Lesson Overview
Lesson Title: Walking Rates/Blinking Hands Teachers: Mrs. Sarah Crose (Primary) Ms. Vicki Sorensen Brief Description:
Students will calculate walking rates and then apply this information to an engineering problem about regulating crosswalk lights. Students will have the opportunity to connect their classroom math lessons to a realworld problem.
Topics Introduced:
Pedestrian walking rates
Transportation, Distribution, and Logistics Curriculum Framework Components Addressed:
Transportation Operations
Transportation Systems/ Infrastructure Planning, Management and Regulation

Suggested Grade Levels: 6^{th} Grade 7^{th} Grade 8^{th} Grade Subjects: Mathematics Engineering Standards Taught: 8.2.2 Math 2006 8.2.3 Math 2006 8.3.2 Math 2006 8.5.1 Math 2006 8.5.4 Math 2006 
Lesson Information
Learning Expectations:
Expectations:
Â
Students will gather data from various sources:Â peers,Â traffic video,Â provided data set
Students will use onestep equations/formulas to calculate walking rates & walking times.
Students will use ratios & proportions to describe traffic problems.
Students will find the mean, maximum, & minimum walking rate for a data set
Students will work cooperatively in groups to gather data and solve problems.
Â
Â
Objectives:
Students will use one step equations to determine speed, distance, and time in a reallife problem.
Students will gather data on walking speeds and find the mean, median, mode, range, minimum, & maximum of the data.
Students will analyze data and make conclusions based on the data.
Students will explore a traffic engineering realworld problem.
Â
Â
Students will gather data from various sources:Â peers,Â traffic video,Â provided data set
Students will use onestep equations/formulas to calculate walking rates & walking times.
Students will use ratios & proportions to describe traffic problems.
Students will find the mean, maximum, & minimum walking rate for a data set
Students will work cooperatively in groups to gather data and solve problems.
Â
Â
Objectives:
Students will use one step equations to determine speed, distance, and time in a reallife problem.
Students will gather data on walking speeds and find the mean, median, mode, range, minimum, & maximum of the data.
Students will analyze data and make conclusions based on the data.
Students will explore a traffic engineering realworld problem.
Â
Plan Of Action:
The Problem/Question:
When crossing at crosswalk with a traffic signal, pedestrians expect to have sufficient time to cross safely.Â
How is the rate or speed at which a pedestrian walks calculated?
How are walking rates used to determine the optimum time length for the final warning signal at a crosswalk?
Â
Needed Data:
Walking speeds of people crossing the street
Distance a person must walk to reach safety
Â Â Â Â Â Â Â Â rÂ = walker's rate or speed; Â Â Calculate usingÂ Â r = d/t
Â Â Â Â Â Â Â Â d = measure of distance to be walkedÂ Â
Â Â Â Â Â tÂ = average of the timed results
Â
Â
Data Set Collection (use student worksheet page 1)
Â Â Â Â Â Â 1.)Â Â Determine the walking rate of two sample students from the class.
Mark off a distance (d) in the classroom.
Ask the first student volunteer to walk at a normal pace.
Have two students timers time the walk with stop watches.Â Take the average of the two times to get (t).
Compute the rate (speed) of the walker.
Repeat this procedure with the second student volunteer.
Â Â Â Â Â Â Â 2.)Â Â Watch the pedestrian video and calculate the walking rate of four different pedestrians.
Students will be provided with the distance (d) across the street.Â Â Â Â Â Â d = 39 ft
Student pairs will time the pedestrians and calculate the walking rate (r).
Â Â Â Â Â Â Â 3.)Â Â Students will need to calculate four additional walking rates for a total of ten rates.
Could use additional classroom walkers.
Could use provided data retrieved from large data set records.
Could select special cases (i.e. handicapped walker, bike rider/walker, etc.).
