Zach Powers
Sample Lesson Plans
Sample Lesson Plans for Projectile Motion Overview
1. Central Focus: • Projectile motion • Independence of horizontal and vertical components of motion 2. Objectives: Over the course of 3 days students will: 1) Recognize independence of perpendicular components of motion 2) Understand forces acting on projectile 3) See and use connections to everything students already learned about 1D motion 4) Identify situations in the real world that exhibit projectile motion 5) Develop vocabulary to talk about 2D motion 6) Collect data in systematic fashion 7) reason about possible sources of error and make efforts to control them 8) Make hypotheses regarding the behavior of a horizontally launched projectile 9) Create, interpret and understand graphical representations that support or refute their hypothesis 10) Work together and communicate as a group to make sense of the lab procedures and data which was collected 11) Solve problems involving projectile motion
Standards Adressed
I - PHYSICS motion and forces 1. Newton’s laws predict the motion of most objects. As a basis for understanding this concept: a. Students know how to solve problems that involve constant speed and average speed. 1
Zach Powers Sample Lesson Plans b. Students know that when forces are balanced, no acceleration occurs; thus an object continues to move at a constant speed or stays at rest (Newton’s first law). c. Students know how to apply the law F␣=␣ma to solve onedimensional motion problems that involve constant forces (Newton’s second law). e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth. i.*Students know how to solve two-dimensional trajectory problems. j.*Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.
II - INVESTIGATION AND EXPERIMENTATION 1. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other four strands, students should develop their own questions and perform investigations. Students will: a. Select and use appropriate tools and technology (such as computer-linked probes, spreadsheets, and graphing calculators) to perform tests, collect data, analyze relationships, and display data. b. Identify and communicate sources of unavoidable experimental error. c. Identify possible reasons for inconsistent results, such as sources of error or uncontrolled conditions. d. Formulate explanations by using logic and evidence. e. Solve scientific problems by using quadratic equations and simple trigonometric, exponential, and logarithmic functions. j. Recognize the issues of statistical variability and the need for controlled tests. III - ELD Standards Listening and Speaking, Early Advanced 9-12 a) Respond to messages by asking questions, challenging 2
Zach Powers Sample Lesson Plans statements or offering examples that affirm the message. b) Prepare and deliver brief oral presentations/reports on historical investigations, problem/solution, or cause/effect. Listening and Speaking, Advanced 9-12 c) Consistently use appropriate ways of speaking that vary based on purpose, audience, and subject matter.
Daily plans
Lesson 1 - 10/25 – monday (day one, 1.5 hours): introduce projectile motion. As a class, discuss the following topics: • Discuss what might be required for an object not to move in a straight line. o Have students give examples of objects that move along a curved path o Discuss what forces are involved in these situations o Ask students think about a situation where a hockey puck is sliding across some ice (they are familiar with making the assumption of zero friction while moving across ice) o Ask what forces are on the puck when it is sliding (after it leaves the stick). I am assuming that some will say that the stick is still exerting a force on the puck, even after it is sliding freely, this will give us a chance to re-visit the idea that if something is moving at a constant velocity, then the net force on it is zero. o Ask how we could make the puck curve. I am assuming somebody will say that you should hit it perpendicular to it’s motion. We can then analyze the motion in that case. Students should be able to reason that the puck will continue to travel in a straight line, except now in a different direction. This case can be demonstrated on the front desk with a tennis ball and a student observer (who stands on the desk and observes from overhead while I roll the ball, then give it a smack in the direction perpendicular to its motion) Draw this situation on the board o If no one suggests it, then suggest a constant force in the direction perpendicular to original movement. Analyze the behavior of this case by thinking about a leaf blower blowing with a constant force on the puck from the side. 3
Zach Powers
Sample Lesson Plans Draw freebody diagram of the forces on the puck (only 1 force, that of the blower) Discuss what the movement of the puck would be. • This is an opportunity to talk about the independence of motion in the x and y direction. • Stress that the motion can be analyzed at two independent motions: constant velocity motion in the x direction, constantly accelerated motion in the y direction. We already know how to deal with each of these motions separately, so all we have to do is put them together. • Hopefully come out agreeing that the velocity in the x direction is constant, and the velocity in the y direction is increasing at a constant rate. • Also that the position in the x direction should be proportional to the time, and that the position in the y direction should be proportional to the time squared. • From these ideas, we should conclude that the puck will move in a parabolic shape o Compare the forces present to the forces present to a tennis ball thrown through the air (ignoring air friction, which they are also comfortable with) Same situation, only one force (gravity, which they are familiar with, from learning about objects in freefall). If thrown horizontally, then the force is again perpendicular to the original direction of motion. Students should be able to make comparison fairly easily Have a student come up to the board and draw the forces on the ball and the path they would expect it to take. Have another student throw a tennis ball horizontally, and ask the class to observe. Have one student report back what they saw, ask others if they agree. o Consider the horizontal and vertical components of the velocity (they have just finished learning about components and addition of vectors, which they have used in the context of a block sliding down an inclined plane). Draw a diagram of a ball rolling off a table horizontally, just draw a line for the flight path. Ask students where the ball will be after 1 second, 2 seconds, etc… 4
Zach Powers
Sample Lesson Plans • They should recognize that each second (when compared to the second before) the ball moves the same amount in the x direction and a bit farther in the y direction. Ask students to copy down the diagram, then add the horizontal and vertical velocity vectors of the ball at each second (qualitative, not quantitative). They can work with a neighbor on this. • While they work I wonder around and see what kinds of drawings the students are making. • Get a student to share their drawing (possibly someone I have already identified as having a correct solution, and who does not often come to the board), if they don’t have it quite right allow the rest of the class to give suggestions on how they might change it. o Now talk about what a graph of the motion would look like. We have already discussed that we think it should look like a parabola How would we plot that? • Have students all draw what they would expect the graph of the motion to look like • Compare with a neighbor. What relationship is that? • y∝x^2 o Tell students that we will be doing a lab to test this hypothesis tomorrow.
