I do origami at all grade levels. So many educational bases can covered. Realizing something starts as a 2-d shape and then becomes 3-d is a concept ODE will test for under the heading of nets on the math test in 4th and 5th grade achievement tests. I use origami to introduce and work on fractions, different shapes, and lot of following directions and listen skills are directly engaged when a student does origami.
In the pics above we had worked on doing cups and when the students get the hang of it, I pass out small strips of paper they can fold and cut into small squares to make small cups. All ages delight in doing small stuff. I still like it too.
We also do bigger cups, as the student above is holding up. Here you can see he has unfolded the cup(as per instructions) and is coloring in the shapes created in folding the cup. 6/8 are triangles and 2/8 are trapezoids.