Applying a Problem-Solving Protocol to Momentum Problems
Lesson 3 of 14
Objective: Students will use the G.I.R.L.S. protocol to solve problems related to the momentum of an object.
The goal of this lesson is to help students use the G.I.R.L.S. protocol to solve problems that relate to momentum. This lesson addresses the HSA-SSE.A.1a and HS-PS2-2 standards because it asks students to use a triangular model of momentum to solve a linear equation for either momentum, velocity or mass. It aligns with the NGSS Practices of Using Mathematical and Computational Reasoning (SP5) because students will use the G.I.R.L.S. protocol to solve a set of practice problems and take notes from a set of slides to explain factors that are related to an object's momentum.
Within this lesson, students begin by using a triangular model of momentum to determine the mass, velocity and momentum of a system in the context of a word problem. Students then work in pairs to use their understanding of momentum to complete a set of practice problems. Finally, students complete a set of physics quick checks on momentum. Within this lesson, I ask students to focus on deepening their current understanding of momentum. I assess student understanding throughout the lesson using informal check-ins, and assess each student's work at the end of the school day on a scale of 1 (Advanced Beginner) to 5 (Highly Proficient).
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 momentum is linearly related to both mass and velocity. Later on within this lesson I ask students to apply the G.I.RL.S. protocol to a set of momentum problems. In this lesson, I want students to get ready to use the G.I.R.L.S. protocol to demonstrate an understanding of the linear relationship between momentum, mass, and velocity.
I use the interactive whiteboard at the front of the room to project a set of problems during this lesson for students to construct a working explanation for each term in the momentum equation. I first talk about the BIG IDEA that momentum relates linearly to both mass and velocity. Then I project a triangular representation of that equation during the notes section to help students solve for any one of the three terms if the other two terms are known. I give an example of how to use the triangle to generate the equation p = m x v. Then I ask students to create equations for mass and velocity using the triangular form of the equation in their notebooks. This task asks students to use their previous understanding of linear expressions to understand a new physics concept of momentum.
Notes: The Momentum Equation
During this section, I project a set of Notes on the interactive whiteboard at the front of the room. I ask students to spend the first 10 minutes writing the notes in their notebooks. Then I ask students to spend the next 5-7 minutes creating two additional equations for mass and velocity using the triangle equation model with their table mates. I project a guiding question on the interactive whiteboard which asks students to "Use the triangular model of the momentum equation to solve for each of the three terms: Mass, Velocity and Momentum" as a focus statement. Then I ask a volunteer to show how to generate the three equations. I then take a temperature reading to see whether students agree with the volunteer student's solution. This activity asks students to identify information from earlier in the school year that we use to understand physics content later in the lesson. After five minutes elapse I ask for volunteers and write the three equations on the interactive whiteboard at the front of the room. I want students to understand how important identifying information from mathematics is to understanding patterns within physics content.
In this section of the lesson, students spend about 10 minutes generating equations using algebra to rearrange the first equation from the notes to solve for mass and velocity respectively. Then students check that the units on both sides of the equal sign for each equation are equivalent. Students are really checking the validity of the triangular representation of momentum.
The goal of this section of the lesson is to use both guided notes and group discussion as ways to make connections between the triangular model and the mathematical model for momentum. At the end of this section I ask for volunteers from each station to provide a verbal summary of where they are because I want students to give me a feedback and to provide candid reflections on the ease of the task and the connections between the information they collected and concepts they already know. This helps me see where they are in terms of their ability to apply mathematical logic to physics concepts. During thenextsection, students are given a chance to apply these skills to using the G.I.R.L.S protocol to solve problems about momentum.
I project an example problem on the interactive whiteboard and show students a step-by-step solution of a word problem on comparing the momenta of two objects. Then I ask students to work in pairs to solve the problems found here by writing solutions in their notebooks or on whiteboards from the resource area in the front of the room.
I give students a set of guided problems where I slowly give guidance as the problems increase in complexity. I highlight all of the important information in the problem statement and solve the first problem using the G.I.R.L.S. protocol. The second problem I highlight key information in the problem statement and partially complete the G.I.R.L.S. protocol. In the third problem, I ask students to identify the key information and apply the G.I.R.L.S. protocol without guidance. I collect student notebooks to grade and return to students during our next lesson.
Throughout this lesson, I give students multiple opportunities to listen to one another and to control the process of their learning. With this in mind, I include a closing activity for this lesson as I do in others so that students are assessed on their ability to use mathematical reasoning to solve for either the momentum, mass or velocity of an object.
The Closure activity asks students to solve real-world problems similar to those we introduce within the lesson and also works to make student thinking visible regarding the mathematical reasoning behind a solution to physics problems. Students write their responses to this activity on the sheets I provide. I check student responses to this closure to determine whether students are proficient in the understanding the mathematical behavior of key momentum terms.