Math+Lesson+Plans

Math Lesson Plans

Wingspan Data Collection
 * || **Overview**
 * || **Overview**

"It has been said that our wingspan is the same as our height. Is this true?" Leading a group of math and science teachers, I thought this was a possible teaching moment and asked others attending. A few had heard of the same relationship, however, no one could present any compelling evidence aside from Leonardo Da Vinci's "Vitruvian Man". We decided to start a collaborative project to answer this question.

The most effective method for data collection is to use a Google Doc spreadsheet and a Google form to allow teachers and students to submit their data and view the complete data set easily and quickly. Students can even have parents and community members enter data from home!

We expanded the data we would collect to include foot and forearm length to see if a relationship existed there as well. The data should be analyzed to see what the ratio is between the wingspan and height as well as the forearm and foot length to see how close that ratio is to 1.0 and to see what accuracy exists in the data. As an further extension, questions based on gender or age variations could be pursued.

Computer with internet access Meter stick Tape measure Level
 * Materials**


 * Instructions**
 * 1) Find a partner or partners to help collect data on each other.
 * 2) Measure each other's dimensions as outlined below. Also review the terms precision and accuracy in the [|Related Links].
 * 3) Enter the data in the Google Doc in the [|Data section] below.
 * 4) Open the spreadsheet, go to File and Export and select .xls if you have Excel and wish to analyze the data in Excel.
 * 5) Analyze the data and see if indeed wingspan and height are related and if forearm and foot length are related.

Measure the following human dimensions using the directions provided:

>
 * 1. Wingspan**
 * 1) While standing, extend arms in opposite directions horizontally at shoulder height.
 * 2) Using a tape measure, measure wingspan (cm). Wingspan is defined as the distance from the tip of the middle finger of one hand to the tip of the middle finger of the other hand.
 * 3) Record measurement.
 * 4) Repeat steps 1 and 2 for your partner.
 * 2. Height**
 * 1) Remove your shoes.
 * 2) One person lean against the chart paper that is taped on the wall. Make sure your head and heels are touching the wall.
 * 3) Place a ruler flat on top of your head to get a good reading. If the person you are measuring is a lot taller than you, use a level to be sure you are holding the ruler horizontal.
 * 4) Have your partner mark your height with a marker next to the ruler.
 * 5) Place tape measure at the bottom of the wall and pull the tape measure to your marked height. Find the height (in cm).
 * 6) Repeat same procedures with your partner.
 * 7) Record data in the appropriate area. Example: Ms. Coppola is 161.0 cm.

Forearm plus hand >>
 * 3. Forearm + hand**
 * 1) Collect Materials (Meter Stick)
 * 2) Move a flat table against a wall to form a 90 degree angle
 * 3) Place meter stick flat on table, tight against the wall.
 * 4) Put elbow against wall and place arm and hand directly on meter stick.
 * 5) Measure the length of forearm and hand in centimeters (keep fingers and forearm straight)
 * 6) Measure to the tip of your longest finger (do not count long nails)
 * 7) Record your measurement.

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 * 4. Forearm**
 * 1) Forearm without hand
 * 2) Collect Materials (Meter Stick)
 * 3) Move a flat table against a wall to form a 90 degree angle
 * 4) Place meter stick flat on table, tight against the wall
 * 5) Place arm and hand on the table right along side the meter stick
 * 6) Locate the wrinkle line on your wrist (as shown in the photograph)
 * 7) Record measurement.
 * 5. Foot**
 * 1) Take off the right shoe.
 * 2) Using a meter stick placed aginst the wall, line your right heel up to the zero line. Keep the meter stick on the inside of your foot.
 * 3) Stand up straight and have another student use a ruler to line up the tip of your longest toe to the meter stick.
 * 4) Measure to the nearest millimeter.
 * 5) Record your measurement.

**Data Collection and Analysis** First create a Google Doc spreadsheet and Google form for your class. Next, have students enter the data they collected in your Google form. If you have a projector for your computer, leave the Google Doc open so students can see their data on your computer as it gets entered. Share the data with your students by either inviting them or let them view the data without signing in. All this is under the Share tab.

You can see the Google form we used and the teacher data we collected from our workshop.

[|Fill out the Google Doc form] [|Teacher Data from 1.27.09]

Once the data collection is complete students can Export or Create A Copy from the Google Doc which allows them to manipulate the data without affecting the raw data that is being collected. Exporting the data to a more powerful spreadsheet program will allow students to draw a best fit line and get an equation of the line and get an r squared value for the best fit line.

In a graphing program, students should plot the data as an X-Y scatter plot. If there is a good link between variables (height and wingspan) then most of the points will fall along a line. Plotting a linear trendline will assist in that assessment. The equation of the line (and the trendline itself) will allow students to interpolate and extrapolate data as well. An r squared value closer to 1 will mean that the data fits the trendline better that an r squared value closer to 0.

[|Size of a Human: Body Proportions] from [|The Physics Factbook]™ Edited by Glenn Elert -- Written by his students
 * Related Links**

[|Primer on precision and accuracy] from Bill Willis at Worsley School, Canada

Students should use the data set that has been accumulated to answer the following questions:
 * Evaluation**


 * 1) Is there a good relationship between variables (height/wingspan, forearm/foot)? How did you determine that? (r squared value)
 * 2) What could you do to improve the accuracy of your data? Play around with the data a little and see what happens when you change or remove points. See how the line and r squared value changes. Can we justify removing points? How could you improve the data set? What affect would more people have on the r squared value? What could you do to make more precise measurements?
 * 3) If Jill is 130 cm tall, what do you predict her wingspan will be?
 * 4) If your little brother is only 85 cm tall, what do you predict his wingspan will be?
 * 5) Measure the height of your favorite teacher. What will be their wingspan?

If you are interested in assessing the impact of student learning, here are a couple of ideas:

Questions that utilize percents and ratios will test student understanding of the nature of fractions and decimals and their relationship to ratios and percents. For instance,


 * If the baseball player has 4 hits in 10 times at bat, what is her batting ratio? What is her batting percent?
 * If the baseball player has 12 hits in 10 times at bat, what is her batting ratio? Why is this not possible?
 * You have missed 3 school days in the first 100 days of the year. What is your attendance ratio or percent? What is the best attendance ratio you can achieve after 200 days? What is the best attendance ratio that anyone can achieve?

However, a more authentic assessment would mimic the whole process of the project better. For instance,


 * I have measured 3 chairs in the room. I measured the height to the seat and the depth of the seat and entered that [|data into a spreadsheet]. What is the seat height to seat depth ratio of each chair? What is the average ratio of seat height to seat depth? Now, when you sit on a seat, you lay your upper leg on the seat and your lower leg hangs to the ground. What would you expect to be the ratio between your upper leg and your lower leg? Why? Collect data from your classmates and others and determine if your hypothesis is correct.
 * Do pets have any dimensions that are closely related? Look at pictures of dogs and cats (your pets or others from the internet) and brainstorm some ideas. What might you measure? How would you measure these dimensions? Create a Google Doc and collect some data from your pet and your friends pets. See if you can find some dimensions that are closely related.


 * Standards**
 * NJ Standard 4.2.7 D Units of Measurement
 * NJ Standard 4.3.7 C Modeling
 * NJ Standard 4.4.7 A Data Analysis

Human Dimensions Project by [|Greg Bartus] is licensed under a [|Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License]. ||