Search for the Greek God and Goddess - Learning Ratios

by: Eric Curts
tech@northcanton.sparcc.org

Description

The ancient Greeks believed perfection was represented by the Golden Ratio (a unit rate of 1.62 to 1). They used this measurement in their art and architecture. Students will use the "Golden Ratio" to determine how close their facial features are to the Greek idea of perfection. In doing so they will work with metric measurement, ratios, unit rates, and subtraction, addition, and division of decimals.

Grade Level(s):   Grade 5     Grade 6     Grade 8    

Subject Area(s):   Mathematics    

Curriculum Standards

Math - Grade 5
Number, Number Sense and Operations
1. Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.
2. Use various forms of “one” to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6.
3. Identify and generate equivalent forms of fractions, decimals and percents.
4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half.

Math - Grade 6
Number, Number Sense and Operations
5. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.
11. Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning.
14. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.

Math - Grade 8
Number, Number Sense and Operations
6. Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.

Technology - Grade 5
Standard 3 - Technology and Productivity Applications
- Collect information for projects using still and video digital cameras, scanners and electronic resources.
- Select and use appropriate software applications to complete content-specific tasks (e.g., use desktop publishing software to create a newsletter, use drawing programs to create artwork).

Technology - Grade 6
Standard 2 Technology and Society Interaction
- Employ the use of measuring instruments to collect data.

Standard 3 - Technology and Productivity Applications
- Use content-specific tools, software and simulations to support learning and research (e.g., thermometers, graphing calculators).

Technology - Grade 8
Standard 3 - Technology and Productivity Applications
- Incorporate all available technology tools and resources to research, investigate, solve and present findings in a problem situation.
- Use content-specific tools, software and simulations to support learning, and research societal and educational problems.
- Apply technology resources to support personal productivity, and learning throughout the curriculum.

Detailed Plan

The point of this lesson is to teach ratios, specifically unit rates, through the concept of the Golden Ratio as it applies to human beauty. In brief, students will

Step One: Background on the Golden Ratio
Begin by asking what famous people the students think are attractive. If possible, keep this list from year to year to show the students how much the idea of beauty changes over time.

If you want, show the PowerPoint presentation "History of Beauty" (in the Files section) on the history of beauty to further explain the changing nature of attractiveness. This is an important point since you do not want any student to take this activity personally as a reflection on their own looks.

Next explain that the Greeks had a very specific idea of what was beautiful. The belived that to be attractive, the height and width of an object needed to be int he same ratio as the Golden Ration, which was 1.62 to 1. They applied this belief to their architecture and art, including people's faces.

Explain that in this lesson the students will be measuring features of their faces to see which students in class are the closest to the Greek ideal of perfection, and therefore be declared the "Greek God and Goddess" of the class.

Step Two: Measuring
Next you need to give each student the "Measurement Worksheet" (in the Files section). This is where they will record their facial measurements.

As for doing the actual measuring, that can be done many ways:
- With a partner (which can be a problem with middle school kids)
- In a mirror
- With a photograph

However, I would suggest the following for best results:
Step 3: Calculations
This step can now be done outside of the lab, such as back in the classroom or even for homework.
Step 4: Checking
Since each student will have 12 unique measurements, all of their answers will be different than other students. This can be time-consuming to grade by hand. To help with this, you may want to use the Excel Spreadsheet "Greek Face Calculations" (in the Files Section). This spreadsheet lets you quickly check the students' work by inputting their original measurements and getting the correct answers.

Step 5: Crown the God and Goddess!
Once you determine which guy and girl are the closest to Greek perfection, announce them as the class Greek God and Goddess. You may want to take a picture of each student posing like a statue, perhaps with a sheet wrapped around them like a toga. In the past I also got coupons for a greek oriented restaurant to give them.

Files

General

Links

General

Needed Resources

Although this lesson can be accomplished in many ways, I find the following items make it most efficient and effective:

- Computer lab (so each child can work)
- Digital camera, preferably one that saves the pictures to floppy disks (so each child can quickly get a picture of the face)
- Ruler for each student (to measure the facial features on the computer monitor)
- "Measurement Worksheet" (in the Files section)
- "Calculation Worksheet" (in the Files section)