Graphing and Linear Motion by Jason Kozel

Transformation 2013 Design Challenge Planning Form Guide Design Challenge Title: Accelerating Toward the Finish Line Teacher(s): Pamela Miller School: Harlandale High School Subject: Graphing Motion, 1-Dimensional Motion Abstract: Students will calculation the velocity and acceleration of a runner. Students will track the runner’s progress and coach the runner.

MEETING THE NEEDS OF STEM EDUCATION THROUGH DESIGN CHALLENGES

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Begin with the End in Mind The theme or â&#x20AC;&#x153;big ideasâ&#x20AC;? for this design challenge: Students will apply their knowledge of velocity and acceleration to track the progress of, and coach a runner. TEKS/SEs that students will learn in the design challenge: 4) Science concepts. The student knows the laws governing motion. The student is expected to: (A) generate and interpret graphs describing motion including the use of real-time technology; (B) analyze examples of uniform and accelerated motion including linear, projectile, and circular;

Key performance indicators students will develop in this design challenge: Vocabulary development (displacement, speed, velocity, vector, acceleration, average velocity, instantaneous velocity, average acceleration, instantaneous acceleration); measure displacement; measure time elapsed; calculate speed; calculate average and instantaneous velocity; calculate average and instantaneous acceleration; calculate time, displacement, and velocity for free-fall acceleration; draw and analyze position vs. time graphs; draw and analyze velocity vs. time graphs

21st century skills that students will practice in this design challenge: www.21stcenturyskills.org Collaboration, written and oral communication, critical thinking STEM career connections and real world applications of content learned in this design challenge:

Career(s): Coach Connections: Students will connect concepts of velocity and acceleration to situations in their daily lives.

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The Design Challenge You have just been hired by an aspiring Olympic athlete. Your employer is a runner and needs you to keep track of her progress and give her coaching suggestions that will help her reach her goals. Her approach is unconventional and she wants to not only track her times, but also her velocity and acceleration. She wants you to use this information to direct her on how to train her muscles in order to improve her performance.

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Map the Design Challenge Already Learned

Taught before the project

Taught during the project

1. Vocabulary development (displacement, speed, velocity,

vector, acceleration, average velocity, instantaneous velocity, average acceleration, instantaneous acceleration) 2. measure displacement

3. measure time elapsed

4. calculate speed

5. calculate average and instantaneous velocity

6. calculate average and instantaneous acceleration

7. calculate time, displacement, and velocity for free-fall

acceleration 8. draw and analyze position vs. time graphs

9. draw and analyze velocity vs. time graphs

Performance Indicators

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Team-Building Activity It is important that teachers provide team-building activities for students to help build the 21st Century Skills that are necessary for success in the workforce. Team-building helps establish and develop a greater sense of cooperation and trust among team members, helps students adapt to new group requirements so that they can get along well in a new group, serves to bring out the strengths of the individuals, helps identify roles when working together, and leads to effective collaboration and communication among team members so that they function as an efficient, productive group. Our students are often not taught how to work in groups, yet we assume that they automatically know how. Use team-building activities with your students so that you can see the benefits which include improvement in planning skills, problem solving skills, decision making skills, time management skills, personal confidence, and motivation and morale.

Frenzy This activity highlights the value of cooperation rather than competition. A large, relatively flat open space at least 30 square feet is required for the activity. The space can be indoors or outdoors. Materials: 5 Hula Hoops and 60-70 tennis balls.

Setup and Objective: 1.

Arrange 4 hula hoops on the ground spread out from each other. Place one at each of the four corners of an imaginary 25 foot square and one in the center of the square.

Place all tennis balls in the middle hoop.

Divide students into four even teams. Have each team pick a hula-hoop and stand by it.

Each team is trying to place all of the tennis balls in its hoop; once you have all the balls, you win.

Rules: 1.

There is no throwing or tossing of the balls.

