Park City Mathematics Institute Japanese Lesson Study Research Lesson

Studying Dimensionality Through a Stair-Step Fractal
by Gail Burrill, Joyce Frost, Tony Anderson, Jennifer Kumi Burkett
Jerry Gribble, Jill Ryerson & Celeste Williams

 Lesson Study: A PCMI Experience [view html page at the College Board site] WHAT IS IT? A background paper and a related classroom activity about studying dimensionality through a stair-step fractal. GRADE LEVEL/STRAND Secondary geometry CLASS TIME 1 class period for the basic activity with a second for possible extensions MATERIALS scissors, quad graph paper (cut to 32 squares by 40 squares), a large fractal model for the 1:2 scale factor, large sticks that can be used to show the height of each stair on the large model, several small models of the 1:3 fractal, a few spare fractals partially created in case students make a mistake, instruction sheets, butcher paper for student presentations if desired

OBJECTIVES
Lesson study can serve different purposes; engaging teachers in the collaborative work of designing a lesson can build a sense of community among the teachers, increase their knowledge of mathematics, increase their understanding of the curriculum, build a reperatorie of strategies for teaching a particular concept and in general, and help teachers learn about how students come to understand and process mathematics. The process itself is the goal; the lesson is a by-product that can

Mathematical Objective of the Lesson, Studying Dimensionality Through a Stair-Step Fractal
When considering the measurements length, area, and volume, students will be able to clearly articulate the effect of scaling one measurement on the two remaining measurements.

ABSTRACT

APPENDICES
Dimensionality Lesson using Stair-Step Fractals