Model-Development Sequence Part IV:
Tiling a Playground and Geometer’s SketchpadÒ
Guadalupe Carmona
Purdue University
Mariana Martini
Purdue University
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.