All the balls must be out of the middle before you can take them from others hoops.

No defending the hoops.

Facilitator Notes: 1.

Play will last for 3-5 minutes, at which point the participants will be out of breath and no nearer to winning. Signal a pause and ask them to regroup with their teams and strategize for two minutes. One group or another may come up with the creative solution (see step 3 below); most groups, however, will try to position the people "strategically," plan for faster ball transfers, etc. After two minutes, signal time, have them return to their starting positions, the Ready, Set, Go.

After another fruitless 3-5 minutes, participants will still be no nearer to winning and starting to become a little frustrated. Signal another pause, and ask them to circle up as a group and perhaps

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"learn from each other." Some person will think to suggest that the groups work together; another might ask if the hoops can be moved (YES). In either event, you know that the group is on the right track. 3.

With some planning and thinking about what you've told them, they should realize that the only way to win (other than all of the other groups agreeing to lose -- not likely) is for them all to win, i.e., place all of the balls in the middle hoop, and then place their hoops around the balls.

Materials: 5 Hula Hoops and 60-70 tennis balls Resources: http://www.firststepstraining.com/resources/activities/archive/activity_frenzy.htm

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5E Lesson Plan Design Challenge Title: Accelerating Toward the Finish Line TEKS/TAKS objectives: 4AB Engage Activity Show students video of Olympic runners. http://technorati.com/videos/youtube.com%2Fwatch%3Fv%3DE5Jl8GUMN8E Discuss what makes one runner better than another (how fast a distance is covered—speed). Link this motion to the motion of a car. How is speed measured in this situation? What does it mean to accelerate in a car (or anytime you move)? Have students log and respond to this discussion in a journal entry. Introduce the challenge: You have just been hired by an aspiring Olympic athlete. Your employer is a runner and needs you to keep track of her progress and give her coaching suggestions that will help her reach her goals. Your employer’s main events are the 100m and 400m dashes. Her approach is unconventional and she wants to not only track her times, but also her velocity and acceleration through out her practice runs. She wants you to use this information to direct her on how to train her muscles in order to improve her performance. Suggestions should include both physical exercise and nutritional adjustments. Give students a chance to begin their research on the physics of running. Group students with a member of the track team or designate one member of the group the “runner” for data collection purposes

Engage Activity Products and Artifacts Journal Entry

Engage Activity Materials/Equipment Computer with internet access, projector

Engage Activity Resources For Engage Activity: http://technorati.com/videos/youtube.com%2Fwatch%3Fv%3DE5Jl8GUMN8E Research resources: http://physicstt.tripod.com/id11.html http://runningtimes.com/Article.aspx?ArticleID=5857 http://www.glenbrook.k12.il.us/gbssci/phys/projects/yep/sports/spinet.html

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Explore Activity Activity 1: Vector Maps Introduction: Explain to students the difference between a vector quantity and a scalar quantity. Give an example: speed is a scalar quantity and velocity is a vector quantity. Before the lesson, set up several different vector maps for your classroom, one for each group (2-3 students). Vector maps will need an appropriate scale and physical reference points (front of the room, doors, etc.). This activity can be extended to a larger area (e.g. football field) with words marked on the floor/hidden in grass. Then students can return to the classroom to look up and share vocabulary definitions. Students should take notes on word definitions as their classmates present. Have the students start from one or two set locations and have all students end up in different locations. At the end locations, provide a textbook and a vocabulary word. Once everyone has found their end location, students will share the textbook definition for their term and then explain it to the class in their own words. List of possible terms: speed, velocity, acceleration, instantaneous velocity/acceleration, average velocity/acceleration, displacement, vector, scalar Activity 2: Draw a Vector Map Have each student group draw their own vector map with an appropriate scale and reference points. Their map should have specific start and end points. Once the map is drawn, groups will switch maps and try to follow the other group’s map. Afterwards student groups will collaborate to discuss the maps and map reading techniques. Each student will write a reflection paragraph about their experience. These maps will be used again later in the lesson. Activity 3: Graph Matching Lab Students will collect motion data in real time and analyze motion graphs using the handout below.

