Constant Acceleration Scenario - FLOW Teacher Guide
Grade levels: 6th – College.
Learning Goals: Students will learn about uniform acceleration, create and interpret motion maps, understand
the difference between vector and scalar quantities, coordinate position vs. time, velocity vs. time and
acceleration vs. time graphs and motion maps. In this way they develop representational fluency. This
scenario is appropriate for classes in the domains of physics, algebra, geometry, and calculus.
Duration: Minimum 2 days or longer.
Prerequisite: students should be thoroughly familiar with the Constant Velocity scenario before using
Constant Acceleration.
Science Standards from NGSS draft standards:
PS2 Motion and Stability - PS2A Forces and Motion; Crosscutting Concepts: Patterns; Cause and effect:
Mechanism and explanation; Scale, proportion, and quantity; Stability and change; Science and engineering
Practices: Asking Questions and Defining Problems; Developing and Using Models; Planning and Carrying Out
Investigations; Analyzing and Interpreting Data; Using Mathematics, Information and Computer Technology,
and Computational Thinking; Constructing Explanations and Designing Solutions; Engaging in Argument from
Evidence; Obtaining, Evaluating, and Communicating Information.
Common Core Mathematics Standards: 6, 7, Ratios and proportional relationships; Functions- Interpreting
functions; Building functions. Modeling-formulating a problem, computing, interpreting and validating a
model. Graphing and representational fluency, constant rate of change.
In addition, overarching: Making sense of problems and persevering in solving them; Reasoning abstractly and
quantitatively; Constructing viable arguments and critiquing the reasoning of others; Modeling with
mathematics; Using appropriate tools strategically; Looking for and making use of structure; Looking for and
expressing regularity in repeated reasoning.
How is this embodied and collaborative? Students move their hands and arms at a constant speed in a
uniform direction to represent constant velocity. They receive immediate multi-modal sonic and visual
feedback. In addition, when a pair of students creates a game or tries to produce a particular pattern on the
graph display, they must coordinate how they move as a pair.
Section
Day 1 –
Exploring the
space
Action
Teacher
Ask for a volunteer, or call on one student to stand with the wand in
the interactive space on the mat. It is important to remember that the
cameras can only track what they see. The students should always stay
in the space and within the border.
Wands should be held out away from their body.
Note: In this scenario, you will need to be in Stage 2 in order to see the
movement of the wand in relation to the ball on the motion map.
Use the keyboard commands or a remote pointer/clicker to advance.
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Keyboard Controls:
Enter = advance to next stage
Space = start in Stage 2
R = reset - erases recorded data in Stage 2
Toggle between graphs in Stage 1 with left & right arrow keys
Scroll through presets in Stage 1 with the up & down arrow keys
Ctrl-C = shows configuration panel in Stage 1 and allows you to adjust
the Initial Position, Initial Velocity and Acceleration of any preset.
Press F to Save New Setpoints.
Ctrl-I = information
Review of Constant
Velocity
When we played Constant Velocity...
What did you see/notice?
What did the arrows represent?
What did each point represent?
What about the length of the arrows?
What about the direction of the arrows?
What happened to the arrows, when you moved faster,
slower?
7. What if you started at different positions?
1.
2.
3.
4.
5.
6.
Students should be able to answer these questions as they will already
from the representations from the Constant Velocity Scenario. Ask
them how the representations used in this this scenario differ from
what they saw in the Constant Velocity Scenario. What can they
visualize now that they could not before?
Day 1 –
Introduction
Constant Acceleration
In Constant Velocity, two students were able to create data to be
compared by the class. Two more students were then asked to
duplicate the motions based on the data given.
In Constant Acceleration, one student is asked to duplicate preset
data. In Stage 1, they are given a choice between three graphs to
follow:
Position vs. Time
Velocity vs. Time
Acceleration vs. Time
Ctrl-C = configuration
panel in Stage 1
Component 1:
Position vs.
Time Graph
Start in Stage 1 – show
Position vs. Time graph
In Stage 2 this student must try to match the graph the picked. In
Stage 3 the class can see how this motion compares in all three graphs.
The presets can be adjusted and saved in Stage1 by opening the
configuration panel. To look through the presets, use the up and down
arrows. The table on the upper right has three sliders that allow you to
adjust the Initial Position, Initial Velocity and Acceleration of any
preset. Press F to Save New Setpoints.
