Friday, July 5, 2013

CPM Geometry (Chapter 1) and Introducing Desmos

During the first chapter of the CPM Geometry textbook, students review a lot of Algebra skills.  At the close of chapter one, students have been introduced to the definitions of special triangles, special quadrilaterals, and regular polygons.

At the beginning of chapter two, I would introduce students to a graphing program called Desmos. Since students work in groups of four, each student would receive a different set of shapes to construct using this program.  If a shape is repeated within the group, the students would construct the shape in different quadrants. To vary the experience further, I would provide the coordinate of one of the vertices of the polygon.

Once completed, each student would send his/her project to my geometry Dropbox account.  Here is an example of a parallelogram and an isosceles triangle.

Click on image to enlarge it.

Saturday, June 29, 2013

Other Geometries ? (Origami)

As I prepare for the upcoming school year, I have been thinking about students exposure to geometry.  Prior to adopting our current textbook, my students would explore hyperbolic, spherical, and Euclidean geometries. (I didn't use a textbook.)  With our current textbook, students explore only Euclidean Geometry.

This posting are my thoughts about introducing my students to origami. I am planning to write a weekly posting about other big ideas for next school year.

Anytime I ask students about origami, they talk about folding a crane or a frog.  I would like students to understand the changes that have occurred with the use of origami in the last few decades. "BETWEEN THE FOLDS (a movie) chronicles 10 stories of several fine artists and theoretical scientists that are abandoning more conventional career paths to forge lives as modern-day paper folders. Featuring interviews with and insights into the practice of these intrepid paper folders. Through origami, these offbeat and provocative minds are reshaping ideas of creativity and revealing the relationship between art and science."

I still believe students should experience the act of paper folding. It is fun and allows us to explore (or extend) ideas in a traditional geometry course.  But I would like my students to learn about these paper folders and how science has been impacted by their work. Of the 10 stories chronicled in Between The Folds, I really enjoyed Robert Lang and Erik Demaine. 

The video is a Ted Talks presentation by Robert Lang. The presentation is called Flapping Birds and Space Telescopes.He discusses how origami has changed because of mathematics.

Erik Demaine is the youngest MIT professor to be hired, at 20 years of age. In this video and the Between the Folds segment, Erik discusses how mathematics and origami are being used to study folding materials (such as a table) and how folding proteins impact our health.

Erik got me thinking about folding proteins being used to predict possible diseases that may impact my health or the health of a family member or a friend.  So I spent some time searching for other resources.  And there are many.  Here are some examples of other work being done:

McGill University
Stanford University
Science Daily

Also Erik talked about sheets of special material that might be used to fold different items for your house.  You simply download a program so the sheet of materials fold into a table, chair, or bed. Here are some examples of other work being done:

Purdue University
Science Daily

The University of Texas has developed an origami test strip to cheaply test a person for malaria and the HIV virus.  At a cost of ten cents per test strip,  people will eventually have the means to test for these diseases.

(Other than ideas, I don't have student materials to share. I am writing a digital document using  Joomag for my students.)

Wednesday, June 19, 2013

Make Over Monday

Dan Meyer, from his blog dy/dan, writes:
Teachers appraise and modify curriculum materials to determine their appropriateness for helping particular students work towards specific learning goals. This involves considering students' needs and assessing what questions and ideas particular materials will raise and the ways in which they are likely to challenge students. Teachers choose and modify materials accordingly, sometimes deciding to use parts of a text or activity and not others, for example, or to combine material from more than one source.
Every Monday, during this summer, Dan will post a problem from a textbook and start a conversation about how we could modify it. The details of that makeover may take the form of a loose sketch or something more formal.  So I am responding to this week's posting.

I. Hodge shared this idea, which was my first thought.  Students lack experiences with home improvements so exposing students to flooring, painting, or any other project that many homeowners will complete or hire a contractor to complete is "eye opening" to most students.

So here is another approach to this problem.

For the last few years, Empire Carpet will run a 60% off flooring special.(see commercial)

Here is the problem:

Rodney and Emile are moving into a new home.  Unfortunately they want the same bedroom.  So their parents decide to use the Empire's 60% off flooring commercial to determine who gets first pick of a bedroom.

The two rooms are showing the amount of carpeting you will purchase based on Empire's commercial.  Your task is determine the dimensions (in centimeters) of both bedrooms.

Monday, June 10, 2013


I have been following many blogging sites for the last few years, and I decided to join the blogging community.

I have been teaching for twenty-six years, with twelve years at the middle level and fourteen years at the high school level.  Currently I am teaching geometry - which is the reason for the name of my blogging site.

My school adopted CPM's Common Core Geometry textbook - which will be the focus of some of my postings.