Fight or Flight?

Lesson Rubric
Worksheet One
Worksheet Two
Worksheet Three
Worksheet Four
Worksheet Rubric
Pre-Test
Post-Test

Name: Erik Brown, Electronics Instructor; Beth Reynolds, Math Consultant
Grade: 11-12
School: Northwest Tech BOCES

Title/Context of Learning Experience

The purpose of this learning experience is to introduce students in the Electronics Program at BOCES to the basic concepts involved in analyzing and describing the effect gear ratio has on torque and speed. Since the students in this program are engaged in a Robotics unit of study in which they design, construct, and evaluate robots for various purposes, they need to have a thorough understanding of the basic principles of the mechanical advantage gained or lost in gear ratio dynamics.

The main focus of the learning experience is a scientific inquiry-based experiment to determine the effect that changing gear ratio has on relative strength and speed of a lifting mechanism built using FTC Robotics materials.

Students construct their own knowledge base by researching definitions and examples to explain basic concepts of gear ratio and torque, then sharing their findings with the class. They apply knowledge gained as they design and build the lifting mechanism to be used in their experiment. Through experimentation, data is gathered to be used in analyzing the relationship between targeted variables. An Excel worksheet is created to record and graph the data. Students are then expected to evaluate the results of their experiment in order to describe mathematically the overall relationship between various gear ratios, torque, and speed.

Given that students are expected to gain knowledge through analysis, synthesis, and evaluation to explain how gear ratios are used in real-world situations to gain mechanical advantage, this lesson falls in the D quadrant of the Rigor and Relevance Framework.

Standards

• MST.S5 Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.
• Performance Indicator – Students assemble and operate simple technological systems, including those with interconnecting mechanisms, to achieve different kinds of movement.
• A.R.6 Use mathematics to show and understand physical phenomena.
• MST.S4.C13 Explain and predict patterns of motion of objects.

Problem Statement
Anyone who has peddled a bicycle up a hill has experienced the effect gear ratio has on speed and torque. However, in order to fully understand the dynamics involved, some scientific experimentation involving manipulation and observation of technological devices coupled with mathematical analysis is essential.

This learning experience seeks to give students the opportunity to gain knowledge and skills necessary to understand how gears work to our advantage in everyday devices and, more specifically, in robotic mechanisms that can be used for a variety of purposes.

Simply put, the problem is: How do gears make mechanical devices more effective at performing the work they are designed to do?

Essential Question
How can gear ratios be used to vary relative strength (torque) and speed of mechanical devices?

Assessment Plan
Students complete a 5 question pre-assessment to measure their level of prior knowledge. A post-test is used to gauge improvement.

Presentations completed in Lesson One are evaluated using the Presentation Rubric.

Each of the three lessons requires students to complete worksheets or tables and charts in Excel. These are evaluated for completeness and accuracy of application of concepts using the Worksheet Rubric.

Student progress is monitored throughout the learning experience by observation and students are made aware of their performance through discussions with the teachers.

Procedure
Lesson One:
To initiate discussion of what mechanical advantage means, students are asked to view a short video presentation entitled Mechanical Advantage. The question of how gears are used to gain mechanical advantage in common devices such as clocks, car engines, electric screwdrivers, bicycles, etc. sets the stage for further investigation into the concept of gear ratio and its relationship to rotational strength and speed.

Students are divided into teams and each team is given the task of researching definitions and examples of gear ratio or torque using Worksheet #1 (Mechanical Advantage – Gear Ratio) or Worksheet #2 (Mechanical Advantage – Torque) as a guide. Teams then present demonstrations that illustrate their topic.

Lesson Two:
To review concepts presented in the previous lesson, students work in teams to create a question related to gear ratio or torque, trade questions with another team, and solve each other’s problems. Discussion of student solutions provides an opportunity for the teacher to revisit essential points from the first lesson.

Teams of students are then given the task of investigating the relationships among gear ratio, torque, and axle speed. They design and build a gear box to be used to measure speed and lifting capability at gear ratios of 1:1, 1:3, 1:9, and 1:45. Each team uses their gear box to conduct an experiment in which they test the axle speeds and lifting capabilities of their device for all given gear ratios. They record their data on the spreadsheet on Worksheet #3 (Mechanical Advantage – Experimental Data) and compare their results to the other teams.

Lesson Three:
Using the data collected in Lesson 2, students use Microsoft Excel® to organize the observations from their experiments and create charts to represent the relationships between gear ratio and axle speed and gear ratio and lifting capability. This is accomplished by the class as a whole, lead by the teacher who uses a projector and computer to demonstrate the use of Excel as students work at individual computer workstations.

Students present their findings to the class and work together to formulate mathematical methods of describing the relationships detected in the investigation.

Summary: Discuss the essential question: How can gear ratios be used to vary relative strength (torque) and speed of mechanical devices? Students then work in teams to complete Worksheet #4 (Mechanical Advantage – Speed).

Resources

• http://hilaroad.com/videos/ for the Mechanical Advantage video used in Lesson 1
• http://www.howstuffworks.com/ for a thorough discussion of how gears work

Instructional/Environmental Modifications
Activities engaged in throughout the lessons may be modified as necessary to meet the needs of the students. When working in teams, students with weaker skills should be matched with those with stronger backgrounds and abilities.

Time Required

• Planning = 1 hour
• Implementation = 1 – 1 ½ hours per lesson
• Assessment = 1 hour

Reflection
This learning experience goes beyond teaching technological knowledge to encouraging students to construct their own knowledge through research, experimentation, and analysis. Students use mathematical principles coupled with technology to learn about interrelationships among variables and how those interrelationships can be manipulated to create devices that meet the needs of humans. As such, it clearly addresses targeted math, science, and technology learning standards.

Creating this series of lessons gave us the opportunity to explore various methods of inquiry-based learning. We benefited from discussions about the advantages and disadvantages of various methods and tried to incorporate what we considered to be the best of those we found.

In our opinion it represents the “best” classroom practice because we built in many opportunities for hands-on activities, students learn and share with each other the knowledge they have gained, and there is a clear connection to application of the concepts in the real world.

It’s unfortunate that we were not able to actually teach this series of lessons his year, but we look forward to full implementation of a Robotics unit within the Electronics program next year and the opportunity to test these ideas on our students.