In my summary of unit 3, I am attempting to connect learning objectives/ instructional goals with the activities that were completed for the constant acceleration model.
Unit 3 Intro– Buggy on ramp.
- Used metronome to mark behind buggy in regular intervals.
- Developed x-t (quadratic) & v-t graphs (linear)
- Explored units of coefficients
- Compared data on board (a and vo from x-t and v-t) to developed two kinematic equations
- Be sure to discuss that t=Δt when displacement.
Learning objectives for Buggy on Ramp lab:
1) Discover x-t and v-t relationships for constant acceleration.
2) Develop first 2 kinematic equations.
Compare Constant Velocity and Constant Acceleration Graph (Area under v-t graph)
Learning objectives for graph comparison:
1) Develop 3rd kinematic equation
Lab extension with motion sensors
Learning objectives for graph comparison:
1) Explore relationship between various x-t, v-t, and a-t graphs.
2) Address preconception – deceleration is not a term used in physics.
3) Early concept development for direction of motion, direction of acceleration and speed up vs. slow down. (will not be resolved)
Unit 3 Worksheet 2 & 3 (not usually done together)
Learning objectives for worksheets 2 &3:
1) Solidify relationships between x-t, v-t and a-t graphs.
2) Model development – connection between graphs and equations
3) Using data to develop graphs (rather than graphs to data)
Introduce instantaneous velocity (worksheet 3)
Note: Number 2 on worksheet 3 could be done separately as a whiteboard group activity/ discussion (this problem addresses some preconceptions/ common errors)
Ramp and Roll Computer Simulation (note: did not work with my school laptop… would need IT help)
In this activity, we were given graphs (handout – not in binder). We needed to adjust the pillar heights for the ramp in order to generate the x-t, v-t and a-t curves on the handout.
Learning objectives for worksheets ramp and roll
1) High cognitive demand activity that requires student analyze motion that is represented by x-t, v-t and a-t graphs.
Stacks of Kinematic Curves
It may be possible to complete this worksheet as group whiteboards instead of worksheet (add motion map and or picture ?).
Learning objectives for worksheets ramp and roll
1) Solidify relationship x-t, v-t and a-t graphs.
2) Explore more difficult x-t, v-t and a-t graphs (change in motion)
3) Exploring x-t and a-t when given v-t
4) Another opportunity to discuss direction of motion, direction of acceleration and speed up vs. slow down.
Ball Drop Lab
Part 1: Drop Ball – generate x-t, v-t and a-t graphs
Part 2: Toss up – generate x-t, v-t and a-t graphs
Notes:
1) Each group used different collection methods. This was interesting.
2) Our group had issues with collection software (vernier motion detectors and software). This was a good experience as how to handle this in a classroom setting. (split up group to join others)
3) Other groups used vernier (Logger pro and were successful). One group used a Vernier app and one group used slow motion camera from an I phone (each pic is 1/10th of a second) – they taped a meter stick to wall and zoomed in. I would like to try these techniques
4) I was in an “outer circle” taking notes about facilitator in this discussion. I may have missed some key pieces of the discussion. There was some discussion on reference points (0meter) and direction of + vs – that accounted for changes in x-t graphs. Data limitations (does it make sense?)
5) At the end conclusion was acceleration of free fall was -10 …. ish.
6) We were reminded that ideas can be planted in small group discussion to bring to large groups in order to “steer the bus”
Learning objectives for Ball Drop Lab
1) Reinforce relationship x-t, v-t and a-t graphs & equations.
2) Similarity in data between groups with hopes to arrive at a= -10.
Unit 3 Worksheet 4
I wrote a separate blog about this activity. This was my first ah ha moment in modeling. As Laura stated day 1 (be patient)… I finally saw the benefit of modeling. I realized how all multiple representations (graphs, equations) can be used to solve problems.
Learning objectives for worksheet 4
1) Connect graphs to equations and vice versa.
