I am going on memory right now and will do some additional research this summer but I seem to recall something on iTunes university about math in nature. This series shows real life examples of math in nature. Then they go on to show the mathematics behind it. I recall watching the episode on nautilus and if I remember correctly, it used 30/60/90 triangles. I am thinking I can show the episode on the nautilus and the math behind it. I can then have them create their own nautalis on the geoboard app on my iPad. This would happen toward the end of the triangle section.
I am adding to this as I was grading papers after having read a bit on fractions and realized I can use the Geoboard app to have students create representations for fractions such as what is 1/3 or 1/3 x 1/2. I can also use it to show the distributive property and multiplication of binomials. This opens more uses of the app for me.
I should be letting you know on Monday when I am offering my e-book for free.