### Summary

Students use three tracks marked on the floor, one in yards, one in feet and one in inches. As they start and stop a robot specific distances on a "runway," they can easily determine the equivalent measurements in other units by looking at the nearby tracks. With this visual and physical representation of the magnitude of the units of feet, yard and inches, students gain an understanding of what is meant by "unit conversion." They also gain a familiarity with different common units of measurement. They use multiplication and division to verify their physical estimated unit conversions. Students also learn about how common and helpful it is to convert from one unit to another in everyday situations and for engineering purposes. This activity helps students make the abstract concept of unit conversion real so they develop mental models of the magnitude of units instead of applying memorized conversion factors by rote.### Engineering Connection

Making measurements and unit conversions plays a significant role in nearly all engineering and science endeavors, as well as ordinary day-to-day situations. Almost all of the data collected by scientists and engineers have units, and these numbers are converted to other units, depending on how they are to be used in equations and calculations. Engineers identify units in all their design documentation, and must be able to convert between units to make the measurements or specifications suitable for the units being used in the projects or locations where the designs are to be implemented.

### Pre-Req Knowledge

Students should be comfortable with basic mathematical skills, including multiplication and division.

### Learning Objectives

After this activity, students should be able to:

- List different units of length.
- Describe different lengths using physical examples.
- Convert one unit of length into another.
- Explain how units, measurements and conversion are used in engineering.

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###
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*.

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

- Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?

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

- Knowledge gained from other fields of study has a direct effect on the development of technological products and systems. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### New York - Math

- Recognize and apply mathematics to other disciplines (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
- Determine personal references for metric units of length (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

Each group needs:

- LEGO® MINDSTORMS® EV3 robot and additional LEGO parts including: 2 motors, 1 touch sensor and 3 wires to connect motors and sensors to the EV3 brain (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) [Alternatively, instead of a robot, have one student use a yardstick or measuring tape to measure and mark the given worksheet values.)
- pre-programmed EV3 brick and set-up instructions; use the online instructions available at https://www.youtube.com/watch?v=Dhe2jXi3Fc4 and the attached EV3 Robot Program (ev3) program file
- Pre-Activity Worksheet, one per student
- Activity Datasheet, one per student
- Post-Activity Worksheet, one per student

To share with the entire class:

- masking tape
- markers
- yardstick or ruler (marked in inches)

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 Base Set

### Introduction/Motivation

(Before starting the activity, administer the Pre-Activity Quiz; see the Assessment section for details.)

The mathematics and concepts behind unit conversion represent fundamental and significant parts of engineering-related work. Engineers deal with many sorts of data obtained from experiments and related to modeling—sometimes data needs to be converted from one unit to another depending on where the numbers will be used! *Engineering examples:* If engineers design an electronic device that is going to be built in another country where they use a different set of units, such as the metric system, then the units used to describe the project need to be converted, say from inches to centimeters. If a robotics engineer in the US wants to have some parts made in another country, s/he might need to convert the units of her/his drawings into units that are used in that country. *Everyday examples: *Your dad says he needs 30 feet of rope, but when your mom is at the store, the rope packages only indicate the lengths in yards. So it would be helpful to be able to convert your dad's 30 feet measurement into yards, so your mom knows which package of rope to buy.

So you can gain experience with an engineering setting, today you will take on engineering design team roles and take distance measurements for a robot car. The engineering firm you work for desires blueprints of various types of race tracks, in different units, so that they have scaled models of race tracks with the correct distance the car travels in different units. To measure the distance the car travels in different units, you will use actual measuring "tracks."

### Vocabulary/Definitions

conversion: An operation used to switch between different units.

measurement: The value of a quantity given in terms of a set of units.

unit: A quantity (length, time or value) adopted as a standard measurement.