Explore Activity Products and Artifacts Vocabulary notes Vector Maps Vector Map Reflection Paragraph Graph Matching Lab

Explore Activity Materials/Equipment Activity 1: (per group) 1 meter stick, 1 protractor, 1 compass, vocabulary card, textbook Activity 2: (per group) 1 meter stick, 1 protractor, 1 compass, graph paper Activity 3: (per group) stopwatch, meter stick, motion detector, LabPro ® or PASCOTM Interface, computer with data collection software for appropriate interface or graphing calculators, graph paper, 2 ft x 2ft cardboard square

Explore Activity Resources http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/vectors/u3l1a.html

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Explain Activity Students will take Cornell notes for each part of the “Motion” PowerPoint presentation. Part 1: Vector Addition and Subtraction Activity 1: Resultants for “Draw a Vector Map” Students will use rules of vector addition to find the sum of all the vectors on their vector maps from explore activity 2. Part 2: Graphs Activity 2: Motion and Graphing Summary Students will complete handout below. Part 3: Velocity and Acceleration Calculations Activity 3: Velocity and Acceleration Practice Problems Students will complete handout below. Part 4: Free Fall Activity 4: Free Fall Practice Problems Students will complete handout below.

Explain Activity Products and Artifacts Cornell Notes Part 1 Cornell Notes Part 2 Cornell Notes Part 3 Cornell Notes Part 4 Resultants for “Draw a Vector Map” “Motion and Graphing Summary” “Velocity and Acceleration Practice Problems” “Free Fall Practice Problems”

Explain Activity Materials/Equipment Computer with PowerPoint and internet access, projector, student vector maps from explore activity 2

Explain Activity Resources Instructions for Cornell notes http://coe.jmu.edu/learningtoolbox/cornellnotes.html www.brainpop.com

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Elaborate Activity

Acceleration PowerPoint Lab Students will work on their own paper and follow along with the “Acceleration Lab” PowerPoint.

Students will complete their research and begin data collection for “Accelerating Towards the Finish Line”

Elaborate Activity Products and Artifacts Acceleration Lab Background information with citations Data for Runner

Elaborate Activity Materials/Equipment Internet/library access, access to track, meter sticks, stopwatches Acceleration Lab: CPO car and ramp, 2 photogates, CPO timer

Elaborate Activity Resources http://owl.english.purdue.edu/owl/resource/557/01/

Evaluate Activity

Students will put together their final report for “Accelerating Toward the Finish Line”. The rubric can be separated if you want to take separate grades for the elaborate and evaluate activities.

Evaluate Activity Products and Artifacts Final report

Evaluate Activity Materials/Equipment Computer access, library/internet access

Evaluate Activity Resources http://physicstt.tripod.com/id11.html http://runningtimes.com/Article.aspx?ArticleID=5857 http://www.glenbrook.k12.il.us/gbssci/phys/projects/yep/sports/spinet.html

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Graph Matching Part 1: The purpose is to measure the distance and time of two walkers traveling with a constant velocity around the track at 5m intervals for a total of 35m. Determine the materials needed to achieve the lab’s purpose: ______________________________________________________________________________ ______________________________________________________________________________ Determine a procedure that will achieve the lab’s purpose: ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ___________________________________________________________________________ Draw a data table for the data collected during the experiment:

On a sheet of graph paper, plot Distance vs. Time. Each walker should be represented by a separate line. The slope of the line for each walker represents that walker’s speed. Calculate the speed of each line by choosing two points and calculating the slope of the line between those points. Show your calculations (with appropriate units) on your graph paper.