Lesson 2 - 10/26 Tuesday (day 2, 1.5 hours): Projectile Lab As a class, review a bit and discuss how the lab will be go • Ask students to describe what we talked about yesterday (I will facilitate this discussion). • Talk about the lab we will be doing today o Ask a student to come up and draw their prediction for the path of the ball o Ask students what data we should collect (x and y, hard to collect time data for a lab like this without video equipment) o Ask students what relationship we expect to see between the variables (y ∝ x^2) o Ask students what graphs we should make from the data we collect (x vs y, and y vs x^2) Why would we make the second one? (if it comes out straight, we know that y is proportional to x^2, and that our prediction was true). • Talk about how the lab will be run o Describe the apparatus they will be using 5
Zach Powers
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Sample Lesson Plans A ramp that launches a ball horizontally A board with a layer of carbon paper under a layer of white paper A steel ball that will roll down the ramp and strike the white paper on the board, leaving a mark on the back of the paper (from contact with the carbon paper) Discuss the basic premise of the lab Ask students what will happen if we move the board back Ask students how to move the board back • Hopefully a student will recognize the importance of moving it at regular intervals Ask students how far they think the ball will go Ask students what they think a reasonable interval would be Describe the procedure as “taking a series of snapshots in time and space” of the ball as it falls. Once all the snapshots are taken, then they can be pieced together to make a coherent picture of the ball falling. Talk about Lab procedures Number of trials • Do three trials at each distance away, take geometric average o Show how to take geometric average (draw line between each point and the other two, then draw another series of lines that go from one point, to the midpoint of the opposite line) • Talk about why we do multiple trials Make sure to do one with the board right against the ramp • Why? (to ensure that we know the starting height of the ball) Make sure the board is nice and straight • Why? (if it is tilted then it won’t be the correct distance from the ramp all the way up and down the board) • Show how to plumb the board by holding it at the top and letting it hang straight down. Get students into lab groups and started on lab Assign one student who will be in charge of making sure that each group has the correct number of people (choose someone who is not always involved in the discussions) Make sure that each group has a steel ball, a ramp, a board, and a meterstick. Students spend time collecting data while I circulate and answer questions. 6
Zach Powers Sample Lesson Plans o After students have collected data, they can remove the white paper strips from the boards and start analyzing data. o Students should be able to do the following on their own. Take geometric averages Measure distance of each of the trial’s average from the starting point Create data table containing the distance the board was from the end of the ramp (x) and how far down the board the ball hit (y) Start graphing the data they collected o I expect that some groups may get all the way to graphing their data while others may only just finish collecting it. HW: Graph the lab data Start working on the lab report Lesson 3 - 10/27 Wed - Students work in groups on problem solving related to projectile motion Discuss lab results with the students. See what kinds of graphs they came up with. Talk about the situation where the ball is not launched horizontally, but has some initial vertical velocity. Student work in groups of 4 on a worksheet which scaffolds their progression from reasoning about projectile motion with only a horizontal initial velocity to an initial velocity with both horizontal and vertical components. Discuss this worksheet as a class, with me leading the discussion and students presenting solutions to each question asked. Give the students a challenge: • They get into randomly assigned groups • Each group is given an initial angle and velocity • These numbers represent the angle and velocity with which a classmate will be shot out of a cannon (not really, just pretend) • They must calculate where to put a mattress so that their fellow student will not die on impact. • The students will then enter their calculated distance into a computer simulation that is projected onto a screen so that the entire class can see. The simulation will show the flight path and tell them whether their calculation was right. HW: 7
Zach Powers Sample Lesson Plans students will write a full lab report that includes • Purpose • Hypothesis • Materials • Procedure • Data • Data analysis • Conclusion • Error analysis
Assessment
Students’ understanding of projectile motion will be assessed multiple times throughout the lessons: • Through interaction (discussion, questioning) during the initial discussion • Through interaction and observation during the lab portion • By reading student lab reports • Through interaction and observation during the group problem solving activity • By watching student presentations of problem solutions • Through a unit test given at the end of the 2-D motion unit.
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Zach Powers Lesson Materials
Sample Lesson Plans
Lab report guidelines and grading sheet used to write up lab done during lesson 2:
Borrowed from master teacher, Bob Fabini.
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Zach Powers
Sample Lesson Plans
The following is the worksheet which the students worked on during lesson 3: Projectile Goalie Tessa is playing goalie in a soccer game. She notices that every time she drop-kicks the ball it stays in the air for a long time, but doesn’t go very far. a) How can Tessa get more distance out of her kick? b) Explain your answer using vector components (use pictures and words) c) What variables can Tessa directly control that effect how far the ball goes? d) If we call the distance the ball goes “R”, what is the relationship between the variables you identified in step c and R? i) represent the relationships in graphical form ii) represent the relationships in the form of equations e) Explain (with words, pictures, and numbers) how Tessa could hit the center-line of the field.
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