### Procedure

Background

Students often fail to grasp the concept of different units of measurements and unit conversion early in their educations. The classroom problems that students are asked to solve, such as converting from yards to feet or feet to inches, may seem simple to adults and teachers, however to students the arithmetic may be difficult and often the concept of "unit conversion" may be abstract. Even though students may have memorized conversion factors, such as one foot is equivalent to 12 inches or one yard is equal to three feet, they often have not developed mental models of the magnitude these units represent (such as, inches make up feet, therefore a foot is larger in magnitude than inches).

Summary

In this activity, students measure the distance a robot travels using different units of length. Three parallel tracks are made on the floor using masking tape. The lengths of these "runways" are marked in yards, feet and inches, respectively. The robot is programed to move a certain distance on one runway, as specified by a student. The EV3 robot has a touch sensor (press of a button) to easily command it to move and stop. Students then convert that distance to two other sets of units by seeing where the same distances fall on the other two runways. They confirm these measurements by using simple mathematical calculations. (Alternatively, instead of a robot, have one student measure the given values on the worksheet. Have the student place an object at each measured value on the track.)

For example, the robot is set to travel a distance of one yard on a "primary runway," which is marked only in yards, while two adjacent tracks serve as "secondary runways," marked in feet and inches, respectively. The secondary runways serve as tools so that students can see the relationship between the conversion of the distance the robot travelled in yards into feet and inches. When the robot travels one yard, they can see that the one-yard distance it travels equates to three feet and 36 inches by looking across to the other two tracks to find the corresponding numbers. The adjacent runways enable them to visually compare the distances and make the conversion of units with ease. Figure 1 shows the layout of the three different "runway" tracks used for the activity.

Students are provided with a datasheet that contains values in inches, feet or yards in a blank table. Using those values, they place the robot in the appropriate runway track and direct it to travel the specified distance. Then, by looking at the adjacent tracks, they record the corresponding distances in the other two units. After recording the distances traveled in different units, they use multiplication or division to show how each value is obtained by mathematical calculation from the given value.

Before the Activity

- Gather materials and make copies of the Pre-Activity Worksheet, Activity Datasheet, and Post-Activity Worksheet, one each per student.
- On a large, smooth floor area, use masking tape to make three parallel 30-foot "tracks" or "runways," about a foot apart (see Figure 1). Use a dark-colored marker to accurately mark Runway 1 in yards, Runway 2 in feet and Runway 3 in inches, so that the three tracks are 10 yards, 30 feet, and 360 inches long, respectively.
- Build the EV3 robot as shown in Figure 1. For detailed instruction on how to build the robot (takes five minutes; a video is available, too), see: https://www.youtube.com/watch?v=Dhe2jXi3Fc4
- Download the EV3 Robot Program (ev3) file onto the EV3. This program makes a robot that will move specified distances. Make sure motors and sensors are connected to appropriate ports: Connect the motors to ports A and B of the EV3 brick and the touch sensor to port 1 of the EV3 brick.
- Make sure all EV3 brick battery packs are fully charged before starting the activity.

With the Students

- Before beginning the activity, distribute the Pre-Activity Worksheet and give students about 10 minutes to complete it.
- Conduct the Introduction/Motivation.
- As necessary, discuss different units of length: What are some different units of measurement that we use when describing distances and length? (Listen to student ideas. Possible answers: Inch, foot, yard, mile, millimeter, centimeter, meter, kilometer, light year.) Which of these would you use to measure the length of the hallway by our classroom? To measure the dimensions of a window opening? To measure the distance from the school to your house? Which of these is the shortest? Which is the longest? Once you learn how to do unit conversion, you could use any of these units to describe any length.
- Provide students with a quick review session on conversion and associated conversion factors. One way to do this is to review as a class the Pre-Activity Worksheet that students just completed. Make the following points:

**To convert larger units to smaller units, use multiplication**. For example, to convert from yards to feet, multiply the number of yards by 3; to convert from feet to inches, multiply the number of feet by 12; to convert from yards to inches, multiply the number of yards by 36.- In contrast,
**to convert smaller units to larger units use division.**For example, to convert from feet to yards, divide by 3; to convert from inches to feet, divide by 12; to convert from inches to yards, divide by 36.