Review what horizontal axis represents – what is time, what are the
units? Note the difference between an instant in time and a time
interval.
Review what the vertical axis represents – what is position? How is the
direction of the motion represented in the graph? Note the difference
between position and displacement (a spatial interval).
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Component 2:
Velocity vs.
Time Graph
Toggle between graphs in
Stage 1 with left & right
arrow keys
What does the slope of the line represent?
Change to view the
Velocity vs. Time graph
Review what the vertical axis represents – what is velocity? How is the
direction of the motion represented in the graph?
What would a position vs. time graph of uniformly increasing velocity
look like? What would the corresponding velocity vs. time graph look
like? Make a prediction.
What does the slope of a velocity vs. time graph represent? What are
the units this slope?
What would a graph of acceleration vs. time look like in comparison?
Make a prediction.
Component 3:
Acceleration vs.
Time Graph
Change to view the
Acceleration vs. Time graph
Review what the vertical axis represents – what is acceleration? How is
the direction of the motion represented in the graph?
What does the slope of the line represent?
Stage 1:
Setup
If you had to choose one graph to follow in order to match the graph,
which graph would you choose from the three? Why?
What do think the graph will look like?
Once they choose the graph they would like to match, press enter to
advance to Stage 2.
Stage 2:
Match
One student in the space
Press the space bar in Stage 2 to start. Have the student hold out the
wand and walk along the motion map using the graph they chose to
follow.
Enter = advance to next
stage
Space = start in Stage 2
R = reset - erases recorded
data in Stage 2
Stage 3:
Compare
Play around with moving wand so that the velocity is increasing at a
constant rate. What does this require the students to do? When they
are satisfied that they have produced a graph of uniformly increasing
velocity reveal Stage 3 so that they can check to see if they succeeded.
All three graphs are visible in Stage 3. Discuss the extent to which the
predictions match the graph. (They should have been successful in
matching the Position vs. Time graph, but may not have been
successful in matching the Acceleration vs. Time graph.)
Discuss what the slopes of these graphs represent.
 The Position vs. Time slope represents velocity.
 The Velocity vs. Time slope represents acceleration.
 The Acceleration vs. Time slope represents change in
acceleration, also known as “jerk.” Examine the
correspondence of the motion map with the Acceleration vs.
Time graph.
Have them compare their predictions to the actual graphs. Is it what
they expected? What’s different?
Day 2 –
Theories and
Predictions
Display velocity vs. time
graph and motion map
First display velocity vs. time graph and motion map. Create a plot of
pre-agreed shape. Have the students predict what the position vs.
time and acceleration vs. time graphs will look like.
To the extent that it is possible, guide the students to try to achieve a
straight line graph on the velocity vs. time graph. They should try for
graphs with positive, negative and zero slopes.
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Testing
different slopes
Ctrl-C = shows
configuration panel in
Stage 1 and allows you to
adjust the Initial Position,
Initial Velocity and
Acceleration of any preset.
Press F to Save New
Setpoints.
The table on the upper
right has three sliders that
allow you to adjust the
Initial Position, Initial
Velocity and Acceleration
of any preset.
Speeding up and slowing down uniformly:
How do these graphical representations (speeding up and slowing
down) differ (you are leading them to a comparison of their slopes)?
What is the relationship between the slope of the graph and the speed
of the moving object (your hand)?
If you were either speeding up or slowing down uniformly and
traveling backward, can you predict what the position vs. time and
velocity vs. time graphs would look like? Test your prediction.
What will the graph of an object standing still look like? Test your
prediction.
What does it mean if the line on the position vs. time graph is curved,
rather than relatively straight? What if the line on the velocity vs. time
graph is curved?
Open the configuration panel and adjust the sliders to create different
possible slopes. Go through cycles of predictions and testing, allowing
students to coach one another in making motion maps.
Please feel free to share with us at the website below any ideas you have for other things to do in the
scenario!
Created at Coronado High School, Phoenix AZ and in conjunction with Arizona State University by David
Birchfield, Colleen Megowan-Romanowicz, Norm Colling and Erika Mills.
Last Updated 10/3/12
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