### Summary

Students learn about and practice converting between fractions, decimals and percentages. Using a LEGO® MINDSTORMS® NXT robot and a touch sensor, each group inputs a fraction of its choosing. Team members convert this same fraction into a decimal, and then a percentage via hand calculations, and double check their work using the NXT robot. Then they observe the robot moving forward and record that distance. Students learn that the distance moved is a fraction of the full distance, based on the fraction that they input, so if they input ½, the robot moves half of the original distance. From this, students work backwards to compute the full distance. Groups then compete in a game in which they are challenged to move the robot as close as possible to a target distance by inputting a fraction into the NXT bot.### Engineering Connection

Understanding the concepts of decimals, fractions and percentages and how to convert between them is fundamental to the field of engineering. Engineers, such as civil and mechanical engineers, use these three forms of numbers in endless different applications. For example, the factor of safety for a structural member may be represented by a fraction or a decimal. In the field of risk assessment, analysis often includes applying a probability to a certain event; this probability ranges from 0 to 1 (in decimal form), which can be converted into a percentage (0% to 100%). Although decimals, fractions and percentages all essentially represent the same thing, it is important to be able to fluently convert between the three forms for situations in which it is more beneficial to express a number in one format over another.

###
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

- Develop understanding of fractions as numbers. (Grade 3) Details... View more aligned curriculum... Give feedback on this alignment...
- Use decimal notation for fractions with denominators 10 or 100. (Grade 4) Details... View more aligned curriculum... Give feedback on this alignment...
- Understand decimal notation for fractions, and compare decimal fractions. (Grade 4) Details... View more aligned curriculum... Give feedback on this alignment...
- Perform operations with multi-digit whole numbers and with decimals to hundredths. (Grade 5) Details... View more aligned curriculum... Give feedback on this alignment...
- Convert like measurement units within a given measurement system. (Grade 5) Details... View more aligned curriculum... Give feedback on this alignment...
- Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. (Grade 5) Details... View more aligned curriculum... Give feedback on this alignment...
- Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (Grade 6) Details... View more aligned curriculum... Give feedback on this alignment...

###### International Technology and Engineering Educators Association: Technology

- Tools, materials, and skills are used to make things and carry out tasks. (Grades 3 - 5) Details... View more aligned curriculum... Give feedback on this alignment...
- Various relationships exist between technology and other fields of study. (Grades 3 - 5) Details... View more aligned curriculum... Give feedback on this alignment...

###### New York: Math

- Develop understanding of fractions as numbers. (Grade 3) Details... View more aligned curriculum... Give feedback on this alignment...
- Understand decimal notation for fractions, and compare decimal fractions. (Grade 4) Details... View more aligned curriculum... Give feedback on this alignment...
- Use decimal notation for fractions with denominators 10 or 100. (Grade 4) Details... View more aligned curriculum... Give feedback on this alignment...
- Convert like measurement units within a given measurement system. (Grade 5) Details... View more aligned curriculum... Give feedback on this alignment...
- Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. (Grade 5) Details... View more aligned curriculum... Give feedback on this alignment...
- Perform operations with multi-digit whole numbers and with decimals to hundredths. (Grade 5) Details... View more aligned curriculum... Give feedback on this alignment...
- Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (Grade 6) Details... View more aligned curriculum... Give feedback on this alignment...

### Pre-Req Knowledge

Students should already have be introduced to the concepts of decimals, fractions and percentages, and be able to multiply and divide decimals.

In order to conduct this activity, it helps if the teacher is familiar with building and operating the LEGO MINDSTORMS NXT kit and programming the robot with the NXT software, although the necessary program is provided.

### Learning Objectives

After this activity, students should be able to:

- Convert between fractions, decimals and percentages.
- Explain how fractions, decimals and percentages are related to each other.

### Materials List

Each group needs:

- LEGO MINDSTORMS NXT robot, such as the NXT Base Set (5003402) for $159.98 at https://shop.education.lego.com/legoed/en-US/catalog/product.jsp?productId=5003402& isSimpleSearch=false&ProductLine=NXT
- LEGO MINDSTORMS Education NXT Software 2.1, available as a single license (2000080) for $39.97 or a site license (5003413) for $271.96 at https://shop.education.lego.com/legoed/en-US/catalog/product.jsp?productId=prod120017&isSimpleSearch=false&ProductLine=LEGO+MINDSTORMS+Education+NXT
- computer, loaded with NXT 2.1 software
- DFP Program (an rbt file), programming for the NXT intelligent brick
- paper and pencils, for calculations by hand
- yardstick, meter stick or tape measure, for measuring robot distances traveled
- DFP Pre-Activity Quiz, one per student
- DFP Worksheet, one per student
- DFP Post-Activity Quiz, one per student

To share with the entire class:

- computer with internet access and projector to show a PowerPoint file
- DFP Presentation (a PowerPoint file)

### Introduction/Motivation

Throughout the course of our lives, many situations will arise in which we will be faced with using decimals, fractions and percentages. Gaining a complete understanding of what they are and knowing how to convert between these number forms is imperative.