2) Multiple methods arrive at same answer :)
Quantitative Motion Map for a Tossed Ball
The class had been struggling with motion maps. We plotted ONLY the dot first. Once an agreement was made on the dots, velocity arrows were added.
During discussion v-t and a-t graphs were made.
Learning objectives for Motion Map
1) Clear up confusion of motion map (which dots get arrows, how long should arrows be at various dots, etc.) At each dot, the instantaneous velocity at that moment should be represented.
2) Reinforce relationship between displacement, velocity and acceleration in free fall. (reinforce -10m/s/s)
Unit 3 Practicum
I love idea of using practicum at end of unit ! They tie the model together to solve realistic problems in a super fun way!
We used same groups as previous. (Group that was successful last time received Scenario 3 – two accelerating objects)
Scenario #1: Constant velocity car in motion. When it passes accelerating car, the car is released and needs to “catch up to “ constant velocity car at exact location of post-it note.
Scenario #2: Ball on ramp, and constant velocity car moving at right angle to ramp. Ball is released from an undermined height. It must hit car as it passes. Height is given after calculations are done. The group has to determine starting position of car after height is given. No more runs can be made from ball after height it given.
Scenario #3: Same scenario as #2 except car has constant acceleration (fan car instead of buggy).
Our group had scenario #1. We found the constant velocity (buggy 1= 0.5m/s) and constant acceleration (buggy 2 = 0.26m/s/s)
It was interesting because ½ of the group solved the problem using equations. We set both the constant velocity (Δx=vt) and constant acceleration (Δx=1/2at^2+vt) and solved for t= 3.84s. Then Δx=1.92m ( I solved it slightly different making solving for t from constant velocity (t=Δx/v= Δx/0.5 t= 2Δx (when v= 0.5) equation and substituting it into constant acceleration and solving for Δx. I also had 1.92m.
The other half of the group graphed the x-t graph for both cars and found intersection point to be at 1.9m and 3.8 seconds!
We placed our post it note 1.9m from point of release and were successful.
Model Summary and development of 4th kinematic equation.
Unit 3 Intro– Buggy on ramp.
- Used metronome to mark behind buggy in regular intervals.
- Developed x-t (quadratic) & v-t graphs (linear)
- Explored units of coefficients
- Compared data on board (a and vo from x-t and v-t) to developed two kinematic equations
- Be sure to discuss that t=Δt when displacement.
Learning objectives for Buggy on Ramp lab:
1) Discover x-t and v-t relationships for constant acceleration.
2) Develop first 2 kinematic equations.
Compare Constant Velocity and Constant Acceleration Graph (Area under v-t graph)
Learning objectives for graph comparison:
1) Develop 3rd kinematic equation
Lab extension with motion sensors
Learning objectives for graph comparison:
1) Explore relationship between various x-t, v-t, and a-t graphs.
2) Address preconception – deceleration is not a term used in physics.
3) Early concept development for direction of motion, direction of acceleration and speed up vs. slow down. (will not be resolved)
Unit 3 Worksheet 2 & 3 (not usually done together)
Learning objectives for worksheets 2 &3:
1) Solidify relationships between x-t, v-t and a-t graphs.
2) Model development – connection between graphs and equations
3) Using data to develop graphs (rather than graphs to data)
Introduce instantaneous velocity (worksheet 3)
Note: Number 2 on worksheet 3 could be done separately as a whiteboard group activity/ discussion (this problem addresses some preconceptions/ common errors)
Ramp and Roll Computer Simulation (note: did not work with my school laptop… would need IT help)
In this activity, we were given graphs (handout – not in binder). We needed to adjust the pillar heights for the ramp in order to generate the x-t, v-t and a-t curves on the handout.
Learning objectives for worksheets ramp and roll
1) High cognitive demand activity that requires student analyze motion that is represented by x-t, v-t and a-t graphs.
Stacks of Kinematic Curves
It may be possible to complete this worksheet as group whiteboards instead of worksheet (add motion map and or picture ?).
