CI 402 Lesson Plan IIDay 8 of Unit ProjectSteven Pavlakis

Goal(s) The goal of this lesson is to relate parabolic motion to the lives of the

students via experimentation with parabolic trajectories.

Objectives O1: Students will be able to find the vertex of a parabola given just the x-

intercepts and the leading coefficient. O2: Students will be able to write an equation to match a given parabola.

Materials Overhead Projector (1) Computers (15) Motion detectors (Logger Pro) (8) Meter sticks (8)

Motivation/Hook First, we will play this video http://www.youtube.com/watch?

v=P0gsgyY_QW0. After the video has finished, say “Well, I don’t know that any of you can jump as high as JJ Watt, but you’re going to get your chance to prove me wrong today. We’re going to test how high you can jump.”

Procedure Introduce both activities, the “How high can you jump?” worksheet and the

Angry Birds game. Explain that each group will spend approximately 20 minutes at each station, and that we would flip halfway through. Have students break into groups of two or three (three being preferable), and go to the computer lab. Once the students have broken into groups, say “I’m going to count off each group, 1, 2, 1, 2,… OK groups I counted 1 start with the jumping activity and groups I counted 2 start with Angry Birds. We’re going to the computer lab now, so take everything with you.” Once the norms for hallway behavior have been reexamined, head to the computer lab and make sure that students are going to the correct stations.

In the lab, have 8 computers on one side of the room equipped with the Logger Pro motion detectors. Stress to these students that when they jump, it is important not to bend their knees in the air. The teacher can then ask, “Why do you think it’s important that we don’t bend our legs?” Don’t let them start the activity until they say how it would change when the person hits the ground again, or something to that effect. Once one person has gone, ask “So what does the graph on the computer screen tell us?” The graph actually is measuring distance from the censor vs. time, so the graph will be discontinuous with three line segments. “Does this graph tell us how high (Student X) jumped?”(A1) This is an important step for students to understand for this activity. We do not know how high the student jumped from the computer reading exactly, but we can read other information from

the readings gathered. Many students may believe that the second distance reading is indeed the height of the jump, but we must attack that misconception early. “What information does this graph actually tell us that we can use to find the height of the jump? And how can we use those bits of information?” Would be great follow-up questions.

The other half of the class will go to the other side of the lab, and, in groups, will work on the activities found at http://www.teachmathematics.net/page/16049/angry-birds-1. The teacher would try to stop by each group and ask something along the lines of “What is your strategy for coming up with these parabolas?” Once they explained their strategy, assuming it’s sound, a great follow-up question to check for understanding of transformations, would be “Explain to me what would your strategy be if, instead of these points being on the x-axis, they were on the line y=2?” (A2) Hopefully they would understand that they would just shift the graph up two by adding two to the entire expression. This is even more important for levels 3 and 4, for which the leading coefficient is no longer 1. A second question to assess their understanding would be “How can we find a parabola that goes through those two points and also (x, y) (arbitrary point)?” (A3) This will show that students understand the concept of the leading coefficient, and did not just enter in random numbers on the website to match the graph.

At the halfway point in the class, students will switch to the station that they had not already completed.

“Alright folks, let’s bring it back together. Everyone has had a chance to calculate their own jump height, right? So let’s see how everyone did. I need everyone to stand up where they are, and I’m going to say a height. If that’s higher than you jumped, sit down where you are. Last one standing wins a prize!” At this point, the teacher starts, in increments of 5 centimeters, counting up. Increments can decrease when few are left. Be sure to pay attention to top male and female performers, and congratulate everyone on a job well done.

