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HS-ETS1-2. Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

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Timeline for the Year

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Warm-up on a whiteboard: Practice Modeling a Complex Scenario with thinking through Ordering a Pizza

Who has ever ordered a pizza?

Model (pictures + words) the 10 -15 things that have to happen for a pizza to arrive at your door; from the moment you place the order, to you eating it.

Now chunk these into three big groups

Bonus points if you can make the names of the chunks rhyme.

Use this protocol

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Use private thinking and reasoning time.

Form Small Groups.

A/B Partners divergently verbally brainstorm all kinds of ideas, being careful to avoid getting in a rut.

A: with the one marker, writes down an idea on whiteboard, and passes the marker to A

A: with the one marker, writes down an idea on whiteboard, and passes the marker to B

B: with the one marker, writes down an idea on whiteboard, and passes the marker to B

...

Many Minds, One Marker

A1

A2

b3

b4

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It’s easier to find a solution to a complex, real-world problem if you break it down into smaller, more manageable pieces.

Think of an example where you have used this technique in your daily life. Tell your group about somewhere in your own life that you have already done this.

A1

A2

b3

b4

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By the End of this Activity �You Should Be able to Answer:

Focus Question

How do we analyze complex systems?

Language Focus

Organize information in order to generate “next steps” for solving a complex problem.

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A Request from our Health Teachers

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Best option: have a student messenger from Health Teacher/Class or get and show an email similar to these two options below:

Example email (very explicit):

Hey Physics Teachers,

We're studying the risks of texting while driving in our health class and need to better understand how far a car travels during a texting and driving incident. We want to quickly try out different situations, like different speeds, time of distraction, etc. and see how far the car travels. Could you code a spreadsheet for this?

Thanks in advance for your help.

Best,

[Health Teacher]

—---------------------

Example Email (this one leaves more for students to figure out)

Hey Physics Teachers,

We are looking at the dangers of texting and driving in our health class and we didn’t really know how far a car goes during a texting and driving situation. We really want is a way to quickly input some different texting and driving situations, like in a parking lot, driving in a neighborhood, or driving on the freeway and see how far the car travels. Is that something you can do? Thank you in advance for your help on this.

Best,

[Health Teacher]

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What are we going to do?

Let us start with all agreeing to what we are aiming to do.

We as (role) seek to (problem/ constraint) in order to

(major criteria/goal) for (stakeholders).

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Tools for Solving Complex Problems

It is often beneficial to explore a straightforward example

1. Let’s watch and rewatch a texting and driving scenario

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This slide is for Teachers only

Note that this video does show a staged car accident with a student actor playing injured.

Video Resources:

2V - Long - No Graphics or ad-free version

2V - Long + Graphics or ad-free version

2V - Short - No Graphics or ad-free version

2V - Short + Graphics or ad-free version

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2V - Long - No Graphics

Ad-free link below YouTube Link below

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2V - Long + Graphics

Ad-free link below YouTube Link below

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2V - Short - No Graphics

Ad-free link below YouTube Link below

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2V - Short + Graphics

Ad-free link below YouTube Link below

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Optional Philosophical Chairs Question:

In a couple of years you are likely to be in the passenger seat with your friend driving. If they receive a text and begin to read it, would you ask them not to?

If yes, go to the right side of the room.

If no, go to the left side of the room.

The mediator will call on each side to make an argument for their side, if you find the argument compelling, please move to that side.

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Tools for Solving Complex Problems

Create a System Model

1. Let’s watch and rewatch a texting and driving scenario

2. Using pictures and words draw a model of the scenario with the things that we have to consider in a texting and driving scenario; from the moment the distraction happens, to the car coming to a stop.

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Tools for Solving Complex Problems

Break the Problem into Simpler,

More Manageable Parts

2. Using pictures and words draw a model of the scenario with the things that we have to consider in a texting and driving scenario; from the moment the distraction happens, to the car coming to a stop.

3. Now, chunk these into three big groups

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Tools for Solving Complex Problems

Create a System Model

and identify key parameters

3. Now, chunk these into three big groups

4. Using a red marker: identify or write what variables that might affect the end result of the texting and driving scenario.

