Readers of this blog probably realize that I'm very much into geometric construction. This is in part related to my general interest in puzzles, in and out of the classroom. (In my other life, I construct cryptic crosswords.) My first math education publications were books of geometric puzzles for grades K-10. My pentomino puzzle books stayed… Continue reading Geometric Construction, continued
Tag: Geometry
Asilomar Report: Think First
I attended the California Math Council meeting last Saturday. This post is a report on one talk I attended. It was given by Scott Farrand, a prof at Cal State University Sacramento. (I also reported on one of his talks last year.)This year's talk was called "Think First", which can be interpreted a few ways,… Continue reading Asilomar Report: Think First
One More Pythagorean Proof
I added a third dynamic proof of the Pythagorean theorem on my Web site. It is better-looking, but more difficult to justify than the previous two. You can see all three, starting here. For a brief discussion of how you might use these in the classroom, see this post. --Henri
Geometric Series
... geometric in more than one way! Start with a right triangle ∆ABC, with hypotenuse AB = 1, and AC = b.Draw a parallel to AB through C.Draw a circle centered at C, with radius b.Label the intersection of the line and the circle D.Drop a perpendicular from D to line AC, intersecting it at… Continue reading Geometric Series
Pythagorean Proofs
I just added a second dynamic geometry proof of the Pythagorean theorem on my Web site.Both are proofs "without words", which in reality means that you should use them to generate discussion. Indeed, many words are needed for students to fully grasp what they see, but the words should not come exclusively from the teacher.… Continue reading Pythagorean Proofs
Proportional Relationships
One good thing about the Common Core middle school standards is the emphasis on proportional relationships, and the fact that they are approached in a multidimensional way. In addition to "set up a proportion and solve it", which is probably the most common way to teach this, the standards propose multiple representations and a variety… Continue reading Proportional Relationships
Triangle Similarity Update
As you may remember from my previous posts on this subject, I have been thinking a lot about the Common Core approach to secondary-school geometry, specifically the logical switcheroo that makes triangle congruence and similarity a consequence of assumptions about geometric transformations, rather than the other way around. To support this change, I have started… Continue reading Triangle Similarity Update
Rethinking Triangle Congruence and Similarity
As you may know, I have discussed transformational geometry and the Common Core State Standards for Math (CCSSM) several times on this blog. This summer, I have already been a presenter in two professional development workshops on transformational geometry, and will be involved in two more. This has pushed me to move forward on writing… Continue reading Rethinking Triangle Congruence and Similarity
World Cup Fever
The World Cup happens mostly during summer vacation, which is unfortunate, because it provides a great context for a geometry exploration.I start my book Geometry Labs with lessons about angles, starting from the very basics, and moving on to the inscribed angle theorem. (The book is available in its entirety as a free download here.… Continue reading World Cup Fever
Doctor Dimension
Twenty-some years ago, I started teaching an advanced high school geometry elective class called Space. I offered it every other year until I retired last year. Most of the course was about transformational geometry and symmetry. (That turned out to be excellent preparation for Common Core geometry. I will be presenting and co-presenting four workshops… Continue reading Doctor Dimension
Henri's Math Education Blog 