Origami provides a wealth of opportunities for studying angles, both during the process of folding and after the figure is complete. For example, have students complete the first five or six steps of an origami figure, then unfold their paper and lay it flat. Have students label three or four sets of complementary and supplementary angles, and measure the angles of two or three shapes with a protractor.
The triangle is one of the most prevalent shapes in origami. Have students identify the different types of triangles based on side length (scalene, equilateral, or isosceles) and/or on internal angles (right, obtuse, or acute). This exercise can be done both with the finished figure or with a paper unfolded from a figure.
For younger students, the first steps of any origami figure can serve as a great visual illustration of how fractions work. For example, when students fold the paper in half diagonally, ask them how the area of the triangle you now have compares to the original. That is, how many of these triangles would you need to get the area of the original? This will help students visualize the fraction 1/2 as being just like the paper -- the whole unit of the square folded into two smaller triangles.
The completed product of an origami figure provides many examples of geometric reflection. Have students look at the figure from a top-down perspective, keeping the line of symmetry at the center of their vision. Using the line of symmetry as the y-axis, how many reflected shapes can they find?