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Tools for Solving Complex Problems

Collaboration and

Learning from Others

4. Using a red marker: identify what variables that might affect the end result of the texting and driving scenario.

5. Gallery Walk: walk around and look at how other groups illustrated the important moments in the texting and driving scenario and find what important variables they identified.

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Tools for Solving Complex Problems

Iterate your System Model so it guides you to Analyze the Problem

5. Gallery Walk: walk around and look at how other groups illustrated the important moments in the texting and driving scenario and find what important variables they identified.

6. Using a blue marker: Iterate your System Model based on what you learned.

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Tools for Solving Complex Problems

Iterate Your System Analysis

6. Using a blue marker: Iterate your System Model based on what you learned.

7. On the brainstorming page of your packet, refine your initial System Analysis of the texting and driving scenario.

Going for the simplest model, what can we ignore (and save for later) from our initial divergent brainstorming?

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Tools for Solving Complex Problems

Iterate Our System Analysis to Generate Next Steps

7. On the brainstorming page of your packet, refine your initial System Analysis of the texting and driving scenario.

8. Let’s converge on a simple system model (on page 4) with the key parameters clearly identified and plan of how to find or figure them out.

Engineers often start with drawing simple diagrams of a simplified system, then build to more complex models.

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Let’s get systematic

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Answer Key for System Analysis

(in Packet)

*Note: this is matched to future Spreadsheet Program

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Zooming Out:

What are doing here that is transferable to many other areas of your life?

How do we use STEM to

enhance a social discussion?

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Going question by question: A starts, then A, then B, then B; then next question shift: A, then B, then B; then A.

What are doing here that is transferable to many other areas of your life?
How do we use STEM to enhance a social discussion?

Zooming Out:

What are doing here that is transferable to many other areas of your life?

A1

A2

b3

b4

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Check-In: �You Should Be able to Answer:

Focus Question

How do we analyze complex systems?

Language Focus

Organize information in order to generate “next steps” for solving a complex problem.

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Patterns Physics

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
System Analysis	We used system analysis to define and operationalize the problem. This included breaking the situation into: distracted, reacting, and braking. We also ran mini-experiments to get data-informed times of distraction and reaction.	This framework allows us to figure out the next steps to estimating how far a car will travel while texting and driving.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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What should we do next?

Using System Analysis to Guide us.

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Teacher Resource Slide for Mini-Labs

good websites and apps for mini-labs:

Distraction https://www.troyburchlaw.com/cards-of-distractibility/

Reaction:

https://www.justpark.com/creative/reaction-time-test/

https://scratch.mit.edu/projects/152575080/

https://faculty.washington.edu/chudler/java/redgreen.html

https://www.thephysicsaviary.com/Physics/Programs/Labs/StoppingDistanceLab/

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Let’s Work through our System Analysis:

Mini-Experiments & Arguing from Evidence

Let’s first divergently think together, then break off to Optimize a few solutions to the typical times of distraction and reaction times while driving.

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Let’s Work through our System Analysis:

Mini-Experiments & Arguing from Evidence

Left half of class:

Brainstorm how we could determine the typical time of distraction.

Right half of class:

Brainstorm how we could determine the typical reaction time.

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Let’s Work through our System Analysis:

Mini-Experiments & Arguing from Evidence

Distraction Time Groups: share out your time and evidence we should consider it. Then we will reconcile what to do with the range of times we have.

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Lets update our System Analysis.

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Let’s Work through our System Analysis:

Mini-Experiments & Arguing from Evidence

Reaction Time Groups: share out your time and evidence we should consider it. Then we will reconcile what to do with the range of times we have.

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Lets update our System Analysis.

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Texting & Driving - Day 2

Due This Class

Reading + Reply on Article

Agenda:

Choosing the right model

for Constant Velocity

Working through

our System Analysis

Due Next Class

The Ultimate Graph Challenge 1

Warm-up Question:

Explain your System Analysis with

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A1

A2

A1

A2

A	Share your ideas I think…… Something that reminded me of this is……. Evidence I have is…...	1 minute
B	Share your ideas I think…… Something that reminded me of this is……. Evidence I have is…...	1 minute
A	Borrow Ideas: Tell B which ideas they shared that you would like to use in the next round to clarify or support your explanation Something you said that really helped me was….	20 seconds
B	Borrow Ideas: Tell A which ideas they shared that you would like to use in the next round to clarify or support your explanation I thought it was interesting when you said…..	20 seconds

Use private thinking and reasoning time. Then line up and:

Stronger and Clearer

Then, A’s rotate one and repeat stronger and clearer.

b3

b4

b3

b4

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What should we do next?