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Part 2: The purpose of this lab is to use a motion detector to analyze motion in real time. Materials: Meter stick LabPro interface Computers with LoggerPro data collection software Motion detector 2 ft x 2ft square cardboard.

distance (m)

Procedure: 1. Connect the motion detector to the DIG/SONIC 1 port of the Labpro interface. Open LoggerPro software. 2. Open “Physics with Computers”, and then double click on “01a Graph Matching” 3. Stand 1m in front of the motion detector with the cardboard square at detector level. Click the “collect” button and walk towards the detector at a constant velocity. Sketch the graph on a separate sheet of graph paper. 4. Repeat step 3 for these additional situations: a. Walk away from detector at constant velocity b. Walk toward the detector quickly with constant velocity c. Accelerate towards detector. 5. Describe the motion that matches each of the following graphs: a. Distance vs. Time 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0

time (s)

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Distance vs. Time 3.5

distance (m)

3 2.5 2 1.5 1 0.5 0 0

time (s)

Analysis Part 1 1. Which walker was the fastest?

2. What are some possible sources of error in your experiment?

3. Summarize in 2-3 sentences what you learned during this activity.

Part 2 1. What is the significance of slope in a Distance vs. Time graph?

2. Describe the motion of an object when the slope of the Distance vs. Time graph is zero.

3. Describe the motion of an object when the slope of the Distance vs. Time graph is constant.

4. Describe the motion of an object when the slope of the Distance vs. Time graph is changing.

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Motion and Graphing Summary Part 1:Julie’s Journey Her skin crawling with fear, Julie runs out of the haunted house and continues to run 1.5 km in 7 min. Exhausted, she stops by a pond to rest for 15 min. She then walks 1 km quietly and carefully among the creepy looking trees which takes her 10 min. Suddenly a horrible howling sound causes her to sprint 2 km to the safety of her apartment in only 3 min. After calming down and resting for 19 min she takes 60 minutes to walk to the police station 2.5 km away. In the story above, underline the distances, circle the times, and box words that indicate how fast Julie was going. Fill in the following table for Julie’s Journey: Total Time ( )

Total Distance ( )

What is the formula for average speed? Calculate Julie’s average speed during this journey.

Graph the distance v. time of Julie’s journey. Be sure to include all parts of a graph.

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Using the graph, find the areas where Julie was stopped and show what the graph looks like.

Find the areas on the graph where Julie was going fast and draw them below.

What does the slope of a line on a distance-time graph show you?

Using the story and the formula below, calculate Julie’s instantaneous speed at each point.

s

d t

Distance

Time

Instantaneous Speed

Do the speeds you calculated agree with your graph? Give two examples that support this.

Part 2: Review 1. If you look at the speedometer of your car, you are seeing ________________ speed. 2. What are three ways you can accelerate? 3. List three appropriate units for distance. 4. List three appropriate units for time.

5. List three appropriate units for speed/velocity.

6. List three appropriate units for acceleration.

7. If the speedometer in a car reads a constant speed of 40 mi/h, can you say that the car has a constant velocity? Why or why not?

8. What is the difference between displacement and distance?

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9. What does the slope on a distance v. time graph tell you? _______________________ 10. What does the slope on a velocity v. time graph tell you? _______________________ Tell a story that matches the following graphs: D istan ce v. T im e o f ...

Distance v. Time of...

4.5

12 10 Distance (cm)

Distance (km)

4 3.5 3 2.5 2 1.5 1 0.5

8 6 4 2 0

0 0

Time (s)

T im e (m in )

11.

12.

13. What kind of acceleration is shown on the following graphs? ______________________ ______________________ Velocity v. Time

1 0 0 1 2 3 4 5 6 7 8 9 10 11

6 5 4 3 2 1 0

Velocity (m/s)

3 2

6 Time (s)

Time (s)

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Velocity v. Time

6 5 4

__________________

6 5 4 3 2 1 0 0

Time (s)

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Velocity and Acceleration Practice Problems 1.

