Part 1
Have you ever heard that twice the circumference of your neck is equal to the circumference of your waist; or your arm span from fingertip to fingertip is equal to your height? Well, today you are going to investigate if the length of your forearm is the same as your length of your foot or did Da Vinci have the answer when he said, "The whole length of the foot will lie between the elbow and the wrist." (Dove, 2018)
You will need to measure five different people. Record your measurements on a piece of paper. Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). Refer to the diagrams below. You will have two measurements for each person.
Part 2
Organize your data and find the rate of change.
Create a table of the measurements for your data. Label the forearm measurements as your input (x value) and the foot measurements as your output (y value)
Table:
Name
Length of forearm (x)
Length of foot (y)
Select two sets of points from the table above. Find the change in y over your change in x to determine the rate of change for your data. (The table is to help organize your numbers. Take the rate of change in the table and write it as a fraction below the table.) Be sure to simplify!
Point 1
Point 2
Rate of change
y value
-
=
x value
-
=
The rate of change is :
Describe your results. If you were to graph this data, what is the association between your points? (What happens to the foot length as the forearm increases in length?)
Part 3
(length of the foot) = 0.860 • (length of the forearm) + 3.302
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302.
Using this equation, how long would the foot of a person be if his forearm was 17 inches long? Be sure to show your work using the equation above.
What is the rate of change of the equation from Part A above?
Compare the rate of change from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different?
Is the relation in your data a function (all functions do not have to be linear)? Why or why not?
Could the equation in Part A represent a function? Would this be a linear function? Why or why not? Explain your answer.
Based on your data, is your foot the same size as your forearm or is Da Vinci correct and your foot would fit between your wrist and your elbow or does your data show something else?