Students will demonstrate their understanding of the connections between mathematical models of kinetic and potential energy and roller coaster design.

The conservation of energy can be used to determine the velocity, height, kinetic energy or potential energy of a roller coaster without direct measurement.

This lesson addresses the HS-PS3-1 standard as a way to effectively distinguish between kinetic and potential energy using both a mathematical and a roller coaster model. Students explore physics concepts that relate to roller coasters using the NGSS Practices of Developing and Using Models (SP2), Using Mathematical and Computational Logic (SP5), and Constructing Explanations (SP6) that illustrate ways to manipulate the mathematical models for kinetic and potential energy when analyzing a roller coaster model.

At this point in the semester, students have constructed an explanation of the concept of energy and have used mathematical models, interactive activities, and simulations to study and learn more about the concepts of kinetic energy, potential energy, and work. Students begin by creating short presentations that extend their prior knowledge of the energy changes within a system using a roller coaster model. Students then share their presentations with small groups of their peers and receive warm and cool feedback to help them improve their understanding of the connections between roller coaster design and physics concepts like kinetic and potential energy.

I assess student understanding throughout the lesson using informal check-ins and assess each student's work at the end of the school day. I want students to learn to integrate information from various points of this course into a coherent presentation. Within this lesson, I ask students to leverage skills like proportional reasoning, applying mathematical models of kinetic and potential energy to a system, and working effectively in teams. One goal of this lesson is to help students extend the idea that the total mechanical energy of a system is conserved to determine the mass, velocity, height, kinetic energy and potential energy of a model roller coaster at different points on its track.

5 minutes

This portion of the lesson follows a routine to communicate the ideas that students need to be proficient in by the end of the semester and it also highlights the goals of the lesson to students. I summarize the key ideas through the bell-ringer activity and take attendance while students transfer the projected information into their notebooks.

Today's additional piece of information is a BIG IDEA which states that the conservation of energy can be used to determine the velocity, height, kinetic energy or potential energy of a roller coaster without direct measurement. In this lesson, I want students to get ready to use information from an EDpuzzle and prior knowledge from using roller coaster models, simulations, and interactive activities to demonstrate an understanding of the connection between physics concepts and roller coaster design.

25 minutes

During this lesson, I discuss the connections between kinetic and potential energy and their relevance to roller coaster design. I include a set of notes that I project at the interactive whiteboard in the front of the room. This part of the lesson focuses on determining the velocity at the top of a loop and the height of a hill on a roller coaster track with a known maximum height and mass. For the first ten minutes, I play the video at the front of the room for the entire class and pause at the pause points I have embedded as green question marks in the video.

During this twenty-minute period, students take notes in their notebooks. Students then spend the last five minutes of this section creating a similar problem using a value of 9.81 N/kg instead of the approximation of 10 from the video. I ask students if they have any questions or concerns about the methods discussed in the video. Some student responses include, "Will the initial height always be known for roller coaster problems?" and "Why do so many examples use 10 instead of 9.81 if 9.81 is more accurate?"

35 minutes

During this section of the lesson, students spend twenty minutes leverage their understanding of the mathematical models for kinetic and potential energies to create solutions for an unknown physical quantity. The unknowns in this section of the lesson include:

- kinetic energy
- potential energy
- velocity
- height

In this section, students will work in pairs to:

- Distinguish between Kinetic Energy and Potential Energy
- Use the conservation of energy to determine either the kinetic or potential energy of a roller coaster cart
- Use given factors of a roller coaster cart to determine unknown heights or speeds.

I project a sketch of a roller coaster on the interactive whiteboard at the front of the room with different labeled points and ask students to determine the unknowns. Students write their solutions in their notebooks. I ask students to each generate a similar problem and to solve it on poster paper.

Students spend five minutes each presenting the solution to their individual problems to a different group of up to four other students who grade them on this rubric. Click here to see an example of student work.

10 minutes

The closure activity asks students to write down ideas about energy and roller coaster design in their notebooks using a Free Write Routine. A free write routine asks students to write for a short amount of time, between 1 and 10 minutes on a certain topic without regard to structure. Student responses include: "You can predict the final velocity of a roller coaster if you know the height", "Once you know the initial height, you can find the total mechanical energy of the system", and "If you know the total mechanical energy and the height you can determine the speed of the roller coaster".

This type of closure activity asks students to demonstrate their understanding by writing key points without regard to the structure of the writing task in their notebooks. To wrap up this section of the lesson, I ask students to look at a tutorial from the Physics Classroom that I post on the class Edmodo wall.