For most of you, school started recently, or will start soon. For me, this is the beginning of the third year of my retirement, and I'm starting to get used to the weirdness of my new life.It turns out that August is by far the most intense work month for me, because that's when I… Continue reading First Day of School
Author: hpicciotto
Triangle Congruence and Similarity tweaks
I just tweaked my documents on a transformational approach to triangle congruence and similarity, thanks to feedback from Bill McCallum.- Version 1 (more opinionated and footnoted)- Version 2 (co-authored with Lew Douglas, better section on similarity)The main change is to the SAS proof, which did not correspond to its illustration. If you downloaded earlier versions,… Continue reading Triangle Congruence and Similarity tweaks
Handwritten Pythagoras
Geometric Construction for Middle School
If you've been reading my blog for a while, you know that I'm a big fan of geometric construction. I have written about it here more than once, and my Web site includes quite a bit of curriculum involving construction. See the end of the post for additional links. I have many reasons for this… Continue reading Geometric Construction for Middle School
Ariadne’s String
This post is about a problem I learned about at Unsolved K-12, and was reminded of at Integer Sequences K-12. Both conferences were joint meetings of mathematicians and educators, organized by Gord Hamilton. Like several of my favorite problems from those conferences, this problem involved explorations on a lattice.Here is the problem:- You must get… Continue reading Ariadne’s String
Integer Sequences
Last winter, I attended an interesting meeting of mathematicians and math educators in Banff, Canada. Our charge was to compile a list of integer sequences that would offer suitable problems for students (and teachers) at each level from Kindergarten to 12th grade. It was a sequel to 2014's Unsolved K-12 meeting, and once again was… Continue reading Integer Sequences
Spirograph
Perpendicular bisector theorem
Under the assumptions of the Common Core, the triangle congruence criteria (SSS, SAS, ASA) are no longer postulates. Instead they are to be derived from transformational geometry. There are many consequences to this state of affairs, and I have written about it on this blog: one, two, three. I have developed bits of curriculum, which… Continue reading Perpendicular bisector theorem
Themed courses?
This is the third in a series of summer posts on big-picture planning for a math department. Previous installments: Pruning the Curriculum, and Mapping Out a Course. Today's post represents a further zooming out, to discuss my thoughts about how to organize content across courses. Of course, many if not most teachers are not consulted… Continue reading Themed courses?
Geoboard Triangles
One way to discover or apply the formula for the area of a triangle is to explore area on the geoboard. The initial activities should be along the lines suggested in my Geometry Labs Lab 8.4. (Free download.)After that, one can zero in on triangles, by asking a question like: "Find triangles of area 15."… Continue reading Geoboard Triangles
