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
    [view html page] || [download MS Word file]

APPENDICES
Dimensionality Lesson using Stair-Step Fractals
    [view html page] || [download MS Word file]
Instructions for Creating the Stair-Step Fractal
    [view html page] || [download MS Word file]
Homework Assignment
    [view html page] || [download MS Word file]
Working Group Members
    [view html page] || [download MS Word file]

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