Where might we use decimals, fractions and percentages? (Listen to student ideas and examples.) Well, of course we use them in our school classes, such as math and physics, but in most other classes, too (such as "percent of the planet's surface covered in oceans" or "8 of the 12 beans sprouted" or "ratio of basketball game wins to losses"), and even grading! We'll use them in our future jobs and careers, almost all of them, including engineering (such as: representing the safety factor for a structural part by a fraction or a decimal, or indicating the probability of a certain risk, ranging from 0 to 1, in decimal or percentage forms). And in we use them in our everyday lives, such as leaving a tip at a restaurant, or making salad dressing using a specific ratio of oil to vinegar.

When shopping, have you ever noticed signs such as "50% off" or "half off"? To double-check the price of something, or to compare prices, we often do quick calculations in our heads that require us to convert percentages or fractions to decimals to more easily work it out. A number such as 50% may be easy to understand, but if something costs 120% more, it might be easier to convert this number to a decimal to do the math. When tax is added to the purchase price, say 8.875%, we commonly convert this percentage into its decimal format to make it easier to do a quick calculation.

These and many more examples show the advantages to being able to convert easily between the decimals, fractions and percentages in everyday life.

### Vocabulary/Definitions

decimal: A system of numbers in which each place has a value 10 times the place to its right. For example, the first position after the decimal point is 10 times less in value and referred to as tenths, then to the right again is hundredths, etc.

fraction: A numerical quantity written as a ratio of two numbers.

percent : (%) Out of one hundred; per hundred. For example, 25% means 25 out of 100.

### Procedure

Background

The LEGO MINDSTORMS NXT robot is an ideal tool for teaching students math and science concepts. By having fun while learning new concepts, students remember what they are taught. This is the primary motivation behind the use of NXT robots in the classroom.

The LEGO NXT robot used in this activity is a simple "five-minute bot" with a touch sensor added. The touch sensor serves as an interface to enable students to enter any fraction of their choosing. The first use of the touch sensor selects the numerator; the next use of the button selects the denominator; pressing the enter button on the NXT brick stores each number. Then students convert this fraction, by hand calculations, into a decimal and then a percentage. As they proceed, they use the robot to double check their work. Next, the robot moves a distance, based on the input fraction, so students must apply their prior knowledge about multiplying and dividing decimals to calculate the full distance that the robot is moving. This works well as a game. Groups each select a fraction, which in turn instructs the robot to move that fraction of the unknown full distance, with the goal being to determine the correct fraction to move the robot a target distance. The group that gets the robot the closest to a target wins.

Before the Activity

- Gather materials and make copies of the DFP Pre-Activity Quiz, DFP Worksheet and DFP Post-Activity Quiz one each per student.
- For each group, prepare a Five-Minute Bot according to the instructions at http://www.nxtprograms.com/five_minute_bot/steps.html. Then attach one touch sensor to any part of each robot, for example, the rear of the robot is a good spot that provides easy student access to the sensor.
- Download the DFP Program (a rbt file) onto the each NXT brick. Alternatively, write and download your own program such that:

- The robot first instructs students to use the touch sensor to enter a value for the numerator (for example, if the button on the touch sensor is pressed once, the numerator is 1; if pressed 7 times, the numerator is 7). Once finished, pressing the enter button on the NXT brick stores this value.
- Depending on students' level of comfort with the concept, the program asks students to enter a value for the denominator using the same method described above (denominator can be incremented by 10s). Alternatively, a denominator (such as 10) can be automatically generated instead of having the students choose one). Again, once finished, pressing the enter button on the NXT brick stores this value as the denominator.
- Next, have the NXT brick display the fraction. Since the brick is not capable of showing numbers in fraction form, use the different lines on the display screen to place the numerator on the top and denominator on the bottom, creating the illusion of a fraction.
- This "fraction" appears on the NXT brick until the enter button is pressed again. Once this is done, the robot converts the fraction into a decimal.
- This decimal remains on the NXT brick until the enter button is pressed again, at which time the NXT robot converts the decimal into a percentage.
- Finally, pressing the enter button one final time commands the robot to move a certain distance. An initial distance is chosen (such as 10 feet) and the fraction that is created by students is the fraction of this initial distance that the robot moves. Thus, in this case, if the fraction 5/10 is input, the robot moves 5 feet.
- Putting these instructions in a loop enables students to rerun the program and keep using it to check their conversions.