Students will find the mean, median, mode, & range (maximum rate & minimum rate) of the data set. (use student worksheet page 2)Â
The classroom distance most likely will not be the same distance as the actual street distance. (use student worksheet page 2)Â Â Â Students will calculate the time needed for each classroom walker (and for any other walk rates not associated with the actual crosswalk distance)Â to actually cross the street at the rate determined in Data Set Collection step 1. Â Students may use onestep equation solving skills to do this or they may use: Â Â t = d/t
Â
Application/Discussion
1.)Â What are characteristics of a pedestrian crosswalk light system?
(Suggested crosswalk characteristics)
Do Not WalkÂ â€“ pedestrian orangehand signal
Walk â€“ white light walking figure pedestrian signal
Walk soon to end warning â€“ orangeblinking hand signal (may have seconds count down)
Assumption: walkers will not start across when the warning signal is blinking.
Assumption: calculating only for walkers who have stepped out on the white signal but then the signal changes to blinking before the next step.
2.)Â Would it be best to use the time needed for the fastest walking rate to cross the street for the BlinkingHand time length? The slowest rate? The average rate?
3.)Â Â View the three pedestrian simulations simulating a long, short, & mean blinkinghand time.Â (simulation courtesy of University of Nebraska, Lincoln)
Discuss pros/cons of each simulation.Â
Guide students to these observations.
Short Time:Â based on the maximum walk rate â€“ results in the shortest blinkinghand time:Â Vehicle traffic has the least amount of delay but many pedestrians at risk of not getting across safely.
Mean Time:Â based on the mean walk rate.Â Vehicle traffic has a longer delay; some but not all pedestrians get across safely
Long Time:Â based on the minimum walk rate â€“ results in the longest blinkinghand time. Vehicle traffic has longer delay but pedestrians are able to all get across safely
What is the best rate to use for the blinking hand?Â (Best to use time needed for the minimum walking rate  safety is always most important.)
Â
Extensions
Traffic Engineers use the 85th percentile rate.Â (i.e. the 85th slowest rate for a data set of 100 rates).Â Why do they use the 85th percentile instead of the very slowest rate?
Why not give pedestrians extra time beyond the time needed for the slowest walker to cross?Â (too much delay for traffic) Â
How might the blinkinghand time be different near a:
Senior citizen homeÂ (seniors walk slower so times should be longer)
Athletic fitness centerÂ (members walk faster so times could be shorter)
Any other unique situations?
Â
ExerciseÂ (use student worksheet page 3)
Â
Suppose classroom volunteer number one lived 2 miles from school.Â What is the latest he/she can leave home and still arrive at school on time?
Students can create walking rate problems related to other situations.
When crossing at crosswalk with a traffic signal, pedestrians expect to have sufficient time to cross safely.Â
How is the rate or speed at which a pedestrian walks calculated?
How are walking rates used to determine the optimum time length for the final warning signal at a crosswalk?
Â
Needed Data:
Walking speeds of people crossing the street
Distance a person must walk to reach safety
Â Â Â Â Â Â Â Â rÂ = walker's rate or speed; Â Â Calculate usingÂ Â r = d/t
Â Â Â Â Â Â Â Â d = measure of distance to be walkedÂ Â
Â Â Â Â Â tÂ = average of the timed results
Â
Â
Data Set Collection (use student worksheet page 1)
Â Â Â Â Â Â 1.)Â Â Determine the walking rate of two sample students from the class.
Mark off a distance (d) in the classroom.
Ask the first student volunteer to walk at a normal pace.
Have two students timers time the walk with stop watches.Â Take the average of the two times to get (t).
Compute the rate (speed) of the walker.
Repeat this procedure with the second student volunteer.
Â Â Â Â Â Â Â 2.)Â Â Watch the pedestrian video and calculate the walking rate of four different pedestrians.
Students will be provided with the distance (d) across the street.Â Â Â Â Â Â d = 39 ft
Student pairs will time the pedestrians and calculate the walking rate (r).
