Golden Ratio Webquest

By Michelle Daniel •

Grade Level	9th
Subject Area	Integrated Math
Duration	5 - 70 minute blocks
Setting	PC Computer Classroom
Background Knowledge	Graphing Scatter Plots, Ratios, Trigonometry, Similar Triangles, Slope, Linear Equations, Trend lines, Solving Equations, Geometry Sketchpad, Microsoft Excel
Author	Michelle L. Daniel

Summary
This webquest will provide students with an academic opportunity to explore the Golden Ratio. Students will be required to use a variety of technologies including Excel, Geometry Sketchpad and the Internet to investigate the Golden Ratio. Students will also be required to apply their knowledge of ratios, trig ratios, slope, linear equations and similar triangles. They will also learn about the Fibonacci sequence and how it applies to the Golden Ratio. A major part of this webquest involves students researching professions to find the Golden Ratio. Two of those professions relate directly to engineering and science (engineer and biological scientist). Student will be divided into groups of 4 and each will be required to research one of the professions and report their findings to their team. To do this, each will be required to write a summary paragraph, summarizing their findings. Then, collaboratively, the student groups will each create a group poster, summarizing their findings on the Golden Ratio, supporting the idea that “The Golden Ratio is Everywhere!”

Objectives
1. Understand the importance of the Golden Ratio 2. Know and understand applications of the Golden Ratio in the world around them 3. Apply mathematics and technology to construct a Graph of the Golden Ratio 4. Apply technology to construct the Golden Ratio 5. Research a profession for applications of the Golden Ratio 6. Summarize research found on the internet 7. Incorporate research into a creative and interesting poster presentation

Mateirals Required
Computer • Microsoft Excel • Geometry Sketchpad • Internet Explorer Printer Poster board Poster materials: (glue, markers, scissors, rulers, protractors, construction paper, letter stencils, etc)

Ohio Standards

Mathematics

* Standard: Measurement
Grade 9
o Benchmark D : Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.
o Indicator 3 : Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.
o Indicator 4 :Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures.

* Standard: Number, Number Sense and Operation
Grade 9
o Benchmark G : Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

* Standard: Geometry and Spatial Sense Standard
Grade 9
o Indicator 1 : Define the basic trigonometric ratios in right triangles: sine, cosine, and tangent.
o Indicator 2 : Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures.

Grade 10
o Indicator 4 : Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software.

* Standard: Data Analysis and Probability
Grade 9
o Indicator 2 : Create a scatterplot for a set of biveriate data, sketch the line of best fit, and interpret the slope of the line of best fit.

* Standard: Patterns, Functions and Algebra
Benchmark A : Generalize and explain patterns and sequences in order to find the next term and the nth term.

Science
None

Technology

* Standard: Technology for Productivity Applications
Grade 9
o Benchmark B : Identify, select and apply appropriate technology tools and resources to produce creative works and to construct technology-enhanced models
o Indicator 2 : Demonstrate proficiency in all productivity tools (e.g. word processing, spreadsheet, data base, desktop publishing)

* Standard: Technology and Information Literacy
Grade 9
o Benchmark B : Apply a research process model to conduct research and meet information needs.
o Indicator 2 : Select and evaluate appropriateness of information from a variety of resources, including online research databases and Web sites to answer the essential questions.