Using System Analysis to Guide us.

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By the End of this Mini-Lesson �You Should Be able to Answer:

Focus Question

How does a slight change to our experimental setup change how we mathematically model the system?

Language Focus

Describe how changes in experimental setups are expressed mathematically.

Physics

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Two different groups do the same experiment, how will their graphs look?

0

The two cars are moving a constant velocity, the starting positions are shown.

Group A

Group B

Physics

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How did two different groups, using the same car, get different mathematical models?

Group A:

Distance = 5 × time

Physics

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Compare back and forth, why different?

Group A:

Distance = 5 × time

Physics

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Compare back and forth, why different?

Group B:

Distance = 5 × time + 10

Physics

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How did two different groups, using the same car, get different mathematical models?

Distance = 5 × time

Distance = 5 × time + 10

Physics

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Critical Thinking

Distance = 5 × time + 10

What explains this y-intercept?

Why does it still have the same slope?

What Pattern or Patterns is this?

Physics

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So We have a “New” Pattern

Similar to Proportional but slightly different.

It is the combination of Horizontal and Proportional.

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This can also be thought of as:

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When

Δx doubles

Δy doubles + the starting value

Linear

Pattern

y

x

y = 5x + 10

y = cx + B

Distance_Final = velocity ∗ time + Distance_start

x	y
0	10
1	15
2	20
5	35

0

10

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Toolbox of Big Ideas

Physics

1 - Inquiry & Patterns

2 - Texting & Driving

4 - Engineer a Shoe

5 - Waves & Technology

Fold

Here

3 - Engineering & Energy

6 - Electricity, Power Production, & Climate Science

7 - Space & the Universe

* - Professionalism in STEM

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When

Δx doubles

Δy doubles + the starting value

Linear

Pattern

y

x

y = 5x + 10

y = cx + B

Distance_Final = velocity ∗ time + Distance_start

x	y
0	10
1	15
2	20
5	35

0

10

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Now for our Scenario...

Both the proportional and linear patterns are beautiful and are found throughout nature.

Let’s now focus on our texting and driving scenario during the Reaction Phase of an incident, how could framing the question of distance travelled lead to using proportional in one case and linear in another framing?

Since the Reaction Phase in our system model has us only putting in the distance travelled while reacting, which mathematical model should we use for constant velocity?

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t	d
0	0
1	5
2	10
5	25

d

t

d = vt

When

time doubles

distance doubles

distance = velocity ∗ time

0

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Getting more Practice with Choosing Models

What pattern will model the

velocity of the car vs time while distracted.

or

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t	v
0	5
1	5
2	5
5	5

v

t

v = v_i

velocity = velocity_initial

When

time doubles

velocity remains the same

0

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Toolbox of Big Ideas

Physics

1 - Inquiry & Patterns

2 - Texting & Driving

4 - Engineer a Shoe

5 - Waves & Technology

Fold

Here

3 - Engineering & Energy

6 - Electricity, Power Production, & Climate Science

7 - Space & the Universe

* - Professionalism in STEM

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Check-In: �You Should Be able to Answer:

Focus Question

How does a slight change to our experimental setup change how we mathematically model the system?

Language Focus

Describe how changes in experimental setups are expressed mathematically?

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Lets update our System Analysis.

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Patterns Physics

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
System Analysis	We used system analysis to defined and operationalized the problem. This included breaking the situation into: distracted, reacting, and braking. We also ran mini-experiments to get data-informed times of distraction and reaction.	This framework allows us to figure out the next steps to estimating how far a car will travel while texting and driving.
Finding Models	We found the model for distance while distracted and reacting was distance = velocity * time.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Using Humor to Enhance a Social Discussion

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What is next?

Using System Analysis to Guide us.

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What have we done the least of?

