Scatter Plot - a graph with points plotted to show a relationship between two variables.

Correlation - the apparent relationship between paired data - described as positive, negative, or relatively none.

Line of best fit - A line drawn on a scatter plot to estimate the relationship between two sets of data

Linear regression - the process of finding the best-fitting line to model a set of data (best done using technology)

Median - the middle number in a list of ordered numbers

Box and whisker plot - a graph for showing a summary of data using median, quartiles, and extremes of data. 

Students will develop strategies for collecting and analyzing data.

Students will:

Day 1

• Collect data using a stopwatch, measuring tape, and clip board.
• Calculate speed in meters per second.
• Measure the length of student legs to the nearest centimeter.
• Calculate the median leg length of the class.

Day 2

• Use the data collected to construct a scatter plot on graph paper.
• Use the scatter plot to and draw a line of best fit.
• Determine the type of correlation between two related data sets.
• Choose the appropriate scale for the graph.

Day 3

• Calculate the equation of the line using linear regression (technology) utilizing the Thinkifinity resources. 
• Predict what leg length will yield the fastest speed.

This lesson is a multi-day lesson/ mini-unit.  Based on a 45-minute day:

Day 1 - Running Lab - run 40 meters, record data in table

Day 2 - Calculate Median; Speed; Graph Scatter Plot

Day 3 - Line of best fit; Equation by hand

Day 4 - Thinkfinity scatter plot activities

Day 5-6 - Extensions - Box and Whisker Plot

                             - Excel/ Graphing Calculator/ Conclusions

• Video clip of Usain Bolt's 100m world record race.
• Linear Regression - This applet from thinkfinity.org allows you to investigate a regression line, sometimes known as a "line of best fit."
• Scatter plot  - This activity from thinkfinity.org allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit.
• Fastest Legs Data sheet 1.doc - recording running times
• Fastest Legs Data sheet 2.doc - speed calculation
• Fastest Legs Data sheet 3.doc - graphing and analysis
• Linear Regression Graphing Calculator instructions.doc- Graphing Calculator instructions
• Fastest Legs Data sheet 3.doc - conclusions and analysis
• Directions for graphing in excel.doc- instructions on how to create a scatter plot and perform linear regression
  
• Stop watches (4)
• Clipboards
• Metric measuring tape
• Meter sticks
• Graphing Calculators
• Computers (Net books) with access to Microsoft Excel and Internet
• Paper/ Tag Board labeled:  Upper Quartile, Lower Quartile, Median
  

"Pbs Mathline." Pbs Math Line. Pbs, 23 Feb. 2003. Web. 27 Feb. 2010. <https://www.pbs.org/teachers/>.

"Line of Best Fit" Illuminations.Nctm.org. - from Thinkfinity.org. Web. 1 Mar. 2010. <http://illuminations.nctm.org/ActivityDetail.aspx?ID=146.>

"Linear Regression" Illuminations.Nctm.org.- from Thinkfinity.org. Web. 1 Mar. 2010.<http://illuminations.nctm.org/ActivityDetail.aspxid=82

Suggested Instructional Strategies

Scaffolding, Active Engagement, Modeling, Explicit Instruction, Simulation, Project Based Learning, Visual/Spatial

W: In the lesson, we are going to try to answer the question, “Who’s got the fastest legs?” [We will brainstorm ideas of how we can determine this as a class.] The activity we will be doing will compare the speed of the longer-legged students with those of the shorter-legged students. We will then go outside to run, timing the runners for a 100-meter distance. When we return to the classroom, we will calculate the speed of the runners. Finally, we will construct scatter plot graphs by hand and by using technology to help us answer the question, “Who’s got the fastest legs?”

H: Use THINK-PAIR-SHARE strategy to get them to discuss how we might conduct the activity to answer the question. Use this before explaining the details of the activity. Follow up by showing the video clip of Usain Bolt winning the gold medal in the 100 meters at the Beijing Olympics in 2008. Ask the class to see if they observe anything about who is faster vs. their leg length. (This is an example of a runner with longer legs running faster than those with shorter).

E: The students will measure each other’s legs, run 100 meters outside, and calculate their speeds. They will separate the group into long/short legged runners. They will then graph the results on a scatter plot graph.

