In this lesson, the students are analyzing the data collected from the previous lesson's homework to determine whether or not the Golden Ratio is in nature.
1. Form groups of four or five
2. Open the student survey on the internet using the LCD projector.
3. Have students open the internet survey in their groups using their laptops.
4. Allow students time to enter their data into the survey.
5. Using the LCD projector, demonstrate to students how to properly import the data from the internet survey into Fathom 2.
a. Open Fathom 2
b. Open the survey online.
c. Go to import, import from URL, and type in URL or copy and paste the URL (or more simply, click on the URL and highlight entire address and drag into Fathom window).
d. After importing survey into Fathom, highlight the collection by clicking on it, then drag a new table from the tool bar into the window. This provides a table which should look similar to an excel spreadsheet.
e. We want Fathom to calculate the ratios of our new measurements. When in the table, click on new and type a ratio heading. Click on "table" at the top of the page, and then click "show formulas." Double click on the box that is in the row = and the column under the ratio you want to calculate. Now you can type in the formula of the ratio you want by giving the column names. Example: leaf length/leaf width.
f. Next, we want to graph each of the ratios that have been calculated. Click and drag graphs from the tool bar onto the Fathom window.
g. Click on one of the ratio columns and drag the column on to the x-axis of one of the blank graphs. Do this for all ratios to see the distribution of the ratios. (Click here to see a sample of what this may look like.)
6. Do you notice any patterns in the distributions?
7. Which ratios conform more to the golden ratio?
8. Which ratios are most varied in their distribution?
9. Are any of the ratios more skewed than others?
10. Extention: It may be interesting to see if students are convinced of the Golden Ratio, based on data analysis, in the body, nature, and other aspects of the surrounding world. Allow students to debate in a whole class their opinions of the Golden Ratio. Teacher should encourage data support in opinions.