Talk:Polygon Exercises

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Instructor Notes

I like problems 3, 6 and 7. These problems address some topics that will come back later in the course.

In problem 3 we ask people to show that if a quadrilateral has congruent opposite angles then it has to be a parallellogram. I have the students use the "fact" that if a transversal meets two lines so that opposite interior angles are congruent then the lines are parallel.

Problem 3 helps answering problem 7 and will allow us to later show that all triangles tessellate. (They combine into parallelograms which are easily shown to tessellate the plane).

Problem 6 is the first step to creating fractals (the Sierpinski triangle) and helps illustrate the difference between congruent and similar.

Problem 7 will help us later when we show that all triangles tessellate.

--Barta 15:29, 17 September 2007 (CDT)


Problems 8-12 don't really fit here. Or at least they're not written to fit here. I think they make a good preview of things to come, but the wording makes them impossible to assign unless students have read further into the book. I'd suggest we move those problems to a new set of exercises associated with the Introduction to Tessellations page, maybe call them Basic Tessellation Exercises. Possibly some of the Polygonal Tessellation Exercises could join them there (maybe the pentomino problems, or some of the basic 'what tiles are in this picture' questions).

My alternate suggestion would be to rewrite them using less technical terminology (basically, don't assume 'tessellation' or 'line of symmetry', etc.)

As a further note, #8 doesn't make any sense - "indicated"? Pattern blocks?

A separate issue is that we don't define kite in the text. It's only in the Quadrilaterals Exploration. I'd suggest rewriting the two problems that have kite so that they define what a kite is. Or, we could define it in the text, but that seems like a lot of trouble for a term that's somewhat esoteric. Bryan 11:23, 6 February 2009 (CST)

I have no problem with moving problems 8-12.

In number 8, the idea is to have the students make multiple copies of the polygons mentioned ("indicated") in the problem and use the physical copies of the polygons to check if / how they tile. If it didn;t make sense to you, it needs to be rewritten I'd say. Barta 21:27, 11 February 2009 (CST)