R: Students will construct scatter plot graphs using the Thinkfinity resources. They will analyze the graphs for line of best fit, strength of correlation, and drawing conclusions on the lesson essential questions.

E: Once the students have had the chance to make their Scatter Plot graphs by hand and using the computer applets, they should be able to draw conclusions and answer the introductory question. Discuss the conclusions and their bearing on our introductory question. They can also make a prediction on what the length of a leg would be to give the fastest time – based on their data.

T: Use the activities and strategies listed below under “Extensions” and “Interventions” to tailor the lesson to meet the needs of your students.

O: The focus of the lesson is making a Scatter Plot of related data. Students learn how to plot points, draw a line-of-best fit, and perform linear regression during this activity. They will look for relationships between the data, identifying the type of correlation they see. This can be used for students in middle school who have a basic understanding of graphing as well as for an Algebra I level class.

Extensions:

Box and Whisker Plot Activity: make a human box and whisker plot

1. Have students form a line in order from the smallest leg length to the longest leg length.
2. Have them count off towards the middle until you find the MEDIAN. Give that student a card to hold that says “MEDIAN”. The students to the left (smallest to MEDIAN) now have the SHORTER LEGS. The top half has the LONGER LEGS.
3. Count off in the first half of students to find the median of the first half, or LOWER QUARTILE. Identify that student with a card that says “LOWER QUARTILE.”
4. Repeat for the UPPER QUARTILE.
5. Wrap the students between the LOWER and UPPER QUARTILE in yarn, string, or cash register tape to form the “BOX”.
6. Have the student with the smallest measurement hold string that extends to the beginning of the box. Do the same for the student with the highest measurement. You will have created a “human” box and whisker plot.
7. Take a picture and display for all to see.
8. You can then discuss the Box and Whisker in terms of its bearing on the Introductory Question – “Who has the fastest legs?”.

Other Extension Activities:

• Linear Regression Graphing Calculator instructions.doc- use to make Scatter Plot or Box and Whisker graphs
• Slope and Y-intercept analysis – use with Algebra I classes to analyze the data
• Directions for graphing in excel.doc – is another option to chart the data

Ideas for Remediation/ Intervention Options:

• Review a practice/sample scatter plot graph. Make it step-by-step with the students.
• Use Graphic Organizer to assist students with graphing procedures.
• Provide extra help on calculating speed. Give practice examples. Review rounding procedures.
• Monitor students individually during leg measurements. Check for use of correct units.
• Provide extra time in using Thinkfinity graphing resources. Provide 1-on-1 help if needed.
• Review basics of using graphing calculator [see attached notes].
• Provide Microsoft Excel template that students can use to enter their data - posted to school/class website.

Day 1

W:

1.  INTRO:  In today's lesson, we are going to try to answer the question "Who's got the fastest legs?"  (Have this question on the board/smart board at the start of class).  Explain that we will be starting an activity where we will compare the speed of the longer legged students with those of the shorter legged students. 

Use # pairs to allow the kids to share their results with each other.  Then, bring them back together, make a tally as a class if they think people with longer legs run faster, people with shorter legs, or that the length of the leg makes no difference.  Save the results to compare with their conclusions at the end of the activity.  You may want to add the results of each class as the day goes on.

H: 

2.  ACTIVATING STRATEGY:  "I want you to write the question in your math notebooks and take a minute to think about how we might answer that question by conducting an experiment with the class." Give students time to brainstorm on their own.  After a few minutes, conduct the rest of the THINK-PAIR-SHARE strategy by asking them to "turn and talk" to a partner, sharing with them what they wrote.  Then, pull the class back together by asking volunteers to share their ideas with the class.  Ideas could be written on the board or on chart paper by a student. 

Follow up by showing the video clip of Usain Bolt winning the gold medal in the 100 meters at the Beijing Olympics in 2008.  Ask the class to see if they observe anything about who is faster vs. their leg length.  (This is an example of a runner with longer legs running faster than those with shorter). 

3.  Students should have mentioned that somehow we will need to determine the length of everyone's legs.  From that idea, a discussion can be had with separating the class into 2 groups, "Long Legs" vs. "Short Legs".  We will use the concept of Median (which we will review) to help us figure that out.

After students have shared, you can outline the "experiment" we will perform as a class. 

