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LOOPS Curriculum 

Activity 1:  Vector Treasure Hunt 

A very good introductory activity to vectors.  It does not require much prior knowledge and it quickly gets students understanding that position is defined in relation to some choice of a standard reference point and a set of reference directions (CA standard 8PC1.a).  I have attached some additional notes that I compiled as I went through this activity, keeping in mind questions that could be asked to give teachers immediate feedback. 
I originally thought that students should next complete "Hanging with Friends" but I don't think that is the next logical activity.  Before students complete activity one of Hanging with Friends they are determining the best mode of transportation for each person based on the distance that needs to be covered in 10 minutes time.  To do this, students need to understand something about speed and velocity, and must solve for speed in meter/sec with distance in meters and time in minutes (obviously it is not too difficult; students just need to determine how many seconds are in 10 minutes, but it could be enough to throw off many students). Proficiency in working with mixed units (seconds and minutes) and calculating speed given distance and time are skills we assume students have.  The remaining activities all focus primarily on understanding speed and velocity and being able to solve problems involving speed, distance, and time.  This is a very good activity for students but should come after students determine the relations between and among speed, velocity, distance, displacement, and time.
 
Therefore, after students complete the Vector Treasure Hunt, they should work with discovering the mathematical model for constant speed using combinations of simulations (PhET's Moving Man, use of motion detectors, and possibly video analysis).
 
 

Activity 2:  Video Analysis of Hover Puck 

A hover puck can be purchased from just about any science supply company; the following link is for PASCO's version, which sells for $19. http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&PartNumber=SE-7335B&Detail=1 

The video capture part of the activity can be performed by students, which students love to do, or, if time and money are issues, the movie can already be created for students to analyze using Tracker.   

This is similar to PhET's Moving Man, but the motion of the puck is all in the same direction.  Students click on the puck, advancing the frame every 1/30^th of a second, collecting data for position and time. 

To begin, the teacher should demonstrate to the students how the hover puck works.  The teacher should then tell students their goal will be to determine how fast the puck is moving.  What variables will they need to measure (position and time)?  Show the video and video analysis software (since they will be using this software again when analyzing free-fall motion, this will serve as a good introduction).  Students generate a graph of x vs. t and, for the first time, calculate the slope of the line and determine that it represents the speed of the object.  What units does the slope have?  What does the slope represent?   

I can generate a series of steps and questions for students to answer if this is an activity you like. 

After completing this activity, students have now been introduced to speed (not velocity, just speed). 

Activity 3:  PhET Moving Man 

Students can enter initial conditions for position and velocity on the left (we'll ignore acceleration for now). 

Students should be asked to enter a series of different values for x and v (such as x_i = -10 meters and v = 2 m/s) and make predictions for what each graph will look like.  Then, run the simulation and compare predictions to actual results.  They should be given several trials with the same speed but different starting locations and compare and contrast the graphs.  They should also be given both negative and positive velocities and have them describe the difference (different directions of motion for the man and different slopes - positive and negative - for the graphs.  Students can be asked to compare the magnitude of the slopes for a +1 m/s velocity to a -1 m/s velocity.  Did the man move any faster in one over the other?  Why is one positive and one negative?  Essentially, students will know the velocity of an object must be described by specifying both the direction and the speed of the object (CA standard 8PC1.d).  This activity takes the Hover Puck activity a step further by changing directions (introducing the velocity vector) and also changing the speed (different slopes). 

In a summarizing set of questions, students can solve problems involving distance, time and average speed (CA standard 8PC1.c). 
 

Activity 4:  Motion Detector Lab 

Students gain a kinesthetic experience in the relationships between verbal and graphical representations of motion, whereby students analyze the motion of a student walking across the room making predictions of position vs. time and velocity vs. time graphs and then comparing them to the actual results. 

Students are asked to complete a series of tasks, all of which involve walking toward and/or away from the detector at different rates.  Students make and sketch predictions before completing each task.

1.      Move away at a slow, steady speed.  Observe graphs of position vs. time and velocity vs. time.  Calculate the slope of the line from the position vs. time graph.  How does it compare to the constant value from the velocity vs. time graph?

2.      Move away again, but this time at a faster, steady speed.  Observe graphs of position vs. time and velocity vs. time.  Why does this graph of position vs. time have a greater slope than the first one?

3.      Start about 4-5 meters in front of the detector and walk toward it a slow, steady speed (as close to step one's speed as possible).  What is different?  What is the slope from the position vs. time graph?  How do these graphs compare to the first set you saw?  Why is the slope negative and the "speed" negative?

4.      Move toward the detector again at a faster, steady pace.  How does the slope of this one compare to the slope's from the previous two steps?

5.      Move away slowly and steady and then change to a constant faster speed while still moving away.

6.      Move away slowly, stop, come back faster.

7.      Give students a graph of position or velocity vs. time with a pre-sketched motion on it (a graph rather than words that describe the motion) and students must match it as closely as possible.

8.      Give students a graph of position or velocity vs. time and, based on that graph, must produce the other, matching one (velocity or position vs. time, respectively). 

By the end of this activity, students will further solidify their understanding of speed and velocity and will know changes in velocity may be due to changes in speed, direction, or both (CA standard 8PC1.e). 
 
Activity 5:  Graph Matching
 
This is sort of an on-line quiz / worksheet.  Students are given a number of graphs of either position vs. time or velocity vs. time and they have to sketch the matching, missing graph as well as describe the motion in writing.
 
For instance:
xtimevtimeDescribe the motion: 
 
 

This can be set up so that students submit each graph one at a time and the responses are categorized by question; all submissions for the first velocity sketch are compiled together for viewing by the teacher, who can quickly peruse the sketches and identify those that are not correct.  The teacher can then read the description of the motion for those students who sketched incorrectly to identify what went wrong.  The teacher does not have to read all the written responses, just those that correspond to incorrect drawings.  Additionally, a few slope questions can be placed on this activity whereby students are given a number of graphs with lines drawn on them and students must enter the correct slope of the line.  

By completing this activity and the ones preceding it, students know how to interpret graphs of position versus time and graphs of speed versus time for motion in a single direction (CA standard 8PC1.f). 

Activity 6:  Hanging with Friends 

At this point students have worked extensively with graphs of position and velocity versus time and have calculated the speed of objects through graphical analysis and problem solving.  They have used video, motion detectors, and simulations.  Hanging with Friends is a great culminating activity that makes use of everything that has been learned in the five previous activities.