Students create rules to form new quadrilaterals from existing ones, use dynamic geometry software to construct and make conjectures about these, and attempt to prove their conjectures.
A five-part proof progression can support diverse populations when engaging in proof-and-reasoning tasks.
Nicholas J. Gilbertson, Samuel Otten, Lorraine M. Males, and D. Lee Clark
For many American students, high school geometry provides their only focused experience in writing proofs (Herbst 2002), and proof is often viewed as the application of recently learned theorems rather than a means of establishing and understanding the truth of general results (Soucy McCrone and Martin 2009).
Dick J. Smith and Eric F. Errthum
Many mathematics instructors attempt to insert guided exploration into their courses. However, exploration tasks frequently come across to students as contrived, pertinent only to the most recently covered section of the textbook. In addition, students usually assume that the teacher already knows the answers to these explorations.
A set of problems of many types.