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Monique gave us a nice overview of some her mental math tricks and tips.  I had never really considered thinking of numbers left-to-right before!  Monique also talked about friendly numbers, and I liked her caution:  “What’s friendly to one person isn’t necessarily friendly to another.”

Check out this page for more mental math techniques.

Mila showed us some beautiful geometry problems that I have taken to calling “intuitive” geometry problems.  I have talked about these problems in every one of my classes, from Sophomore Math Analysis to Multivariable Calculus.

A mathematician friend of mine had a birthday party this weekend, and this was my gift to him:

So far we’ve come up with six different solutions, including one that references Cavalieri’s Principle, which I had recently illustrated with CD cases on my website.

Julie shared with us the “Which Cup Will Roll the Biggest Circle?”  investigation (hat-tip to Dan Meyer).  I shared this with a few colleagues, and we all enjoyed exploring the idea and discussing it.  There is a lot of commentary and a fully-fleshed out lesson at Dan Meyer’s blog:  http://blog.mrmeyer.com/?p=4018.

Flannery shared with us here first day of school activity:  small groups are given a bunch of polygons that can fit together to make squares.  The groups task for everyone to make a square, but there no talking or taking is allowed.  A fun team-building activity, and she is looking for more of these types of problems.  In addition, Flannery talked about some math trails she has created for the students at her school.

Chanel shared three nice activities with us:  a quick trisecting-the-square problem, a nice medians and coordinate geometry activity, and a structured investigation into elementary graph theory.   All three are nice ideas to have in the repertoire, and nice handouts to have in the desk.

Japheth shared with us a nice structured introduction into how Cardano solved the cubic equation.  A similar approach, not as cleanly presented, can be found here.

At the end, I talked for about 20 minutes about the ways I use various technologies in and out of the classroom.

Click here to return to CMT Workshop Homepage.

www.MrHonner.com

After attending a brilliant MoMath talk on Mathematical Origami given by Erik Demaine, I have been folding, cutting, and taping more than I ever thought I would.  Here are a few of the ways I have been inspired.  In addition, I have also posted some folding photos on my facebook page.

Intoduction:  Some Basic Mathematical Folding

Basic Folds  Simple demonstrations of the basic folds:  a line through two points; midpoint of a segment; perpendicular bisector of a segment; angle bisector of an angle.

Incenter of a Triangle  Use basic folds to find the incenter of a triangle!

Circumcenter of a Triangle Use basic folds to find the circumcenter of a triangle!

Centroid of a Triangle  Use basic folds to find the centroid of a triangle!

Introduction:  The One-Cut Challenge

One-Cut Challenge:  Triangles  Start investigating the one-cut problem by playing around with triangles.

One-Cut Challenge:  Quadrilaterals  Investigate the one-cut problem with squares, rectangles, and other quadrilaterals.

Fun with One Cut:  Exploring some fractal folding and cutting.

Time 2000 — Fun With One Cut:  My workshop on mathematical folding at the 2013 TIME 2000 conference.

Miscellaneous Folding

Paper Pyramids:  Turning triangles into solids!

Foam Pyramids:  Trying out a new medium.

Foam Tables:  Folding inspired by the American Invitational Mathematics Exam (AIME)!

Fractal Origami:  Turn A1 paper into Pythagoras’s Tree!

Math Art!

Math Art:  Paper Cut-Outs:  A lovely student-created cut-out; accidental art in math exploration.

Math Art:  Smashing Cones:  Pretty soon we were cutting, taping, and smashing cones!

Math Photo:  A Peck of Paper Pyramids

Applications of Mathematical Origami

Real Life Transformers:  An amazing application of origami; truly revolutionary thinking!

Folding Steel:  Another innovative application of mathematical origami.

Automatic Origami:  Check out this origami that unfolds itself!

Other Resources

“How to Fold It“, a book and website by Joseph O’Rourke, Smith College.

Consider the following triangle ABC.

If AC = 15, AB = 20, and BC = 25, and AD is perpendicular to BC, find the length AD.  Try to come up with a few different methods!

We will be talking about right triangles and the Pythagorean Theorem in Session 2.  Please come to the workshop with a favorite proof of Pythagoras in mind, or an activity or approach you use with students when you work with right triangles.

 

www.MrHonner.com