Body Benchmarks: Analyze the Data and See How You Measure Up!
I first used this activity in an Algebra I class when I wanted students to have a hands-on experience gathering data and modeling it with a linear function. Later, I used this as an “all-ages” station at our elementary school’s Family Math Night. Let’s explore this problem situation and look at low-tech and high-tech methods to analyze this real-life data.
Here are the Instructions: [link to file]
- Write your name on the Record Sheet.
- Use the measuring tape to measure your forearm in inches from elbow to tip of middle finger.
- Record forearm measurement on the Record Sheet next to your name.
- Use the measuring tape to measure your height (if you don’t know it, in inches.)
- Record height measurement on the Record Sheet next to your name.
- Place a mark on the Group Graph that corresponds to your Forearm Length (Horizontal Axis) and Height (Vertical Axis).
There are some interesting discussions that can occur during data collection and recording. Why did we use inches? How precise should our measurements be (to nearest inch, half-inch, quarter-inch)? Are there some measurement activities that are better served by the metric system? Why did we choose to put Forearm Length on the X-axis and Height on the Y-Axis (is one variable clearly the independent variable and the other depends on it, or does it not matter)? What scale did we use on the large graph paper and did I graph my data point accurately? Is there any point that is clearly an outlier? [Not all of these topics came up in every class setting; are there other conversations you experienced or think are important for the teacher to orchestrate?]
Once the data is collected, the group graph shows a positive correlation that could be modeled by a linear function. A low-tech way to find a line of best fit is to graph the data on graph paper, and use a ruler or dry spaghetti/linguine pasta to approximate the line with this criteria: “Follow the trend of the data points, and have about half the points above and half below the line”.
Then select two points (must they be data points? Or just graph grid intersections?) and find the equation of the line (point-slope form or slope-intercept form?). Don’t stop at the equation… what does this formula do for us? Can we predict someone’s height if we know their forearm length? Can you describe the shape of the graph, and how does this relate to the equation? What other questions do you want to ask about this situation?
When technology is available in the classroom, we can use a high-tech approach to analyze the Body Benchmarks data. On the TI-84+ family of graphing calculators (including 83+, 84+, and the color devices 84+C and 84+CE), enter the data into L1 and L2. Then turn on the StatPlot and choose an appropriate window. [What else do you want to discuss with your students… do you have them choose a window or use ZoomStat? Are the students to be responsible for knowing the key presses?]
Then we can analyze the data using the options in the StatCalc menu. I used go directly to the LinReg choice to perform a linear regression. Then I recently discovered that at the bottom of this menu, there is option D:Manual-Fit. This is a high-tech version of the dry pasta best fit line! Note that this feature is available on ALL the TI-84+ graphing calculators, even though my images below are of the color devices.
When Manual-Fit is chosen, you are prompted to designate a location to store the equation. Press ALPHA-TRACE and select Y1. Then arrow down to “Calculate” and press ENTER.
On the graph, move the cursor to place the first point to model the line and press ENTER. If desired, the STYLE of the line can be changed by pressing GRAPH and choosing a new color or line style. Then move the cursor to the second point and press ENTER.
Now, you may have noticed that the line I have chosen is a bit below my set of data, although my slope is a reasonably good fit. BEFORE you are done, you can edit the two parameters M and B in the y = Mx + B equation. Simply enter the new value into the highlighted parameter. When you are happy with your line of fit, press GRAPH to select DONE.
Body Benchmarks Instructions and Record Sheet [click here for file]
Body Benchmarks Data that I used in these screenshots [click here for file]
Body Benchmarks Questions [click here for file]
Step-by-step overview of basic STAT EDIT, STAT PLOT, and STAT CALC functions [click here for file]
Extensions: What other measurements can you take and analyze? Consider armspan, foot length, hand size, and head or wrist circumference.
For more information on hands-on lab activities that generate linear data, see the book: Algebra Experiments 1 Exploring Linear Functions (1992) by Mary Jean Winter & Ronald J. Carlson. [link]