Regina Turner Washington, Franklin Military Academy, Richmond Public Schools High School Math Introducing Fractal Geometry Concepts to the existing Virginia State Standards of Learing (SOL)
Existing SOL	Description	Suggested Additions, Revisions and Examples	Subject
A.6	The student will select, justify, and apply an appropriate technique to graph linear functions and linear inequalities in two variables. Techniques will include slope-intercept, x- and y-intercepts, graphing by transformation, and the use of the graphing calculator.	Using applets such as http://csdt.org/african/CORNROW_CURVES/ practice the application of iteration and transformations	Algebra 1
G.2	The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include a)investigating and using formulas for finding distance, midpoint, and slope; b)investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and c)determining whether a figure has been translated, reflected, or rotated.	Using applets such as http://csdt.org/african/CORNROW_CURVES/ Practice the application of iterations and transformations, with attention to symmetry of designs.	Geometry
G.5	The student will a) investigate and identify congruence and similarity relationships between triangles; and b)prove two triangles are congruent or similar, given information in the form of a figure or statement, using algebraic and coordinate as well as deductive proofs.	Use the concept of a scaling transformation (see http://csdt.org/african/CORNROW_CURVES/ and http://csdt.org/african/African_Fractals/background2.html) �to show how similar triangles differ only in size. �Use scaling ratio (see http://csdt.org/african/CORNROW_CURVES/cornrow_tutorial.html) and http://csdt.org/african/African_Fractals/background11.html) �to determine proportions of the sides.	Geometry
G.12	The student will make a model of a three-dimensional figure from a two-dimensional drawing and make a two-dimensional representation of a three-dimensional object. Models and representations will include scale drawings, perspective drawings, blueprints, or computer simulations.	Add the concept of fractal dimension and how a dimension can exist between a one and two dimensional object (see http://csdt.org/african/African_Fractals/background8.html)	Geometry
G.14	The student will a)use proportional reasoning to solve practical problems, given similar geometric objects; and b)determine how changes in one dimension of an object affect area and/or volume of the object.	Use scaling ratio (see http://csdt.org/african/CORNROW_CURVES/cornrow_tutorial.html) and http://csdt.org/african/African_Fractals/background11.html) �to determine proportions. Use Mangbetu design (http://csdt.org/african/MANG_DESIGN/culture/mang_homepage.html) and show how proportion can be combined with the Cartesian distance formula http://csdt.org/african/MANG_DESIGN/teaching/instr.htm	Geometry
AII.9	The student will find the domain, range, zeros, and inverse of a function; the value of a function for a given element in its domain; and the composition of multiple functions. Functions will include exponential, logarithmic, and those that have domains and ranges that are limited and/or discontinuous. The graphing calculator will be used as a tool to assist in investigation of functions.	Use the logarithmic spirals of cornrow curves to explore the relations between measurement, graphing, and the logarithmic function (http://csdt.org/african/CORNROW_CURVES/teaching/crproinstr/cpi1.htm)	Algebra 2
AII.15	The student will recognize the general shape of polynomial, exponential, and logarithmic functions. The graphing calculator will be used as a tool to investigate the shape and behavior of these functions.	Use the logarithmic spirals of cornrow curves to explore the relations between measurement, graphing, and the logarithmic function (http://csdt.org/african/CORNROW_CURVES/teaching/crproinstr/cpi1.htm)	Algebra 2
MA.9	The student will investigate and identify the characteristics of exponential and logarithmic functions in order to graph these functions and solve equations and practical problems. This will include the role of e, natural and common logarithms, laws of exponents and logarithms, and the solution of logarithmic and exponential equations. Graphing utilities will be used to investigate and verify the graphs and solutions.	Use the logarithmic spirals of cornrow curves to explore the relations between measurement, graphing, and the logarithmic function (http://csdt.org/african/CORNROW_CURVES/teaching/crproinstr/cpi1.htm)	Mathematical Analysis