- Prepare a computer and projector to show the class the DFP Presentation (a PowerPoint file) to review the methods used to convert between decimals, fractions and percentages.

With the Students

- Administer the pre-activity quiz.
- Present the Introduction/Motivation content to students.
- Hand out the worksheets and go through the 12-slide PowerPoint presentation with the class to review the methods used to convert between decimals, fractions and percentages. Pause at appropriate times to allow students to complete the related worksheet conversion problems.
- Hand out a NXT robot to each group and explain the program to them. As they convert fractions (of their own choosing) into decimal and percentage forms through hand calculations, they can double check their work with the robot.
- Direct students to use the touch sensor to run the program and enter fractions of their choosing. (The first use of the touch sensor button selects the numerator, locked in by pressing the enter button on the NXT brick; the next pressing of the touch sensor button selects the denominator, again stored by pressing the enter button on the NXT brick.)
- Once this is done, students make calculations by hand to convert the fraction they entered into decimal form. They press the NXT brick's enter button to double check their work, to see if they got the correct answer.
- Next, they convert, by hand, the decimal into a percentage. Again, pressing the enter button reveals the correct answer so they can verify whether their hand calculations were done correctly.
- Pressing the enter button again causes the robot to move a certain distance. Students measure this distance. Explain that the robot only moves a fraction of the full distance. Their challenge is to figure out what distance the robot would have moved if the fraction was 1/1. Expect students who are fully understanding the concepts to be able to use the known fraction and robot travel distance to figure out the full distance.
- Once this is understood, let students have fun by creating fractions that result in the robot moving whatever distances they want. Using the numbers above as an example, if they wanted the robot to move 8 feet, students can enter a fraction of 8/10.
*Competition:*Conduct a game in which competing groups must enter a fraction that causes the robot to travel a specified distance. To do this, they must work backwards to calculate the initial distance based on the first fraction entered and the distance that the robot moved as a result of this fraction. The group whose robot moves the closest to the specified target wins the game.- Collect the completed worksheets.
- Conclude by administering the post-activity quiz.

### Attachments

### Troubleshooting Tips

Make sure all motors and sensors are correctly connected to the ports specified in the program.

### Assessment

*Pre-Activity Quiz:* Before beginning the activity, administer the DFP Pre-Activity Quiz to determine how familiar students are with the topic of converting between decimals, fractions and percentages. This assessment also alerts students to what they will be learning.

*Worksheet:* During the DFP Presentation, have students use the DFP Worksheet to practice solving conversion problems. The worksheet provides the same type of problems as the pre-quiz and post-quiz. Review students' work and answers to assess how much they learned from the presentation. In addition, ask students be come up to the classroom board to solve examples from the worksheet and presentation.

*Post-Activity Quiz:* At activity end, administer the DFP Post-Activity Quiz to determine how much students have learned from the activity. Questions are similar to the pre-activity quiz and worksheet.

### Activity Extensions

For additional explanation and practice problems, direct students to the video and problems at the Kahn Academy, as described in the last slide of the presentation and listed in the Additional Multimedia Support section.

Expand the activity by teaching students about fractions greater than 1. For example, based on a robot with a target distance of 10 feet, a robot input fraction of 15/10 would move the robot a distance of 15 feet.

### Additional Multimedia Support

Five-Minute Bot building instructions: http://www.nxtprograms.com/five_minute_bot/steps.html

LEGO NXT touch sensor information: http://mindstorms.lego.com/en-us/products/default.aspx#9843

Khan Academy video instruction and practice problems on "Representing a number as a decimal, percent and fraction" (5:25 minute video): https://www.khanacademy.org/math/arithmetic/decimals/percent_tutorial/v/representing-a-number-as-a-decimal--percent--and-fraction-2

### Contributors

Javed Narain### Copyright

© 2013 by Regents of the University of Colorado; original © 2013 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.

Last modified: July 21, 2016

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