf file that you can use to make any of the above Parallelogram Machines. Print it on cardstock, cut the strips out with a paper cutter, and fasten the vertices with small paper fasteners.