This activity would be most appropriate for middle school students. Have them use different colors of paper when they are working on their origami pieces. Break them up into groups, and distribute worksheets with questions such as "What percentage of the exterior surface is red?" and "What percentage of the total surface of the blue paper used is visible?" You could ask them to find the total area of different colored papers that the entire group used, as well.
Have students in late elementary school or middle school use the Wonderful Whale handout to create a whale using origami. As the handout indicates, you should include terms and definitions that go along with the specific project. For example, quadrilateral, line of symmetry, congruent, triangle and scalene triangle are all listed with their definitions. You might want to include some more of your own. Engage in a discussion with your students about where else they can find these terms illustrated in every day life.
Follow directions from Teacher Lesson Plan and Resource to create your origami cube. Allow the students to watch you make the cube one or two times, or to work in groups, since this project can be a bit tedious. Once the cubes are completed, ask what the students notice about the cubes. Let this discussion lead into a lecture focused on properties of cubes, such as the fact that it has 12 sides, eight corners and six faces.
Although you can use origami to demonstrate other components of math, origami also has its very own set of mathematical rules. After creating pieces of origami, ask students if they can figure out what some of the rules might be. For example, they might find that the crease pattern of a squash fold will always bisect an angle twice, or that a single straight cut is all it takes to cut a planar straight-line drawing after folding.