Learning objectives for worksheets ramp and roll
1) Solidify relationship x-t, v-t and a-t graphs.
2) Explore more difficult x-t, v-t and a-t graphs (change in motion)
3) Exploring x-t and a-t when given v-t
4) Another opportunity to discuss direction of motion, direction of acceleration and speed up vs. slow down.
Ball Drop Lab
Part 1: Drop Ball – generate x-t, v-t and a-t graphs
Part 2: Toss up – generate x-t, v-t and a-t graphs
Notes:
1) Each group used different collection methods. This was interesting.
2) Our group had issues with collection software (vernier motion detectors and software). This was a good experience as how to handle this in a classroom setting. (split up group to join others)
3) Other groups used vernier (Logger pro and were successful). One group used a Vernier app and one group used slow motion camera from an I phone (each pic is 1/10th of a second) – they taped a meter stick to wall and zoomed in. I would like to try these techniques
4) I was in an “outer circle” taking notes about facilitator in this discussion. I may have missed some key pieces of the discussion. There was some discussion on reference points (0meter) and direction of + vs – that accounted for changes in x-t graphs. Data limitations (does it make sense?)
5) At the end conclusion was acceleration of free fall was -10 …. ish.
6) We were reminded that ideas can be planted in small group discussion to bring to large groups in order to “steer the bus”
Learning objectives for Ball Drop Lab
1) Reinforce relationship x-t, v-t and a-t graphs & equations.
2) Similarity in data between groups with hopes to arrive at a= -10.
Unit 3 Worksheet 4
I wrote a separate blog about this activity. This was my first ah ha moment in modeling. As Laura stated day 1 (be patient)… I finally saw the benefit of modeling. I realized how all multiple representations (graphs, equations) can be used to solve problems.
Learning objectives for worksheet 4
1) Connect graphs to equations and vice versa.
2) Multiple methods arrive at same answer :)
Quantitative Motion Map for a Tossed Ball
The class had been struggling with motion maps. We plotted ONLY the dot first. Once an agreement was made on the dots, velocity arrows were added.
During discussion v-t and a-t graphs were made.
Learning objectives for Motion Map
1) Clear up confusion of motion map (which dots get arrows, how long should arrows be at various dots, etc.) At each dot, the instantaneous velocity at that moment should be represented.
2) Reinforce relationship between displacement, velocity and acceleration in free fall. (reinforce -10m/s/s)
Unit 3 Practicum
I love idea of using practicum at end of unit ! They tie the model together to solve realistic problems in a super fun way!
We used same groups as previous. (Group that was successful last time received Scenario 3 – two accelerating objects)
Scenario #1: Constant velocity car in motion. When it passes accelerating car, the car is released and needs to “catch up to “ constant velocity car at exact location of post-it note.
Scenario #2: Ball on ramp, and constant velocity car moving at right angle to ramp. Ball is released from an undermined height. It must hit car as it passes. Height is given after calculations are done. The group has to determine starting position of car after height is given. No more runs can be made from ball after height it given.
Scenario #3: Same scenario as #2 except car has constant acceleration (fan car instead of buggy).
Our group had scenario #1. We found the constant velocity (buggy 1= 0.5m/s) and constant acceleration (buggy 2 = 0.26m/s/s)
It was interesting because ½ of the group solved the problem using equations. We set both the constant velocity (Δx=vt) and constant acceleration (Δx=1/2at^2+vt) and solved for t= 3.84s. Then Δx=1.92m ( I solved it slightly different making solving for t from constant velocity (t=Δx/v= Δx/0.5 t= 2Δx (when v= 0.5) equation and substituting it into constant acceleration and solving for Δx. I also had 1.92m.
The other half of the group graphed the x-t graph for both cars and found intersection point to be at 1.9m and 3.8 seconds!
We placed our post it note 1.9m from point of release and were successful.
Model Summary and development of 4th kinematic equation.
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