Model-Development Sequence Part IV:

Tiling a Playground and Geometer’s SketchpadÒ

 

Guadalupe Carmona

Purdue University

lupitacarmona@purdue.edu

 

Mariana Martini

Purdue University

mmarti10@purdue.edu

 

In this poster session, the fourth of a four-part project, we present a Model-Development Sequence: a Model-Eliciting Activity followed by a Model-Exploration Activity, designed for upper elementary through middle school mathematics curriculum.  The math concepts elicited on this sequence include: rotation, translation, reflection, and analysis of angles in regular polygons.

Model-Eliciting Activities present a problem, based on a real-life situation, to be solved by students in small groups.  The solution calls for a mathematical model to be used by an identified client, or the person who needs to solve the real-life problem.  In order for the client to implement the model adequately, the students must be very clear in describing their thinking processes that justify their solution.  Thus, they need to describe, explain, manipulate, or predict the behavior of the real world system to support their solution as the best option for the client.  Like in real life, there is not a single solution but there are optimal ways to solve the problem.

Model-Exploration Activities are a follow-up for Model-Eliciting Activities.  Through the use of computer microworlds, these activities allow students to encounter new representational systems that help them formalize some of the math concepts involved in the solution of the Model-Eliciting Activity.

The Model-Eliciting Activity presented, Tiling a Playground, is about a contest to design a creative tiling pattern for a school, and the winning design will decorate the playground.  Students are asked to explain the process of creating a tiling pattern using given geometrical shapes.  Tessellations is the Model-Exploration Activity that follows Tiling a Playground.  Through Geometer’s SketchpadÒ, students are encouraged to explore and generalize properties of vectors and translations, while developing their own tessellation.