### Summary

As part of a design challenge, students learn how to use a rotation sensor (located inside the casing of a LEGO® MINDSTORMS ® EV3 motor) to measure how far a robot moves with each rotation. Through experimentation and measurement with the sensor, student pairs determine the relationship between the number of rotations of the robot's wheels and the distance traveled by the robot. Then they use this ratio to program LEGO robots to move precise distances in a contest of accuracy. The robot that gets closest to the goal without touching the toy figures at the finish line is the winning programming design. Students learn how rotational sensors measure distance, how mathematics can be used for real-world purposes, and about potential sources of error due to gearing when using rotation sensor readings for distance calculations. They also become familiar with the engineering design process as they engage in its steps, from understanding the problem to multiple test/improve iterations to successful design.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Electrical and mechanical engineers design motors that provide mechanical energy in all sorts of machines, everything from electric can openers to pin ball machines to cars and biycles. In the activity, the way the robot motor's rotation sensor is used to measure distance is the same as in other wheeled vehicles.

Computer programming is an important component of many modern engineering designs. As students design robot programs in this activity, they must have a "goal" or "concept" of what the program solution needs to do and how, before they begin writing the code. Next, the process of working on the code and "debugging" it inherently constitutes "revising and improving their designs based on the results of testing." Thus, the thought processes required to code programs that meet problem constraints are similar, if not identical, to the thought processes required for traditional engineering design of physical objects and products.

### Pre-Req Knowledge

- Familiarity with the LEGO MINDSTORMS EV3 robot and how to program its intelligent brick (computer).
- An understanding of the information presented in the What Is a Motor? How Does a Rotation Sensor Work? associated lesson.
- Completion of the Our Bodies have Computers and Sensors unit and the What Is a Sensor? lesson.

### Learning Objectives

After this activity, students should be able to:

- Explain how an EV3 robot moves by using a motor.
- Explain how motors rotate and enable motion by converting electrical energy to mechanical energy.
- Determine the relationship between the number of rotations of a robot's wheels and the distance the robot travels through experimentation and data collection and analysis.
- Program the LEGO taskbot to move a specific distance.
- Explain the basic steps of the engineering design process.

### More Curriculum Like This

**What Is a Motor? How Does a Rotation Sensor Work?**

Students learn about electric motors and rotational sensors. They learn that motors convert electrical energy to mechanical energy and typically include rotational sensors to enable distance measuring. Students create a basic program using the LEGO® MINDSTORMS® interface to control a motor to move a...

**Timing a Speedbot!**

Students strengthen their communicate skills about measurements by learning the meaning of base units and derived units, including speed—one of the most common derived units (distance/time). Working in groups, students measure the time for LEGO® MINDSTORMS® robots to move a certain distance.

**Get in Gear**

Students are introduced to gear transmissions and gear ratios using LEGO® MINDSTORMS® EV3 robots, gears and software. They learn how to build the transmission part of a vehicle by designing gear trains with different gear ratios. Once students learn the principles behind gear ratios, they are put to...

**Gears: Determining Angular Velocity**

Students work as engineers and learn to conduct controlled experiments by changing one experimental variable at a time to study its effect on the experiment outcome. Student groups assemble LEGO® MINDSTORMS® EV3 robots with variously sized gears in a gear train and then design programs using the EV...

###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### NGSS: Next Generation Science Standards - Science

- Use evidence to construct an explanation relating the speed of an object to the energy of that object. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
- Apply scientific ideas to design, test, and refine a device that converts energy from one form to another. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
- Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards - Math

- Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve unit rate problems including those involving unit pricing and constant speed. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- The engineering design process involves defining a problem, generating ideas, selecting a solution, testing the solution(s), making the item, evaluating it, and presenting the results. (Grades 3 - 5) Details... View more aligned curriculum... Do you agree with this alignment?
- Modeling, testing, evaluating, and modifying are used to transform ideas into practical solutions. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Missouri - Math

- Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve unit rate problems including those involving unit pricing and constant speed. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

Each group needs:

- LEGO MINDSTORMS EV3 robot, such as EV3 Core Set (5003400) for $389.95 at https://education.lego.com/en-us/products/lego-mindstorms-education-ev3-core-set-/5003400; LEGO MINDSTORMS EV3 taskbot, assembled using the core set materials and instructions at https://www.youtube.com/watch?v=Dhe2jXi3Fc4; while three motors come in the core set, if needed, additional LEGO EV3 Servo Motor, available for $24.99 at https://shop.lego.com/en-US/EV3-Large-Servo-Motor-45502
- LEGO MINDSTORMS Education EV3 Software 1.2.1, free online, you have to register a LEGO account first; at https://www.lego.com/en-us/mindstorms/downloads/download-software
- computer, loaded with EV3 1.2.1 software
- ruler
- calculator
- Master Driver Worksheet, one per group

Alternative: LEGO MINDSTORMS NXT Set:

*Note: This activity can also be conducted with the older (and no longer sold) LEGO MINDSTORMS NXT set instead of EV3; see below for those supplies:*

- LEGO MINDSTORMS NXT robot
- computer loaded with the NXT 2.1 software

To share with the class:

- Master Driver Presentation, a Microsoft
^{®}PowerPoint^{®}file - computer and projector, to show the presentation
- smooth floor space (such as tiled, not carpeted floor) to use as a track, with a start line and a finish line; make the track ~4 feet (~122 cm) long and ~ 2 feet wide (~30.5 cm)
- tape, to mark the track on the floor
- measuring tape, to position parallel to the 4-foot floor track, for measuring robot distance to finish line; tape down a flexible or rigid tape measure
- 15-25 toy figures, such as LEGO people or any other available small figurines or action figures, to line up across the entire finish line; it is recommended that the teacher and students bring in available figures from home, but if needed, the LEGO DUPLO Community People Set includes 20 adult figures for $67.95 at https://education.lego.com/en-us/products/community-people-set/45010

### Introduction/Motivation

How can math be useful in engineering problems? Today you will perform an activity that shows how math is very important in robot path planning. One important math concept we will use today is the concept of a ratio. Ratios are used to compare two quantities, and you can think of a ratio as a fraction or even as a division problem. You are probably used to hearing values given in the form a ratio and may not even realize it! For example, speed is a value that is a ratio. Think of the speed of a car, which is usually given in miles per hour. This is a ratio of the number of miles that a car is traveling in an hour, given that its speed remains the same. This ratio tells us the relationship between the miles a car is traveling and the time it takes.

Today, your engineering challenge is to make a robot travel a precise distance, no more, no less. To do that, you must understand the relationship between—or the ratio of—the number of rotations of the robot's wheels and the distance the robot travels. Once you know this ratio, you can use it to program the robot with a given number of rotations. The robot's rotation sensor tells the robot's computer (EV3 intelligent brick) how far to move with each motor rotation. Using this information and math calculations, your challenge is to create a LEGO MINDSTORMS EV3 program to make the robot move from a start line to a finish line without hitting the people standing at the finish line.

### Vocabulary/Definitions

constraint: A limitation or restriction. For engineers, constraints are the limitations and requirements that must be considered when designing a workable solution to a problem.

electric motor: A motor is an electrical machine used to create motion. The device converts electricity (electrical energy) into motion (mechanical energy). Typically performed by rotating an object.

engineering design process: A series of steps used by engineering teams to guide them as they develop new solutions, products or systems. Typically, the steps include: defining a problem (including criteria and constraints), brainstorming and generating ideas, selecting a solution, making and testing the solution(s), evaluating it, and presenting the results.

ratio: A mathematical description of the relationship between two quantities. For example, the ratio of legs to noses for humans is 2 to 1 or 2:1 or 2/1.

### Procedure

Before the Activity

- Gather materials and make copies of the Master Driver Worksheet, one for each student group.
- Assemble the LEGO MINDSTORMS EV3 taskbots by following instructions at https://www.youtube.com/watch?v=Dhe2jXi3Fc4 or in the core set.
- Use tape to prepare the track on a smooth floor by marking a start line and a finish line. Define the track width by making both tape lines 2 feet (~30.5 cm) long. Define the track length by placing the lines 4 feet (~122 cm) apart.
- Lay out a measuring tape along the track length for students to use for testing and calibration.
- Use the 8-slide Master Driver Presentation, a PowerPoint file, to teach and conduct the activity. Set up a computer/projector to show the presentation to the class.