E:

4*.  The first step will be to measure the length of their legs.  Pair them up and provide them with centimeter measuring tape or meter stick.  Have each student, with the help of their partner, measure the length of their leg (from hip bone to heel).  Record the measurements on a note card.

5.  The next step will be to calculate the Median of the leg measurements.  Have the students line form a line, from shortest legs to longest.  Have them count in, from each side, until you find the student in the middle.  This student's measurement will represent the Median of the data.  Have the students enter their data on the class Data Sheet 2 on overhead or smart board.  Once they are entered, each student can record the correct measurements in their class table on Data Sheet 1.

6.  Explain that we will have volunteers* run meters outside and record their times.  [Try to encourage at least 10-12 students to run so that you will have more data to compare]  We will run 100 meters down at the track  (Based on the age of your students, you may want to run a shorter distance as well, like 40-50 meters).  You can run 2 students at a time against each other.  You will need 2 students who are not running to be timers.  Timers will be posted at the finish lines.  Students will need their Data Sheet 1 to record the times. 

*NOTE:  You may want to do this part during your 2nd class period due to time constraints.

Day 2

7.  When they return to the classroom, the students will calculate the speed of each runner.  Discuss with the students the units (meters per second), and that they will not want to include the unit in the table as well.  If you do not have enough times to use for calculations, you may want to combine results from other classes.

8.  Now, we have the data we need to make our Scatter Plot and look for what kind of correlation there might be between the lengths of our legs and the speed we run.  Hand out the Data Sheet 3 - with the graph on it to students for them to plot their data.  They will label the x-axis as "Leg Length (cm)", and the y-axis as "Speed (m/sec)".  Discuss the appropriate scale, showing them an example.  Remind them that they want all of their data points to fit on the graph.  Assist them in plotting a few of the points together as a class.  Then, walk around to assist individual students as they work on plotting the rest of the data points.

8.  Now that the students have made their Scatter Plots on paper, we will have a discussion on the type of Correlation, if any, the students have found.  If there is a correlation, we will draw a line of Best Fit.

Day 3

R:

9.  Thinkfinity Activity- Line of Best Fit – you will need access to computers for individual students or for groups of students.

This activity allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit.

Students can enter their data in the text box and click "Update Plot". (Note that two columns of data can be copied and pasted from a spreadsheet program into this text box; the first column represents the x‑coordinates, and the second column represents the y‑coordinates.)

When you check the box for Student Guess, a green line will appear on the grid. Drag the green dots to approximate a line of best fit visually. An equation of this line will appear to the right. When you check the box for Computer Fit, a red least-squares regression line will be displayed. An equation of this line and the correlation coefficient (r) will appear to the right.

<Take time to explain what the correlation coefficient (r) means.> The closer the number is to 1, the stronger the correlation. 

10. Linear Regression Thinkfinity Activity - you will need access to computers for individual students or for groups of students.

This applet allows you to investigate a regression line, sometimes known as a "line of best fit."

Plot the points from the activity and click Show Line. How well does the line approximate the scatterplot?

E:

11. Analysis and Conclusion:

Once the students have had the chance to make their Scatter Plot graphs by hand and using the computer applets, they should be able to draw conclusions and answer the introductory question.  Have them do this by responding to the questions on Data Sheet 3.

When they are finished, use THINK-PAIR-SHARE to discuss the conclusions and their bearing on our introductory question. 

Follow that up with a whole class discussion.

  You may also want to try to make a prediction on what the length of a leg would be to give the fastest time – based on their data.

• Ongoing formal assessments can be done during small-group work, student interaction, and work completed during class time.
• Data sheets can be collected and checked for following directions and accuracy. 
• Scatter plot graph should be checked for accuracy, correct labels and scale, as well as line of best fit.
• Monitor student work on computers using the Line of Best Fit and Regression activities to check for understanding.

Bibliography:

"Pbs Mathline." Pbs Math Line. Pbs, 23 Feb. 2003. Web. 27 Feb. 2010. <https://www.pbs.org/teachers>.

"Line of Best Fit" Illuminations.Nctm.org. - from Thinkfinity.org. Web. 1 Mar. 2010. <http://illuminations.nctm.org/ActivityDetail.aspx?ID=146.>

"Linear Regression" Illuminations.Nctm.org.- from Thinkfinity.org. Web. 1 Mar. 2010.<http://illuminations.nctm.org/ActivityDetail.aspxid=82