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.
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- Common Core State Standards for Mathematics: Math
- 6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4)  ...show
- c. 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)  ...show
- International Technology and Engineering Educators Association: Technology
- New York: Math
- Develop understanding of fractions as numbers. (Grade 3)  ...show
- Understand decimal notation for fractions, and compare decimal fractions. (Grade 4)  ...show
- Use decimal notation for fractions with denominators 10 or 100. (Grade 4)  ...show
- Perform operations with multi-digit whole numbers and with decimals to hundredths. (Grade 5)  ...show
- Convert like measurement units within a given measurement system. (Grade 5)  ...show
- 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)  ...show
- Convert between fractions, decimals and percentages.
- Explain how fractions, decimals and percentages are related to each other.
- 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
- computer with internet access and projector to show a PowerPoint file
- DFP Presentation (a PowerPoint file)
|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.|
|A numerical quantity written as a ratio of two numbers.|
|Out of one hundred; per hundred. For example, 25% means 25 out of 100.|
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.
- DFP Presentation (pptx)
- DFP Presentation (pdf)
- DFP Pre-Activity Quiz (docx)
- DFP Pre-Activity Quiz (pdf)
- DFP Pre-Activity Quiz Answer Key (docx)
- DFP Pre-Activity Quiz Answer Key (pdf)
- DFP Program (rbt)
- DFP Worksheet (docx)
- DFP Worksheet (pdf)
- DFP Worksheet Answer Key (docx)
- DFP Worksheet Answer Key (pdf)
- DFP Post-Activity Quiz (docx)
- DFP Post-Activity Quiz (pdf)
- DFP Post-Activity Quiz Answer Key (docx)
- DFP Post-Activity Quiz Answer Key (pdf)
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© 2013 by Regents of the University of Colorado; original © 2013 Polytechnic Institute of New York University
AMPS GK-12 Program, Polytechnic Institute of New York University
Last modified: February 10, 2016