Â Â Â Â Â Â Â 3.)Â Â Students will need to calculate four additional walking rates for a total of ten rates.
Could use additional classroom walkers.
Could use provided data retrieved from large data set records.
Could select special cases (i.e. handicapped walker, bike rider/walker, etc.).
Students will find the mean, median, mode, & range (maximum rate & minimum rate) of the data set. (use student worksheet page 2)Â
The classroom distance most likely will not be the same distance as the actual street distance. (use student worksheet page 2)Â Â Â Students will calculate the time needed for each classroom walker (and for any other walk rates not associated with the actual crosswalk distance)Â to actually cross the street at the rate determined in Data Set Collection step 1. Â Students may use onestep equation solving skills to do this or they may use: Â Â t = d/t
Â
Application/Discussion
1.)Â What are characteristics of a pedestrian crosswalk light system?
(Suggested crosswalk characteristics)
Do Not WalkÂ â€“ pedestrian orangehand signal
Walk â€“ white light walking figure pedestrian signal
Walk soon to end warning â€“ orangeblinking hand signal (may have seconds count down)
Assumption: walkers will not start across when the warning signal is blinking.
Assumption: calculating only for walkers who have stepped out on the white signal but then the signal changes to blinking before the next step.
2.)Â Would it be best to use the time needed for the fastest walking rate to cross the street for the BlinkingHand time length? The slowest rate? The average rate?
3.)Â Â View the three pedestrian simulations simulating a long, short, & mean blinkinghand time.Â (simulation courtesy of University of Nebraska, Lincoln)
Discuss pros/cons of each simulation.Â
Guide students to these observations.
Short Time:Â based on the maximum walk rate â€“ results in the shortest blinkinghand time:Â Vehicle traffic has the least amount of delay but many pedestrians at risk of not getting across safely.
Mean Time:Â based on the mean walk rate.Â Vehicle traffic has a longer delay; some but not all pedestrians get across safely
Long Time:Â based on the minimum walk rate â€“ results in the longest blinkinghand time. Vehicle traffic has longer delay but pedestrians are able to all get across safely
What is the best rate to use for the blinking hand?Â (Best to use time needed for the minimum walking rate  safety is always most important.)
Â
Extensions
Traffic Engineers use the 85th percentile rate.Â (i.e. the 85th slowest rate for a data set of 100 rates).Â Why do they use the 85th percentile instead of the very slowest rate?
Why not give pedestrians extra time beyond the time needed for the slowest walker to cross?Â (too much delay for traffic) Â
How might the blinkinghand time be different near a:
Senior citizen homeÂ (seniors walk slower so times should be longer)
Athletic fitness centerÂ (members walk faster so times could be shorter)
Any other unique situations?
Â
ExerciseÂ (use student worksheet page 3)
Â
Suppose classroom volunteer number one lived 2 miles from school.Â What is the latest he/she can leave home and still arrive at school on time?
Students can create walking rate problems related to other situations.
Data Set Used:
 Walking rates for 10 pedestrians
 MATC pedestrian video (Fremont & 52^{nd} St)
 MATC “blinkinghand time” simulations :
 Large pedestrian data set
Materials Needed:
Needed:
 Computer
 LCD projector
 Access to the Internet
 Stop watches
 Measuring tools (tape measures, yard/meter sticks)
 Pencils
 Calculators
Provided:
 Pedestrian Walking Rates  Large Data Set
 MATC video: "Pedestrian Footage" (see MATC Video Library
 MATC simulations: "Long Time", "Mean Time", "Short Time" (see MATC Video Library)
Preparation Period:
 Daily prep: 1015 minutes (equipment setup & video queue up)
 Copy time for student materials
Implementation Period:
3 â€“ 4 days (based on 52 minute periods)
Science, Math, Engineering and / or Technology Implications:
Math concepts applied to real world problems.
