# Horizontal Kinematics

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## Objective

Students will be able to develop an understanding of kinematic equations.

#### Big Idea

Today we learn to love kinematic equations by using them to solve problems about horizontal motion.

## Kinematic Curves Review

10 minutes

In the previous lesson we dove into kinematic curves, so today's introduction is meant to refresh students' thinking and help them assess their individual level of understanding. I always have any introductory activity ready to go when students walk into my classroom to help with time management, so today's ranking task activity will already be projected onto a screen at the front of the room.

Once the students are settled, I read the instructions to the activity. My reading of the instructions is to ensure students understand that class has started! After I've finished, I emphasize to students that they should work individually and take about 5 minutes to rank the graphs, explain their reasoning, and then assess their level of confidence. During these 5 minutes of work time, I walk around the room and informally assess how students are doing with simple glances at their work. My changes in location help students stay quiet and focused.

When the 5 minutes are over, I am back at the front of the room and reveal the answers by writing them onto the front screen:  C, D, A=B=F, E. I always start by asking if anyone got all of the graphs in the correct order. Since my students are rock stars, inevitably there is always at least one who did and is willing to admit it. It's that student that I then ask to explain why they ranked the graphs the way they did. If the explanation is complete and clear, I commend the student!  In the event the explanation needs to be expanded, I still commend the student, but then contribute any of that missing information so the whole class has a complete understanding. I end the introductory activity by asking if there are any questions and then collecting the ranking tasks.

## Kinematic Equations Video Activity

20 minutes

Because there are so many great resources out there and I had an introduction that was teacher-led, I've decided to use this Khan Academy video to present the kinematic equations.  Before I start the video I make sure my expectations are clear. Students need to be sitting quietly, listening and watching the video, and taking notes on meaningful material. To me, meaningful material includes any reference to previously learned concepts, equations, vocabulary, and examples. I am telling my students these expectations as I'm on my way to start the video.

As we watch the video I pause it in several places to give my students an opportunity to process and internalize this new information. I use a discussion guide to remind me where to stop and what important material or questions I want to share with the students. When I pause the video I'm somewhat flexible in our discussions, meaning if a student has questions or needs further explanation I take the time to do that. I always write down the 2 equations on the front board so that students are sure they have copied them properly.

## Presenting the Other Kinematic Equations

15 minutes

The video left out some of the important equations used on the AP Physics 1 test, so I go through and derive them with the students on the front board.  I like to show my students where these equations come from, so that if they are unable to remember one of the more complex equations they know that a derivation is possible.

I start with telling my students that from the 2 equations that were just discussed on the video we can derive 3 more for when things aren't quite so neat as in the Khan example.  My first question to the students is "What happens when we don't know our initial velocity?"  If hands go up to answer my question, I choose a person until someone gets that because initial velocity is in both equations we can do a substitution.  In the essence of time, if that idea isn't contributed by the time I've finished calling on everyone, I tell the students what needs to be done.  I then give students 5 minutes to think-pair-share and write down any ideas with a person seated next to them (we call this think-pair-share-write since so much algebra is involved).  My hope is that while the students are working together they can derive our first equation.  After their thinking time is over, I show the students on the front board my derivation for a useful equation when initial velocity is missing.  The notes in red on the derivation are key words that I want to remember to use when I'm going through the solving process.

I ask a second question of "What happens when we don't have final velocity?"  My hope this time is that students were paying attention during our previous discussion and are able to quickly answer that we need to combine equations.  As soon as that is contributed, I direct them to take 5 minutes and think-pair-share-write with a different person seated near them (perhaps behind or in front of this time).  After time has ended, I then show my derivation for a useful equation when final velocity is missing.

The final part of our thinking and deriving encourages students to derive a useful equation for when time is missing.  I purposely leave this equation for last, as it's the most complicated to work through.  I ask students "What happens when we don't have time?" and allow them a third opportunity to think-pair-share-write with another, different person seated near them.  I show students the solution after time has elapsed and encourage students to neatly write all of the equations we've learned today on the same page in their science notebooks.

## Closure & Homework

5 minutes

With about 5 minutes to go in the class, I start a quick closure activity in which students will debrief about today's new material.  I start by asking students to sit quietly and think of one word that describes today's class.  I circulate the room to make sure students are just sitting and thinking - not writing, not organizing materials, not packing up to leave.  This quiet reflection period should last for about a minute.  Then, I direct students to turn to someone near them and share their answers.  The exchange between partners or trios should take the rest of the class time.

While students are debriefing together, I walk around and ask students to share their words with me.  I stop and chat with different groups to gauge their level of understanding and to see if I can answer any questions.  I take this information and use it to reflect on how I need to adjust my teaching practices (Did I go too slow? Too fast? Is this too much information for 1 day? etc).  To make sure I have contact with each group, I also pass out tonight's homework as I'm circulating.  Because tonight's homework is a problem from a previous AP test for homework, I remind my students they need their equation sheet and calculator, and should keep in mind my suggestions to solving practice AP problems.