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## Lesson Plan

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This lesson provided by:
 Author: Amy Adams System: Shelby County School: Shelby County High School

General Lesson Information
 Lesson Plan ID: 10831 Title: Golden Ratios of the Body, Architecture, and Nature Overview/Annotation: Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.

Associated Standards and Objectives
Content Standard(s):
 TC2 (9-12) Computer Applications 5. Utilize advanced features of spreadsheet software, including creating charts and graphs, sorting and filtering data, creating formulas, and applying functions. MA2015 (6) 24. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. [6-G4] MA2015 (7) 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7-RP1] MA2201007070000102.jpg MA2015 (7) 2. Recognize and represent proportional relationships between quantities. [7-RP2] a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [7-RP2a] b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [7-RP2b] c. Represent proportional relationships by equations. [7-RP2c] Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. [7-RP2d] MA2015 (7) 11. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7-G1] MA2015 (7) 20. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7-SP4] Example: Decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. MA2015 (9-12) Geometry 41. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3] MA2015 (9-12) Algebraic Connections 9. Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) Example: Identify the symmetry found in nature, art, or architecture. MA2015 (9-12) Algebraic Connections 11. Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) Example: Use a blueprint or scale drawing of a house to determine the amount of carpet to be purchased. MA2015 (9-12) Mathematical Investigations 3. Use special numbers, including e, i, π and the golden ratio, to solve application-based problems. a. Identify transcendental numbers. (Alabama) Example: Calculate e to ten decimal places using a summation with 1/n!. MA2015 (9-12) Mathematical Investigations 9. Analyze works of visual art and architecture for mathematical relationships. (Alabama) Examples: Use Leonardo da Vinci's Vitruvian Man to explore the golden ratio.                   Identify mathematical patterns in Maurits Cornelis Escher's drawings, including the use of tessellations in art, quilting, paintings, pottery, and architecture. a. Summarize the historical development of perspective in art and architecture. (Alabama)

Local/National Standards:

Primary Learning Objective(s):

Students will calculate ratios from length and width measurements. Students will identify the golden ratio in data. Students will create a poster using desktop publishing with digital pictures, data, and conclusions drawn from the data.

Students will use a digital camera to take photos. Students will import digital photos into a desktop publishing product. Students will measure lengths and widths of objects. Students will create a spreadsheet that will calculate the ratios of lengths and widths.

Preparation Information
 Total Duration: Greater than 120 Minutes Materials and Resources: Rulers, meter sticks, tape measures Technology Resources Needed: Computer(s) with Internet access, digital camera, desktop publishing software, spreadsheet software, Alphasmarts Background/Preparation: Students will need to know how to measure lengths in centimeters.

Procedures/Activities:
 1.)Teacher will give the definition of a ratio. As a class, students will list what they know about ratios and ways they know ratios are used. Students will represent, calculate, and simplify ratios. 2.)Students will research the Fibonnacci sequence and the Golden Ratio using the suggested websites (see attachment for sites). 3.)Students will take digital photos of one another, various objects, architecture samples, or nature samples. Students will measure the length and width of body measures, objects, or buildings, and record on a device such as the AlphaSmart (see attachment for directions on measurements). 4.)Students will create a spreadsheet to display collected data and calculate the ratio of length to width. Students will import the data from the AlphaSmart to the spreadsheet. 5.)Teacher will display student spreadsheets and lead a class discussion about the data. Students will brainstorm in small groups about conclusions that might be drawn from the data. Each group will report on the conclusions. Teacher will make poster assignment (see attachment for handout). 6.)Students will use a desktop publishing program to create a poster with two digital photos, a spreadsheet of the data, and a conclusion statement (see attachment for rubric).

 Attachments:**Some files will display in a new window. Others will prompt you to download. Golden Ratio Websites.doc Golden Ratio Measurements.doc Poster Rubric.doc Poster Assignment.doc

Assessment
 Assessment Strategies The poster will be assessed using the attached rubric.

 Acceleration: Intervention:
 Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems. Presentation of Material Environment Time Demands Materials Attention Using Groups and Peers Assisting the Reluctant Starter Dealing with Inappropriate Behavior Be sure to check the student's IEP for specific accommodations.