# Challenge Problems: Momentum and Collisions

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## Objective

Students will apply their understanding of momentum and collisions to solve physics problems.

#### Big Idea

Total momentum in a system is conserved in the absence of external forces.

## Overview and Bell-ringer

5 minutes

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 HSN-Q.A.1, HSA-CED.A.4, W.11-12.7, and HS-PS2-2 standards because it asks students to use mathematical models of momentum to solve challenge problems that relate to momentum and collisions. It aligns with the NGSS Practices of Using and Developing Models (SP2), Using Mathematical and Computational Reasoning (SP5)  and Obtaining, Evaluating and Communicating Information (SP8) for science because students will use their understanding of momentum to solve a set of challenge problems that are related to an object's momentum. This lesson follows a series of lessons where students construct explanations of momentum using close reading strategies, model elastic collisions using bumper cars and use both simulations and experiments to investigate the conservation of momentum. This lesson is also similar to an earlier one from the projectile motion unit that also uses challenge problems.

During this portion of the lesson, students complete a routine where they write the objective and an additional piece of information in their notebooks. I project a slide with the date, the objective and an additional prompt  on the interactive whiteboard with a red label that says "COPY THIS" in the top left-hand corner. Sometimes the additional prompt is a BIG IDEA for the lesson or the Quote of the Day or a Quick Fact from current events that is related to the lesson. The red label helps my students easily interact with the information as soon as they enter the room and avoids losing transition time as students enter the classroom.

Today's additional piece of information is a BIG IDEA which states that the total momentum in a system is conserved in the absence of external forces. Later on in this lesson, I ask students to review the concept of the 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 challenge problems. Near the end of this lesson, 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).

## Momentum and Collisions Review

15 minutes

During the beginning of this section, I ask students what happens when two objects collide if the collision is perfectly elastic. I open the PhET collision lab simulation and change the settings so that two balls have different masses and velocities. I ask students to create an annotated prediction in their notebooks of what happens to the objects before, during and just after the collision. I remind students that their visual should have mathematical evidence to support their claims and that the visual's annotations are to include a definition of what "perfectly elastic" means physically and mathematically. As I circulate, I remind students to clearly state any assumptions they use in their model.

I then run the simulation and have students record the results which are displayed on the interactive whiteboard at the front of the room. I ask students to provide evidence to support their predictions. I ask students to think back to the quote of the day to try to get students to push past their misconceptions and I ask them about if there are any forces after the initial impulse was imparted. We share out and tease out that there is still motion when the net force of a system is zero.

Then I use poll everywhere and students complete a Yes or No vote on whether their predictions hold true when there is no net force on the system; the results are displayed as a bar graph on the Promethean Board and are used to start a discussion for the next session of the lesson. Poll everywhere offers a free way for educators to create polls that students can access using cell phones or using the web. After the poll, I have a student helper distribute quick checks to get a better assessment of students' understanding of the concept of momentum.

## Momentum Quick Checks

10 minutes

Students are given a choice of Quick Checks that relate to momentum to assess their ability to use units to guide their logic as they work through multi-step problems and draw conclusions from them. I distribute physics quick checks to assess a single standard using our school's five-point rubric. For example, a student who simply writes the momenta for each cart without showing work receives a 1 out of 5. Whereas a student who chooses and applies the correct model for momentum, but forgets to dimension their answers or mixes up the ranking for the carts receives a 3 out of 5 points. The standards I am assessing are how students reason their way through a problem, their ability to use units to help guide their steps throughout their solution, and their ability to summarize their problem and reflect on the physics of the scenario.

I am firm believer that shared authority over student learning allows students to fully buy into owning their learning experiences. To this end, there are two scenarios (one on each side), students choose which scenario to submit as a way to show their understanding. I give students quick checks multiple times within a unit since students must demonstrate proficiency at least three times on a standard to receive credit in our standards-based gradebook.

## Challenge Problems: Collisions and Momentum

45 minutes

After I collect student quick checks to assess, I give Students are a choice of Challenge Problems which are printed on yellow (competent), blue (proficient) and red (highly proficient) card stock. Typically students choose a color that corresponds to a proficiency level that is one level higher than their current level of understanding of momentum according to their grade book scores, but some students work at their current level of understanding. However, I do not allow students to work on a problem that is below their current level of understanding of momentum.  In this section of the lesson, I want students to create a coherent and mathematically supported visual that communicates their understanding of momentum using information from multiple sources.  First students create solutions to the problems in their notebooks. Then I ask students to work in small teams of 2-4 students to conduct background research which they share via google docs information gathered from sources. Click here to see an example of student work.

Then students take turns explaining their understanding of the problem to their team members. After students agree upon a solution they find sources to support their solution choice. Students use easybib.com and SEO tools plagiarism checker to check the credibility of their sources. The minimum components of each visual are given below:

1.  Backstory: Give the audience the backstory (what’s the significance of the problem)
2.  Physics of the Problem (P.o.P.):  Give a Quick overview of the problem
3.  Solution: Step by Step solution including a description of each step, with equations, units and an actual solution with explanation
4.  Framework: Explain the connections between the physical concepts in your solution
5.  Tips: Give tips on how to solve similar problems in the future

I provide a Choice Board: Momentum and Collisions on the methods of communication in this section's resources. Students choose three options from the momentum and collisions choice board that includes:

• A gamer's diary entry about a video game where users manipulate a vehicle's velocity to win a game
• A letter to another physics student about how to predict the velocity of a car involved in a collision
• A poem about the motion of two colliding vehicles
• An 8-panel cartoon about collisions
• A mind map that demonstrates how to predict the velocity of each vehicle involved in a car crash
• An information cubes that illustrates the connections between collisions and momentum
• A short film about the factors that affect a vehicle velocity during a collision
• An app proposal for a collision-based video game
• An infographic on collisions and the conservation of momentum

After students choose three options, they work on completing the tasks as a team. Some teams split the work up and each work on work products that align to their strengths while other teams work on each work product in tandem.

## Closure

5 minutes

During the closing activity, I ask students to quantify how and why their thinking has changed on the topics of collisions and momentum after the recent set of lessons. Students complete the following prompt: "I used to think ... but now I think ... about momentum and collisions" in their notebooks.  This type of closure makes it easier to identify any connections that students make during the lesson to information we previously discussed.

Student responses include, "I used to think that momentum only related to physics, but now I think that momentum connects to chemistry as well", and "I used to think that you need complicated equations to solve physics problems, but now I think you just to take things step by step." I implement closures that focus on student thinking about their thinking because it gives me a better understanding of my students' views on the topics we covered in the current lesson.