With the Students

- Divide the class into student pairs. Distribute the assembled LEGO taskbots, one per group.
- Conduct a quick lesson review as described in the Assessment section.
- (
**slide 2**) Present the activity challenge: Make your robot move in a straight line from the start position, and make it stop accurately, as close to the finish line as possible, without hitting any people or crossing the finish line. - Inform (or remind) students of the engineering design process—which is a series of steps used by engineering teams to guide them as they develop new solutions, products or systems (
**slide 3**). The basic steps of the engineering design process are: defining a problem (including its criteria and constraints), brainstorming and generating different ideas, selecting the best design solution to fit the circumstances and constraints, making and testing the solution(s), and presenting the results. For engineers, constraints are the limitations (restrictions) and requirements that must be considered when designing a workable solution to a problem. This is a cyclical process that requires engineers to test and redesign solutions or products as often necessary so they end up with reliable finished solutions or products. In your engineering challenge today, you also will be going through many of these steps, especially testing and modifying your robot program to improve it for the best accuracy you can achieve. - Inform students that the activity has two parts (described on
**slide 4**). First they learn how to "calibrate" the distance the robot moves with each rotation, and then they tackle the main challenge, the programming and accuracy competition. - Explain the track setup for Part 1 of the activity (
**slide 5**). Identify the track parts (start line, finish line, measuring tape) and the constraints of the challenge (where to start and stop, people not to hit). Show students the track on the floor that was laid out prior to class. - Distribute the worksheets, one per group.
- Direct students to begin
**Part 1: Testing & Calibration**. Have them use the worksheet (also on**slide 6**) to gather data and determine the relationship between the number of rotations and the distance traveled by the robot. To accomplish this task, students adjust the number of rotations by programming the EV3 intelligent brick, which is the robot's computer. The goal is to identify a consistent ratio as the relationship between the distance and rotation. In other words, for each rotation, how far does the robot move? As students are working, check in with their progress to keep them on task to identify this ratio. - Next, direct students to begin
**Part 2: Programming & Accuracy Competition**. Remind them of the challenge objectives and constraints: Make the robot move from the start line to the finish line without crossing the line or hitting any figures. - Explain the track setup for Part 1 (
**slide 7**) and line up the toy people on the finish line. Inform them that the track is 4 feet long. Prompt students to think of how they can use the ratios they found in Part 1 of the activity to correctly program the robot to move 4 feet. If necessary, remind them that a foot is equal to 12 inches. Give them some time to discuss with their partners, and then program their robots to meet the challenge for their first trials. - When ready, run trial 1 of the competition by having groups demonstrate their program designs by taking turns testing the robots on the track. Remind students to record on the second page of their worksheets (also shown on
**slide 8**) how close their robots come to the finish line. - Have groups learn from their trial results and adjust their programming to increase the accuracy in the next trial. After each group has tested three times, the group with the LEGO taskbot that comes closest to the finish line without touching the toy people is the winning group.
- Conclude with a class discussion so students can share their lessons learned and issues encountered during the activity. Cover the topics and questions listed in the Assessment section.

### Attachments

### Assessment

Pre-Activity Assessment

*Lesson Review: *Review topics from the What Is a Motor? How Does a Rotation Sensor Work? associated lesson, including the definition of an electric motor and examples of common machines that use electric motors. Ask students the following questions to gauge their base knowledge of the activity topics:

- Fill in the blanks: An electric motor converts __________ energy to __________ energy. (Answer: electric; mechanical.)
- How does a rotation sensor work? (Answer: A rotation sensor measures how many rotations occur. For example, the speedometer and tachometer dials found on car dashboards are connected to rotation sensors that measure different variables, such as wheel rotation and engine crank shaft rotation. They convert those measurements to useful information, such as the car's traveling speed on the ground in miles per hour, or how fast the engine is spinning in RPM or rotations per minute.)
- What do you know about the engineering design process? (See what students volunteer. Tell them they will learn more during the course of the activity.)

