Saturday, February 27, 2016

7A: Tessellated Ceilings of Iranian Mosques

Celling of Hazrate-Masomeh’s mosque in Qom, Iran, all images courtesy of Mehrdad Rasoulifard (@m1rasoulifard) via Colossal

Tessellated Ceilings of Iranian Mosques

Related to our discussion of tessellations, this article came across my feed. The beauty and artistry of these mosques are stunning. Enjoy.

Wednesday, February 24, 2016

7 Math and Art Connection: M.C. Escher Tessellations

Today, we began exploring how to translate a figure in geometry. We have already looked at line symmetry, rotational symmetry, and reflections. In the course of our discussion, I casually mentioned M.C. Escher's tessellations. I was startled to discover that most of the class had no idea of who M.C.Escher was. I promised the class that I would post a few links so they could explore his work further. 

M.C. Escher (official site) Maurits Cornelius Escher
The Mathematical Art of M.C. Escher - Escher Gallery 

Saturday, February 6, 2016

Snapshot: 8A Documenting the Process

One of the great challenges that my students face in math class is documenting their thinking on paper. Most students are resistant to taking the time to show their work in detail. It is difficult to capture all of the decisions and step that are required to show someone how they achieved their result. Every so often, students are able to capture their thinking in a clear, detailed, and concise manner. These are two exemplar samples of what we hope every student can achieve. 

The eighth grade is learning how to factor polynomials. We began the journey by learning how to multiply monomials, binomials, and polynomials. The class spent several periods looking for the clues on how to factor a trinomial in the form of a^2+bx+c. To solidify their learning, they were asked to write out the steps to teach someone how to factor this type of trinomial. Many found this task difficult because they struggled to generalize the steps. Most could tell you what to do with a specific example, but not how to do it without specifics. These two examples were the most successful at capturing what needs to happen to factor a basic trinomial in the a^2+bx+c form.  Both capture the essence of the procedure in very different ways. One is verbal and the other is expressed with tables. We shared in class to help everyone get better at documenting their thinking. 

Snapshot: 7A Playing Card Proportions

The seventh grade is in the midst of reviewing their understanding of ratios and proportions. They worked with unit rates, did unit conversions in customary and metric units, solved proportions, found percent of change, and applied percents to mark ups and discounts. As we transition into our geometry unit, the class was asked to apply their skills with proportions to make a scale drawing of a playing card. 

Detailed calculations done to scale the playing card.
I like this project because it give the students a sense of how much mathematics is embedded in apps and tools that allow them to proportionally scale images on their devices: click and dragging the corner of an image; pinching or expanding an image on a touch screen; or when a mapping application zooms in or zooms out.

The project allowed for student choice and differentiation. There was a large range of difficulty depending on the card they choose (easy = ace, medium = number cards with increasing difficulty as numbers approached 10, difficult = face card) or the scale factor (easy = 2x, medium = 3.5x, difficult = 1.75x). The project required careful measurement and an understanding of proportional change. 

The students did an outstanding job on the assignment. The scale factor range was 0.5x to 8x. Please stop by the first floor of the sixth street building to check them out in person.