1. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 See Teacher Guide for printing instructions Tree Surveying Interpreting Measurements

2. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Opening Activity 1m 100 square feet 2 acres 2x10 10 angstroms 15 pecks 192 drams (not grams) 2600 19 bizarros Name one thing that is typically around each of the following sizes: –Example: 8 feet = height of most ceilings in the US

3. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Opening Activity 1m ≈ width of a doorway 100 square feet ≈ floor area of a small room 2 acres ≈ land occupied by a neighborhood park 2x10 10 angstroms (2m) ≈ height of a tall person 15 pecks (35 gal) ≈ volume of an outdoor trash can 192 drams (12 oz) ≈ volume of a soft drink can 2600 ≈ ? 19 bizarros ≈ ? Name one thing that is typically around each of the following sizes:

4. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Opening Activity Quantities given in common, standard units are easy to understand –1m = width of doorway Quantities given in unfamiliar, but standard units are hard to understand –2x10 10 angstroms = 2m = height of a tall person Quantities given in unspecified or untranslatable units are impossible to understand –2600… 2600 what? –19 bizarros… what is a bizarro??? Sizes and units:

5. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Opening Activity Quantities given in unspecified or untranslatable units are impossible to understand What units does your auto-caliper use? –What do they mean in terms of a measured object’s size? In order to make the caliper measurements useful, you need some way to convert them back to regular units! Sizes and units:

6. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Scatterplot Graphs Used to illustrate the relationship between two aspects of the same set of data One aspect is represented by the X coordinate (horizontal location) of the data point The other aspect is represented by the Y coordinate (vertical location) of the data point

7. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Scatterplot Graphs Example: This experiment checks for a relationship between a student’s height and the length of his or her stride (distance between steps while walking) Aspect 1 = Student’s height –Let’s make this the X- coordinate Aspect 2 = Length of stride –Let’s make this the Y- coordinate

8. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Scatterplot Graphs Example: X = student height Y = stride length Take a measurement –We find that Sally is 5’2” (62in) and travels 40cm between steps Plot the measurement –Add a point at the intersection of 62in on the X-axis and 40cm on the Y-axis

9. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Scatterplot Graphs Example: X = student height Y = stride length Take many measurements and add them all to a graph Do you see a pattern?

10. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Best-Fit Line When the pattern of points resembles a line, draw the line! The best-fit line comes as close as possible to all the data points on the graph A good best-fit line captures the essence of the relationship between the X and Y axes… which means it captures the relationship between the two aspects being measured –The relationship between height and stride in the example

11. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Best-Fit Line The best-fit line captures the essence of the relationship between the two aspects being measured Straight lines can always be defined by a simple equation in slope-intercept form: –Y = mX + b –m and b are numbers you get by observing the line –Example: Y = (1)X + (-18) –This equation lets you calculate the Y value by simply plugging in the X value

12. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Scatterplot Substitution Example: X = student height Y = stride length In a scatterplot, X and Y are literally the same as what they represent and can be substituted directly! If you say: “this measurement’s Y- coordinate is 5cm more than this other one”, You have also said: “this stride length in this measurement is 5cm more than this other one”

13. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Equation Substitution Example: X = student height Y = stride length X and Y can be substituted directly for what they represent Y = mX + b Stride length in cm = (some number called m) times the student’s height in inches, plus (some number called b) Example: Y = (1)X + (-18) Becomes: Stride length in cm = 1 times the student’s height in inches, plus (-18) Stride length in cm = The student’s height in inches, minus 18. Equations of Student Height vs. Length of Stride

14. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Interpreting Measurements: Technical Review Experimental Averages Spreadsheet Graphing

15. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Experimental Averages Taking multiple measurements of the same experimentally sampled quantity, then averaging them, helps to filter out random variance and give a more robust result To find an average, add all the values together, then divide by the number of values you have Average Formula Add the values together, then divide by the number of values you have Average Value = Value 1 + Value 2 + Value 3 + … Number of Values

16. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Spreadsheet Basics Enter measurements in columns – the sheet should typically look like the data table in your worksheet Use the Enter key to enter a value and move the cursor to the next cell To graph a set of data, select the cells with the numbers you want, then create a new graph Many spreadsheet programs can calculate best-fit lines for you Spreadsheets Spreadsheet software such as the popular Microsoft ® Excel ® lets you enter, graph, and analyze experimental data

17. © 2006 Carnegie Mellon Robotics Academy Designed for use with the LEGO MINDSTORMS ® Education NXT Software and Base Set #9797 Measurements are only useful when they can be converted to standard, understandable units Patterns in the relationship between two aspects of a series of measurements can often be characterized by a best-fit line, and thus by a numeric equation You must find a way to relate your caliper measurements to normal units! Summary Multiple measurements can be taken, and combined by averaging them, to reduce random variance Spreadsheet or numeric analysis software can calculate best-fit lines for you