An aspiring Olympic athlete is jogging at a constant velocity of 3.0 m/s. The athlete is running towards a traffic light that is 90 m away. If you consider the traffic light as the origin, what position will she be at after 20s.

Horses are capable of moving at four different speeds. A horse walks with a speed of 1.8 m/s. A horse trots with a speed of 5.0 m/s. A horse canters with a speed of 7.0 m/s. A horse gallops at 12 m/s. Maria is taking horse riding lessons and her assignment is to work with the horse at all speeds today. She spends 10 min at a walk and then 2.5 min at each other speed. If she maintained a positive direction through out her ride, what was her average velocity?

A tortoise and a hare are racing against each other. The tortoise moves at a constant speed of 0.250 m/s. The hare moves with a constant speed of 5.00 m/s. After 6 minutes, how far has the hare traveled? If the hare stops to nap at this point, how long can he nap before the tortoise catches up?

A runner begins at rest and accelerates to a speed of 8 m/s over 10 s. What is the runnerâ&#x20AC;&#x2122;s average acceleration?

A new commercial for a sports car advertises that if the car can come to a stop in 37.21 m from a speed of 100 km/hr. What would be the average acceleration in this situation?

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Free Fall Practice Problems 1.

You little brother, despite warnings, drops a penny off the observation deck of the Empire State Building in New York City. The observation deck is 381 m above the ground. What is the terminal velocity of the penny? How far has the penny fallen after 3 seconds?

A juggler throws a ball straight up with a speed of 5.0 m/s. After how many seconds will the ball reach its peak? What is the acceleration of the ball at its peak?

Acceleration do to gravity on the moon is 1.6 m/s2. On a trip to the moon, you release an oxygen tank from the entrance to your spacecraft, 7 m above the moon’s surface. How long will it take for the tank to reach the moon’s surface?

After leaving the moon, you and your team of astronauts are thrown off course by a meteor shower and discover a new planet with no atmosphere. On the planet, you climb a 100 m tall cliff and drop a tennis ball (you and your crew are big into space tennis). The tennis ball hits the ground in 17 s. What is the acceleration due to gravity on this planet?

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Plan the Assessment Engage Artifact(s)/Product(s): Journal Entry

Explore Artifact(s)/Product(s): Vocabulary Notes, Vector Maps, Graph Matching Lab

Explain Artifact(s)/Product(s): Vector Map Resultant, Motion and Graphing Summary, Velocity and Acceleration Practice Problems, Free Fall Practice Problems, Cornell Notes Part 1, Cornell Notes Part 2, Cornell Notes Part 3, Cornell notes Part 4 Elaborate Artifact(s)/Product(s): Acceleration PowerPoint Lab, Background information, Runner data

Evaluate Artifact(s)/Product(s): Final report

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Rubrics Accelerating Toward the Finish Line The challenge: You have just been hired by an aspiring Olympic athlete. Your employer is a runner and needs you to keep track of her progress and give her coaching suggestions that will help her reach her goals. Your employerâ&#x20AC;&#x2122;s main events are the 100m and 400m dashes. Her approach is unconventional and she wants to not only track her times, but also her velocity and acceleration through out her practice runs. She wants you to use this information to direct her on how to train her muscles in order to improve her performance. Suggestions should include both physical exercise and nutritional adjustments. Important information: All background information collected should include the source citation. The exercise and diet regimen developed for your employer will be based on this research. The goals set for your athlete should be based on data from the most recent Olympic Games. For all measurements with your runner, establish a materials list and a procedure for measurements and calculations. Include an analysis of your data and a summary of your work. Refer to the rubric below for additional information.

Accelerating Towards the Finish Line CATEGORY Background Sources

4 Several reputable background sources were used and cited correctly. Material is translated into student's own words.

3 A few reputable background sources are used and cited correctly. Material is translated into student's own words.

Materials

All materials and setup used in the experiment are clearly and accurately described.