Exploration of problem solving in dynamic situations.
Exposure to one or more fields of engineering.
Exploration of problem solving in dynamic situations.
Exposure to one or more fields of engineering.
Considerations for Diversity in Education:
Handson activities.
Visual presentations.
Group work.
Visual presentations.
Group work.
Lesson Files
Warm Up for Day 1A short activity to start students thinking about walking rates.
[size: 28672] [date uploaded: Jul 20, 2008, 3:45 pm ]
Student Worksheet Page 1
Student worksheet for gathering data on walking rates from various sources.
[size: 41984] [date uploaded: Jul 20, 2008, 3:47 pm ]
Student Worksheet Page 2
Student worksheet for calculating the mean, median, and mode of the data as well as determining the optimum time needed for a "Blinking Hand".
[size: 43008] [date uploaded: Jul 20, 2008, 3:49 pm ]
Student Worksheet Page 3
Walking rate applications for table groups.
[size: 26112] [date uploaded: Jul 20, 2008, 4:01 pm ]
Large Pedestrian Data Set
A table of walking rates based on a large numbers of people and broken down into age groups and gender groups.
[size: 43008] [date uploaded: Jul 20, 2008, 4:08 pm ]
Large Pedestrian Data Set for Overhead
The large data set table sized for use on the overhead.
[size: 41472] [date uploaded: Jul 20, 2008, 4:10 pm ]
Additional Resources and Links
Web URL addresses and other resouces that relate to engineering. Most have a strong middle school connection.
[size: 34304] [date uploaded: Jul 20, 2008, 4:13 pm ]
Lincoln's Traffic Lights
News article describing how the traffic lights work in Lincoln, NE.
[size: 38400] [date uploaded: Jul 20, 2008, 4:15 pm ]
Rubric
A rubric that can be used to assess student learning and group work.
[size: 33792] [date uploaded: Jul 20, 2008, 4:16 pm ]
Video Pedestrian 1
Actual footage of a pedestrian crossing a 39 ft street.
[size: 2366857] [date uploaded: Jul 20, 2008, 4:32 pm ]
Video Pedestrian 2
Actual footage of a pedestrian crossing a 39 ft street.
[size: 5556024] [date uploaded: Jul 20, 2008, 4:45 pm ]
Video Pedestrian 3
Actual footage of a pedestrian crossing a 39 ft street.
[size: 3471421] [date uploaded: Jul 20, 2008, 4:47 pm ]
Video Pedestrian 4
Actual footage of a pedestrian crossing a 39 ft street.
[size: 4577701] [date uploaded: Jul 20, 2008, 4:50 pm ]
Video Pedestrian 5
Actual footage of a pedestrian crossing a 39 ft street.
[size: 4158825] [date uploaded: Jul 20, 2008, 4:52 pm ]
Video Pedestrian 6
Actual footage of a pedestrian crossing a 39 ft street.
[size: 5624564] [date uploaded: Jul 20, 2008, 4:54 pm ]
Video Pedestrian 7
Actual footage of a pedestrian crossing a 39 ft street.
[size: 5016310] [date uploaded: Jul 20, 2008, 4:57 pm ]
Video Pedestrian 8
Actual footage of a pedestrian crossing a 39 ft street.
[size: 5415044] [date uploaded: Jul 20, 2008, 5:00 pm ]
Video Pedestrian 9
Actual footage of a pedestrian crossing a 39 ft street.
[size: 5391535] [date uploaded: Jul 20, 2008, 5:02 pm ]
Video Pedestrian 10
Actual footage of a pedestrian crossing a 39 ft street.
[size: 4779004] [date uploaded: Jul 20, 2008, 5:04 pm ]
Video Pedestrian 11
Actual footage of a pedestrian crossing a 39 ft street.
[size: 5346936] [date uploaded: Jul 20, 2008, 5:07 pm ]
Some video files may require Adobe Flash to open or view.