“But now, I want to talk about how you got to that height. We’ve been talking about flying objects, or projectiles, today. What kind of paths do projectiles take?” When a student responds, restate their claim, and praise the student saying, “Exactly, a parabola. So what is the are some standard equations for a parabola?” As the students give suggestions, write them on the board. Hopefully, you’ll get standard form, vertex form, and factored form as options. Then ask, to negotiate the utility of the different forms, “Let’s take a poll, which form did we use most today? Standard? Vertex? Factored? Why did you use that one?” Once wait time is given, call on a student, and then restate the contribution. “Based on what we found, which form can we most easily create next in the jumping activity? We found a certain point that might help us here.”(A4) This question focuses on the fluidity of forms, but makes sure that students were able to find the vertex of the parabolas, the important piece for this particular activity. Move into closure.

Closure

“Today, we’ve seen some interesting applications of parabolic motion, and seen how useful factored form can be to visualize a parabola. As we see yet again, not everything in nature follows a linear relationship or path, and you guys are doing a great job understanding where parabolas fit into our lives. No homework today.”

ExtensionThe extension for this activity would be the second set of Angry Birds

problems, not found on the worksheet, but at http://www.teachmathematics.net/page/11419/angry-birds-2. The teacher could write the address somewhere in the room or bookmark the site on all the computers and students at both stations could work on the problems as a group when they’re done with their station or when the material is done.

Assessment Summary Throughout the lesson, the teacher will be walking around the classroom

observing the work done by the students as to be a resource to students. Additionally, the teacher can then ask important questions to students, including but not limited to the questions put above in the procedure. Furthermore, O1 was addressed specifically by A4, which makes sure that students were able to find the vertex and know that that is indeed the highest point. O2 was addressed by A2 and A3, which both ask for modifications to a given parabola, meaning that students must understand transformations of parabolas. The goal of A1 was assessing whether a student can read and understand the meaning of a graph based on the axes labels.

Standards

CCSS.MATH.CONTENT.HSA.CED.A.1Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

The entire lesson was based on creating a parabola through two points in space-time, and evaluating it at a certain point. This quadratic function is in one variable, and they solve the problem of finding the height of the Jumper.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Throughout the lesson, the answers/solutions to the presented problems were not quite apparent. Students had to work as a team to make sense of the information presented to them in order to solve the task at hand.

How high can you jump? Names: ___________________________

1. The general form of a projectile, or something that is flying, is h(t) =1/2 (-g) t2 + vo t + ho

We need to know what ½ (-g) is.

If g = 9. 8 m/s2, find ½ (-g) in cm/s2.

2. Each person in the group has a role. The Jumper jumps. The Data Manager is in charge of the computer,

and collecting the data from the Logger Pro. The Recorder measures the height the Jumper jumps.

Each person will take turns doing each role.

Assign who will do each role first. (If there are only 2 people in your group, the Data Manager and Recorder will be the same person).

3. The Jumper will stand in front of the motion detector, which is placed on the ground. The Jumper will jump straight up, and WILL NOT BEND HIS/HER KNEES IN AIR. Be sure to land in front of the censor again.

4. Record the time the Jumper left the ground, retuned to the ground, and the measured height in the table below.

5. Switch roles and repeat for each member of the group

Name of JumperTime left ground (s)Time return to ground (s)Measured height (cm)

6. Using the time values from 5 and your ½ (-g) constant from 1, construct an equation for each Jumper’s jump. (HINT: Think Vertex form)

7. Find the maximum height each Jumper hit based on your equations.

8. Compare your calculated heights and your measured heights.a. How close are the two measurements? Was one set consistently

higher than the other?

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b. Which do you think is more reliable? Why?

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Angry Birds Names:_______________________________________

1. In groups, open Google Chrome and go to the bookmark called “Angry Birds 1”. If that doesn’t work, go to the following address:

http://www.teachmathematics.net/page/16049/angry-birds-1

2. In your groups, finish levels 1, 2, 3, and 4. Write your solution equations below, and sketch the parabola too.

Level 1: ________________________________

Level 2: _________________________________

Level 3: __________________________________

Level 4: __________________________________

3. What was your general strategy to find the equation for each level?