- Divide the class into groups of three to five students each.
- Distribute the datasheets, one per person.
- Designate each group to do a specific task—either recording data, or positioning and interacting with the robot.
- Follow the datasheet in order, starting from row 1. Place the robot at a specified track and run the program from the "zero" position; press the touch sensor for the robot to start moving. Once the robot has moved some distance, press the touch sensor for the robot to stop. For example: Row 1 of datasheet has the number of yards specified (1 yard) and the equivalent cells for feet and inches are blank. Have students fill in those values by having the robot travel 1 yard by pressing the touch sensor to start and stop the robot. Once the robot has reached 1 yard, students can determine the corresponding values of 1 yard in feet and inches by seeing the equivalent measurements on the other tracks.
- Record the equivalent distances in the datasheet, to fill in the entire row.
- Repeat this process for the rest of the rows on the datasheet. Be sure to move the robot to its start position (beginning of the track) once you are finished with a row.
- Then give students time to verify that all their unit conversions are correct (or close) by using the correct mathematical operation (multiplication or division) to calculate the unit conversions.
- Analyze data: Now think about what our engineering design team is trying to do. Our engineering firm wants blueprints of various types of race tracks, in different units, so that they have scaled models of race tracks with the correct distance the robot car travels in different units. By measuring the distance a robot traveled in one unit, discuss with your design team (the entire class) how long engineers would need to make a race track in another unit. For example:

- If the robot travels 3 yards in total, how long would the race track be in inches? (Answer: 108 inches)
- If the robot travels 72 inches in total, how long would the race track be in yards? (Answer: 2 yards)

- Distribute the Post-Activity Worksheet and give students about 10 minutes to complete it.
- Review as a class the Post -Activity Worksheet that students just completed.
- Conclude with a class discussion to make a real-world connection to the importance of unit conversion. Ask the students: When might engineers need to convert units? (Possible answers: Engineers encounter unit conversion when creating various designs, these include blueprints. Civil engineers tend to work in meters/yards when describing how long bridges are, whereas biomedical engineers use millimeters when designing surgical tools. Say an engineer is designing a bridge that is 30 feet long and the railing material comes measured in yards. The engineer would need to convert them to the same units so s/he could specify exactly how much material is needed.)

### Attachments

### Assessment

*Pre-Activity Worksheet:* Before starting the activity, administer the six-question Pre-Activity Worksheet to evaluate students' base attitude towards and understanding of unit conversion.

*Activity Datasheet: *During the activity, have students use the Activity Datasheet, which provides a data table for them to fill in. Review their answers to gauge their mastery of the subject matter.

*Post-Activity Worksheet:* After the activity, administer the 10-question Post-Activity Worksheet to evaluate students' understanding of the concepts. Comparing the pre- and post-activity worksheets reveals whether the activity made any significant difference in students' comprehension of the subject matter.

### Additional Multimedia Support

To prepare the EV3 robot for this activity, follow the instructions provided for the Five Minute Bot, which can be built quickly, is fairly sturdy and turns easily on smooth floors. See: https://www.youtube.com/watch?v=Dhe2jXi3Fc4

A 4:19-minute video on YouTube shows the steps to build the Five Minute Bot. See http://www.youtube.com/watch?v=wjsJTenhHo8

### References

Dictionary. *Miriam Webster Online*. (Source of definitions for conversion, measure, unit) http://www.merriam-webster.com/dictionary

### Contributors

Akim Faisal### Copyright

© 2013 by Regents of the University of Colorado; original © 2011 Polytechnic Institute of New York University### Supporting Program

AMPS GK-12 Program, Polytechnic Institute of New York University### Acknowledgements

This activity was developed by the Applying Mechatronics to Promote Science (AMPS) Program funded by National Science Foundation GK-12 grant no. 0741714. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.

Additional support was provided by the Central Brooklyn STEM Initiative (CBSI), funded by six philanthropic organizations.

Last modified: January 31, 2018

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