 How is math connected to train safety and sensor technology?
The Hook:
Show students an animated Rail Safety for Kids Video and a Car Driving Around a Crossing Gate video. Ask students what types of sensors are in the school building or in their homes. Have students partner to see who can come up with the longest list of sensors and how they’re used.
Misconceptions:
The misconception that linear relationships do not exist in realworld applications.
Unit Lessons and Activities:
Unit 5: Trains Always Win! – Challenge: Design and simulate a safe and an unsafe train path using robotics, sensor technology and mathematical knowledge.
Pretest (Before Unit)
Lesson 1: Robotics and Sensor Technology (Days 12)
Lesson 1 will focus on students investigating sensor technology used in their everyday lives. Students will work as teams to program robots and explore their sensor controlled movements.
Activity 1: Introduction of the Big Idea, Generating the Essential and Guiding Questions (Day 1)
Activity 2: Robot and Sensor Technology (Day 2)
Lesson 2: Sensors and Train Safety (Days 37)
Lesson 2 will allow students to build understanding of graphs by creating data that matches a predefined graph. The Challenge will be for students to design and simulate a safe and unsafe train path using calculator robots, sensor technology and mathematical knowledge.
Activity 3: Motion Detector Sensors (Day 3)
Activity 4: Challenge: Trains Always Win CBL/EDP (Days 47)
Posttest (After unit)
Description of Challenge
Design and simulate a safe and an unsafe train path using robotics, sensor technology and mathematical knowledge.
List of Constraints Applied
 Use ramps for car and train movement.
 Use hot wheels car and a small toy train.
 Use Vernier Motion Sensor
 Use Norland Calculator Robots
Anticipated Guiding Questions
 How do Engineers minimize or prevent train and car crashes?
 How do we determine when a car and train will intersect?
 What types of sensors are used to control trains?
How will students test or implement the solution? What is the evidence that the solution worked? Describe how the iterative process from the EDP applies to your Challenge.
Select Solution: Students will choose the best design option from at least three of their alternative solutions.
Implement Solution: Design and simulate a safe and unsafe train path using robotics, sensor technology and knowledge of linear equations.
Communicate and Refine: Once students have tested their design, the iterative design process will guide students in determining what type of changes to make to their prototype that will improve it.
Evaluate Solution: The evidence that the solution worked is a safe and unsafe train path that the calculator robot travels, which can be explained using linear functions and utilizes sensor technology.
How will students present or defend the solution? Describe if any formal training or resource guides will be provided to the students for best practices (e.g., poster, flyer, video, advertisement, etc.) used to present work.
Communicate Solution: Students will present their design and simulation and share their results using a 2 minute sales pitch to explain their completion of the challenge.
What academic content is being taught through this Challenge?
Common Core State Standards ACED.A.3, FIF.B.4, FIF.B.5, FIF.B.6, FIF.A.2
 Represent constraints by equations and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
 Interpret key features of graphs and tables in terms of the quantities.
 Domain and range of a graph, application of domain and range in a realworld situation.
 Calculate and interpret the average rate of change of a function over a specified interval.
 Use function notation and interpret statements that use function notation in terms of a context.
Real world applications:
Sensors used to improve rail transport safety can detect potential problems like excessive vibrations, mechanical defects or speed and temperature anomalies.
What activities in this Unit apply to real world context?
Activity 2 – Robot and Sensor Technology, Activity 4 – Trains Always Win
Societal Impact:
Students will understand the importance of creating safe train tracks using sensor technology.
What activities in this Unit apply to societal impact?
Activity 2 – Robot and Sensor Technology, Activity 4 – Trains Always Win
What careers will you introduce (and how) to the students that are related to the Challenge? (Examples: career research assignment, guest speakers, fieldtrips, Skype with a professional, etc.)
We will discuss as a whole group the careers that are related to the challenge such as Railway Systems Engineering, Civil Engineering, Computer Engineering, Electrical Engineering, Mechanical Engineering, Industrial Engineering, Production engineering, and Railroad Engineering (or locomotive engineering, Train operator, Train driver or Engine driver), which is a person who drives a train.
Unit Academic Standards  CCSS
ACED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
FIF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
FIF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
FIF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
FIF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Results:
The data revealed student growth because students scored higher on average on the postassessment than on the preassessment. The class average on the preassessment was about 26% (4/15) and the class average on the postassessment was about %60 (9/15). Unfortunately, a few students with chronic absence resulted in them only taking the post assessment and not the pre assessment or vice versa, which may or may not have an effect on my data.
Reflection
I selected this content for the Unit because the concept of systems of equations, key features of graphs, and calculating and interpreting the average rate of change of a function are important concepts in Algebra I. Students exploring the mathematics in a train and car intersection coupled with sensor technology exposed students to a realworld application of systems of equations and graph formation. The purpose for selecting this Unit was met because students were able to calculate the rate of change and create an equation for the motion of the car and train modeled in the challenge. They were also able to design a safe intersection of the train and car by using their calculations to determine when to trigger the sensor to lower the gate. Students successfully found solutions that resulted in concrete meaningful actions for the Unit’s challenge. A picture of one group’s train and car intersection:
One thing I would change if I retaught this unit would be to have students design a crossing gate connected to the motion sensors using the mathematical calculations to inform them of when to lower the crossing gate for a safe intersection. I would teach this Unit again because it really helped students to see the importance of sensor technology in their lives and it showed them that they could use mathematics to model a car and train intersection. Also, the Unit gave students the opportunity to program robots using software and sensor technology to complete a minichallenge. Students were exposed to a LabCamera application that used motion sensors to engage students in replicating a preset graph. They worked in teams using the Engineering Design Process document to Define the Challenge and Gather Information by researching car and train intersections and sensor technology. Students worked with their teammates to Identify Alternative methods of creating a safe crossing gate at the car/train intersection and most students Implemented the Solution choice that had a crossing gate lowering in a timely manner based on the speed of both the car and train. Students Evaluated their solutions based on the feedback they received from their classmates and Communicated their solutions to the entire class by giving a presentation of the completion of their EDP document. The presentation was to show their full implementation of the Engineering Design Process in completing the challenge. The students used a rubric I developed to score originality, math language usage, design completion, presentation quality, and full implementation of the EDP. One success was that all students were fully engaged in programming the robots; low/med/high achieving, ELL students, and IEP students. One shortcoming was some students showed a lack of understanding of how to solve a system of equations algebraically, and preferred doing it graphically. Also, not having as many Lego Mindstorm robots resulted in each group using two motorized cars instead of one and not being able to download the Vernier sensor software on the student laptops resulted in students using their calculations to determine when to trigger sensor technology for the safe intersection. Students successfully developed an equation to represent the motion of the car and train after a minilesson on finding the rate of change and creating an equation. Many students met my goal for them to be able to answer questions based on the standards for the Unit: graphing and identifying key features of a graph, calculating rate of change, forming the equation of a line using function notation, and understanding the domain and range of a function.
Common Core State Standards  Mathematics (CCSS)

Standards for Mathematical Practice

Make sense of problems and persevere in solving them

Model with mathematics 
Use appropriate tools strategically

Attend to precision
