Unit 2- Constant Velocity

O.k.   Here's is my attempt to summarize what we explored in Unit 2.  I am including what "my" learning targets for these activities are (not in format of I Can statements yet).  In addition, I am including some "key notes" from my messy notebook.  There were also some questions that our facilitators made that I felt were noteworthy because they were instrumental in moving the conversation along.

Buggy Lab
Learning Targets

1. Differentiate between position, distance and displacement
2. Introduction to Position- Time Graphs 
3. Recognize velocity is slope of position -time graph (note: do not define velocity yet) 
• Writing for every statements
• Explore both positive and negative slopes 
4. Recognize y-intercept is starting position
5. Develop constant velocity equation (x= vt +xo) 

Lab Summary:
Pre- Lab Notes: Ask class to come up with definitions for position, distance and displacement (walking demo).

Part 1- Buggy lab (positive direction starting at zero)

Part 2- Each group had a different part 2. Note: To reduce speed of buggy, replace one battery with tin foil. ;-)  Here are some examples.

1. Slower car starting at 100cm (same direction) 
2. Same car with different starting point (behind reference line) traveling same (positive) direction 
3. Slower car starting at reference line
4. Same car starting at reference line but traveling in negative direction
5. Slower car starting at 600cm traveling in opposite (negative direction) 

White board

1. Prediction 
2. Data table
3. Each group to plot data on same graph. 
4. For each part, groups were asked to find equation and the "for every" statement. 

Part 1 Discussion:

1. What do we notice? 
2. Whose car would win a race and how do you notice
3. Discussion on 5% rule

Part 2 Discussion:

1. What do we notice
2. Who changed starting position, what do we notice?
• Can you determine starting position from the equation? 
3. What about lines going other way?
• How do we see car turning the other way in the equation? 
4. Who had different "for every" statements?  How where they different?  Why are they different?  

The discuss was followed with some "teacher guided" notes.  Let's summarize what we have learned.  The teacher asked all the questions in order to develop the equation.  As the teacher, I may need to suggest subscripts.

Post Lab Assignments/ Activities:

Unit 2 Worksheet 1.  Work in lab groups.  Next day discuss answers with a new group.   Each group whiteboards a problem.


Unit 2 Worksheet 1: Learning Targets:

1. Understanding of position- time graphs
• intercepts, slopes (magnitude and direction)
2. Address misconceptions
• Question 1c & Question 1d 

During whiteboard discussion, I noticed some key questions/ comments:

1. Do we have a reference point at on this graph?
2. Who in the class could walk this?  VERY HELPFUL
3. How do we know who is going faster. 
4. Why is the speed not the same?
5. We will come back to this  (this will reassure any student who is still confused)
6. Did they collide? 
7. Did you feel your speed change at any point in the walk? 

Notes:
I liked how a different group worked together to whiteboard assignment.  It allowed for collaboration with more students.

As a teacher continually remind students that we love "wrong answers" are learning opportunities, the challenge right answers, they come from our experiences.

A key phrase that stuck with me during this activity was ABC CBV (activity before concept, concept before vocabulary or equation) - Apply reflect generalize

Unit 2 Worksheet 2 (page 1) :Drawing velocity time graphs.  This assignment was done in a circle in small groups.  Each drew a velocity time graph of the situation the teacher described.

I love this idea! I have done this worksheet in the past.  I loved doing it as a whiteboard assignment.  because it addressed as they came up rather than waiting until the end.

After the first graph, we added a position time graph which was helpful.

Unit 2 Worksheet 2 page 1 Learning Objectives:

1. Introduce V-T graph (better understanding of what  they are and what they tell us)
2. Reinforce relationship between position time and velocity time graphs. 
3. Velocity time graph does not tell us position. 

If it doesn't come up in the circle, facilitator could ask: " Is there another possible line you can draw on your position time graph that would give you the same v-t graph?
" What does velocity time graph Not tell us?"

Unit 2 Worksheet 2 (page 2): Could be homework after page 1.

Unit 2 Worksheet 2 page 2 Learning Targets:

1. Connection between  V-T graph & P-T (slope and area)
2. Area under V-T is displacement.  ( LOVE introducing this here). 

Make sure to discuss that from a V-T graph, We can get displacement, but still do not know position.

Unit 2 Worksheet 3. Roller Skating Robin:
This activity was an "eye opener" for me.  I have always taught problems 3 d & e rather than let students try to figure them out on their own.  I am starting to realize the benefit of this struggle.  I am now regretting all the times I have taken this struggle away from my students!

Unit 2 Worksheet 3 Learning Targets:

1. Start exploring how to solve problems using multiple representations ( equations/ graphs) 
2. Introduce motion that may change  (#3) and how to address these questions.
3. How to solve problems involving average speed and average velocity ( 3d and 3e).  (multiple methods, equations, averages for each interval, etc).

Noteworthy facilitator comments: 

1. During #3 there was some questions if we should draw a straight line or curve between 4-6.  Since we don't know what's in between.  " Let's pick something as stick with it".  "It sounds like a lot of you had that it stopped, do you just want to go with that?"
2. Also, discussed 3 d & e on a separate day.  I think that break would be good.  If you just add it on to the end, students might "check out" when you discuss.
3. "Could this definition work"  ( when discussing average velocity = displacement/ time and speed = distance/ time.)  Note:speed was purposefully not defined as distance/ time until this moment. 
4. "Pick another worksheet graph and try both methods,  Does it work?"

Motion Map 
 Situation 1: constant speed
 Situation 2: At rest
 Situation 3: At rest then travels at constant velocity

Learning Targets:

1. Introduce motion maps (instance in time, velocity vectors ). 

End of Unit Practicum:...  I love to concept of practicum at end of unit :-)
Worked in larger groups.  Groups can only run 1 car at a time.
1) Slower car & faster car are 4 meters apart traveling in opposite directions.  They are released at same time.  Where should camera (post -it) be placed to capture collision?  (collision must occur on post it)
2) Slower car is 2 meters ahead of faster car traveling in same direction.  They are released at same time.  Where should camera (post -it) be placed to capture collision?  (collision must occur on post it)
3) Camera is fixed at a 90 degree intersection.  Each car is 2 m from intersection.  How should cars be released in order for collision to occur on fixed posit.  Note: modify this so more calculations are needed (i.e. maybe do no give distance of faster car until calculations are done).

Model Is Developed! 

Students can summarize (write what they know about Constant Velocity in back of notebook).
Students will discuss what they know.

1. Position - Time Graphs (slope is velocity) 
2. Velocity - Time Graphs ( area is displacement) 
3. Motion maps
4. Constant velocity equation
5. For Every statements (linear) 
6. Position, Distance, Displacement
7. Speed, Velocity, average speed, average velocity