Activity Embedded Assessment

*Testing and Data Collection and Programming:* Observe and assess students based on their participation during the activity. Expect all students to be involved with programming the LEGO brick/computer, measuring the distance the robot travels, and recording measurements on the Master Driver Worksheets. While students are working on the Part 1 of the activity, go from group to group and ask them if they have determined the relationship between the number of rotations and the distance traveled by the robot; in other words, for each rotation, how far does the robot move?

Post-Activity Assessment

*Comprehension Discussion: *Conclude with a class discussion so students can share their lessons learned and problems encountered during the activity. Assess their understanding through the topics and question below:

- What was our design challenge today? What are constraints? What were the criteria and constraints for our challenge? What were your ratios?
- How did you convert 4 feet into inches? (Listen to student explanations. Make sure they understand how to convert 4 feet to 48 inches by knowing 12 inches are in a foot.)
- How did you figure out the closest number of rotations to travel the track distance? (Listen to student explanations. Make sure they understand how to figure out the number of rotations by multiplying 48 inches by the ratio, which is in the form of number of rotations per inch.)
- Did you use math to determine how many rotations to use or estimate (guess) each time? (Discuss the results for each approach and explain how using mathematics can reduce trial and error.)
- What are some problems that you ran into? What errors did you encounter? How difficult was it to get your robot very close to the finish line without touching the people? (Listen to student stories. Expect students to mention that sometimes they were not able to calculate the rotations correctly. Ask them to suggest reasons for this. Possible answers: Their calculations might be incorrect. Gears don't mesh perfectly in general and that causes errors. Positioning the wheel accurately is difficult and if not perfect could lead to errors. All these add up and result in differences between mathematical calculations and actual measurements.)
- What is a LEGO MINDSTORMS EV3 servo motor? What is it used for? (Answer: The EV3 motor is an electrical machine used to create motion. The motor works by converting electricity [electrical energy] into motion [mechanical energy] and rotating an object. The device is similar to many other motors that run various machines that we use every day.)
- How does the servo motor control the distance the LEGO taskbot moves? (Answer: The motor has a built-in wheel rotation sensor that helps it control its motion, that is, it can move precise distances using this rotation sensor.)
- Do you think it is important for engineers to know how motors work? Why or why not? (Possible answer: Engineers must understand how motors work, especially if they design machines, which is what mechanical engineers often do. Many machines that we use every day need to rotate or move a certain distance or make some mechanical motion, and the engineers who design them had to know how to use motors correctly in their designs.)
- What were some of the steps of the engineering design process that you participated in today? (Listen to student answers to gauge their understanding of the process. Answer: Today you designed robot programs, and in doing so, you first had to have an idea of the problem you were trying to solve in order to get started; that's the
**defining the problem, identifying the criteria and specifying constraints**. Those are important first steps because before you began writing the code, you had to understand the problem you are trying to solve. When you and your partner talked together about possible ways to solve the problem—that was**brainstorming**and**generating ideas**. You moved forward by**choosing your best idea**to test. Then, you programmed the robot and tested it by running a few trials. When you modified the code to fix problems, we call that "debugging." And when you revised and improved the program many times based on what you kept learning through testing, you were**testing and refining the design**. So this is how you went through the steps of the engineering design process as you thought through, coded and evaluated code programs to solve our challenge today, to turn your ideas into working solutions.) - Look around the classroom. Think of the different rooms in your house. What are some examples of items you use every day that use electric motors?

*Post-Activity-Quiz: *At activity end, and after the class discussion, wrap up the lesson and activity by administering the three-question Electric Motors Post-Quiz provided in the associated lesson, What Is a Motor? How Does a Rotation Sensor Work? Review students' answers to gauge their comprehension.

### Contributors

Nishant Sinha, Pranit Samarth, Satish S. Nair### Copyright

© 2013 by Regents of the University of Colorado; original © 2013 Curators of the University of Missouri### Supporting Program

GK-12 Program, Computational Neurobiology Center, College of Engineering, University of Missouri### Acknowledgements

This curriculum was developed under National Science Foundation GK-12 grant no. DGE 0440524. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: February 6, 2018

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