Procedures

Procedures are listed in clear steps. Each step is numbered and is a complete sentence.

Almost all materials and the setupu used in the experiment are clearly and accurately described. Procedures are listed in a logical order, but steps are not numbered and/or are not in complete sentences.

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2 A few background sources are used and cited correctly, but some are not reputable sources. Material is translated into student's own words. Most of the materials and the setup used in the experiment are accurately described.

1 Material is directly copied rather than put into students own words and/or background sources are cited incorrectly.

Procedures are listed but are not in a logical order or are difficult to follow.

Procedures do not accurately list the steps of the experiment.

Many materials are described inaccurately OR are not described at all.

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Replicability

Procedures appear to be replicable. Steps are outlined sequentially and are adequately detailed.

Procedures appear to be replicable. Steps are outlined and are adequately detailed.

All steps are outlined, but there is not enough detail to replicate procedures.

Several steps are not outlined AND there is not enough detail to replicate procedures.

Analysis

The relationship between the variables is discussed and trends/patterns logically analyzed. Predictions are made about what might happen if part of the lab were changed or how the experimental design could be changed. Summary describes the skills learned, the information learned and some future applications to real life situations. Report illustrates an accurate and thorough understanding of scientific concepts underlying the project. All calculations are shown and the results are correct and labeled appropriately.

The relationship between the variables is discussed and trends/patterns logically analyzed.

The relationship between the variables is discussed but no patterns, trends or predictions are made based on the data.

The relationship between the variables is not discussed.

Summary describes the information learned and a possible application to a real life situation.

Summary describes the information learned.

No summary is written.

Report illustrates an accurate understanding of most scientific concepts underlying the project. Some calculations are shown and the results are correct and labeled appropriately.

Report illustrates a limited understanding of scientific concepts underlying the project.

Report illustrates inaccurate understanding of scientific concepts underlying the project.

Some calculations are shown and the results labeled appropriately.

No calculations are shown OR results are inaccurate or mislabeled.

Summary

Scientific Concepts

Calculations

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Story Board 

Week 1 Activities (50 minute class periods)

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Day 1 “Frenzy” Team Building Activity (20 min) Engage: Olympic video clips, discussion, and journal entry (30 min)

Day 6 Explore Activity 3: Graph Matching Part 1 (45 min)

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 Week 2 Activities

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Day 11 Acceleration PowerPoint Lab (45- 50 min)

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Week 3 Activities

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Day 2 Introduce design challenge (15 min) Research exercise and diet for runners (3035 min)

Day 7 Explore Activity 3: Graph Matching Part 2 (45 min) Finish Analysis questions for Homework if necessary

Day 12 Complete/Go Over Acceleration PowerPoint Lab (20 min) Explain 4: Free Fall (30 min) Assign “Free Fall Practice Problems” for Homework

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Day 3 Explore Activity 1: Vector Maps (25 min) Vocabulary Jigsaw (25 min)

Day 8 Explain 2: Motion Graphs (30 min) “Motion and Graphing Summary” Complete for homework if necessary. (20 min)

Day 13 Go over “Free Fall Practice Problems” (20 min) Students complete research on exercise/diet regimen and Olympic data for challenge (30 min)

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Day 4 Explore Activity 2: Draw a Vector Map (45 min)

Day 9 Go over “Motion Graphing Summary” in lab groups, then as a class. (20 min) Explain 3: Velocity and Acceleration calculations (30 min)

Day 14 Students gather materials and write procedures for data collection (20 min) Students go out to track and begin Data collection (30 min)

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Day 5 Explain 1: Vectors (30 min) Vector Map Resultants (15-20 min)

Day 10 “ Velocity and Acceleration Practice Problems” (30 min) Have each lab group work one problem (or part of problem) for the class (20 min)

Day 15 Students finish data collection (30 min) Students begin Final Report (20 min) Students complete final report for homework (preferably not due the next day).

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