I adapted Jeff De Varona’s Diamond Building lesson into a 3-act task, but instead of having act 3 be a reveal of the actual height, I had students calculate the height a second way to confirm their results. It took 2 short class periods (about 40 mins each) with my struggling students, but it may be able to be completed in 1 class period if you spend less time noticing/wondering/developing questions. I had students work in randomly assigned groups of 2 or 3. They were engaged the entire time and seemed to enjoy the task.

I started by only providing sheets 1 and 2 at first & running it like a typical 3 act. Then I provided “diamond height method” info via projection & allowed students time to work using big whiteboards and share their conclusions. This activity was followed the next day by providing the pages 3 & 4 of the attached file and having students determine the building’s height by the “clinometer method” then discussion of actual height & sources of error.

I used this lesson as a summary to a unit on right triangles, a few days after doing a clinometer activity based on this. My favorite part was listening to students try to determine how to find the height of 1 diamond using only the fact that it is constructed of 2 equilateral triangles with sides length 7 feet. Some students constructed 30-60-90 triangles and used trigonometry, which is exciting because I did not explicitly teach special right triangles in this geometry class. Most students realized they could use the Pythagorean theorem.

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Love it! I have a question about special right triangles… It isn’t in the geometry standards, and I don’t find them mentioned anywhere in CCSS, except in forth year classes inTF.A.3. Where it says to use special right triangles to determine values of sine, cosine, etc…. Will you teach these explicitly in another unit, or are they omitted from geometry? New are currently discussing this and would love your insights.