The purpose of this Geogebra book is to introduce students to the connections between the Fibonacci Sequence and the Golden Ratio through exploration with Golden Rectangles and Triangles.

[url=http://www.corestandards.org/Math/Content/HSG/CO/A/5/]CCSS.MATH.CONTENT.HSG.CO.A.5[/url][br]Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.[br][br][url=http://www.corestandards.org/Math/Content/HSG/SRT/A/2/]CCSS.MATH.CONTENT.HSG.SRT.A.2[/url][br]Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.[br][br][url=http://www.corestandards.org/Math/Content/HSS/ID/B/6/]CCSS.MATH.CONTENT.HSS.ID.B.6[/url][br]Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.[br][br][url=http://www.corestandards.org/Math/Content/HSS/ID/B/6/a/]CCSS.MATH.CONTENT.HSS.ID.B.6.A[/url][br]Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.[br][br][url=http://www.corestandards.org/Math/Content/HSS/ID/B/6/c/]CCSS.MATH.CONTENT.HSS.ID.B.6.C[/url][br]Fit a linear function for a scatter plot that suggests a linear association.[br][br][url=http://www.corestandards.org/Math/Content/HSS/ID/C/7/]CCSS.MATH.CONTENT.HSS.ID.C.7[/url][br]Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Students will be able to ... [br]- identify the Fibonacci Sequence within the constructions of Golden Rectangles,[br]- connect the Fibonacci Sequence algebraically and graphically to the Golden Ratio through a linear model of best fit,[br]- recognize recursion through rotations and dilation within constructions of Golden Rectangles and Triangles,[br]- develop an "eye" for recognizing shapes that are "Golden,"[br]- and apply previously learn concepts about similarity.