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Researching Deceleration

Survey the text

Questions you have

Predict what you will understand after reading

Read for understanding, not just the words

Respond: answer your questions, evaluate the reading

Summarize at a high school level what you read.

Reading Strategies

Focus on

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Informational Text on Braking

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Check for Understanding

What this article and information from a trusted source?
What was the main point of the article?
We searched out this article for a very particular reason, did you get the information you needed?
If so, what was it?
What other noticings or wondering do you have?

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Lets update our System Analysis.

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2CT Desmos Template - Computational Thinking to Determine Time of Braking

Image links to Desmos activity

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Let’s put what we learned into the System Analysis

Time of Braking =

V_final - V_initial

acceleration

Just one last thing!

However it will take us some time to get it.

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Patterns Physics

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
System Analysis	We used system analysis to defined and operationalized the problem. This included breaking the situation into: distracted, reacting, and braking. We also ran mini-experiments to get data-informed times of distraction and reaction.	This framework allows us to figure out the next steps to estimating how far a car will travel while texting and driving.
Finding Models	We used our prior knowledge of the model distance = velocity * time for distance while distracted and distance while reacting. We found the deceleration due to breaking. We found the mathematical model for the time of braking	This allows us to get the distances while distracted and reacting from the inputs of time and velocity. Also, now we can get the time of braking from the inputs of initial velocity, final velocity, and deceleration of brakes.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Using Humor to Enhance a Social Discussion

Ad-free link below YouTube Link below

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Texting & Driving - Day 3

Agenda:

Review System Analysis

for Next Steps

Due This Class

The Ultimate Graph Challenge 1

Warm-up Question:

Compare and contrast the graphs below.

Due Next Class

The Ultimate Graph Challenge 2

velocity (m/s)

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What is next?

Using System Analysis to Guide us.

For both Time of Braking and Distance car goes while braking we need to investigate the pattern with constant deceleration.

Note: in physics acceleration is a vector, meaning it includes both the rate you change your velocity per second and the direction in which you change your velocity. For example, an acceleration of 10 mph/s, north could be a car speeding up by 10 mph each second while traveling north or equally a car heading south that is slowing down by 10 mph each second. As a result both acceleration and deceleration are often generally referred to as acceleration.

So constant deceleration will be referred to more generally as constant acceleration.

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Start simple

and build to complexity

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Let’s continue to Cultivate our

Inner Scientist

Let’s use some tools from our physics toolbelt:

start with thinking through a easy concrete example
use proportional reasoning
modeling by walking the Triangle

The simplest case of acceleration is acceleration from rest.

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Let’s continue to Cultivate our

Inner Scientist

Let’s use some tools from our physics toolbelt:

start with thinking through a easy concrete example
use proportional reasoning
modeling by walking the Triangle

Again the major variables seem to be distance and time.

What are the major variables?

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By the End of this Experiment �You Should Be able to Answer:

Focus Question

How do we create a mathematical model for the simplest constant acceleration?

Language Focus

Be able to express those patterns graphically, mathematically, visually, and verbally.

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The Phenomenon to Research

Investigation to Determine Mathematical Model for Constant Acceleration

Research Question: What is the relationship between distance and time for constant acceleration?

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The Phenomenon to Research

Investigation to Determine Mathematical Model for Constant Acceleration

What is our System? What is included in the system we will investigate? What is outside the system?

How is energy flowing in the system?

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citation:

The Cross-Cutting Concepts

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Investigation to Determine Mathematical Model for Constant Acceleration

Wild Guess: How far will this ball bearing roll on this angled ramp in ___ seconds?

Guess Based on Observation

Inquiry to Determine Pattern

Making Sense of the Pattern Through Consensus

Data Informed Prediction

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Again, Let’s Be Playful with

our Inner Scientist

Let’s use some tools from our physics toolbelt:

start with thinking through a easy concrete example
use proportional reasoning
modeling by “Walking the Triangle”

Let’s get it down to just two possible patterns.

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Investigation to Determine Mathematical Model for Constant Acceleration

Hypothesis: (What do you intelligently expect to happen?)

Graph Form: In Words:

I think as the time increases, the distance travelled will ________ in a ________ pattern, because I think __________.

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Controls: ClickHereToType			Qualitative Data: ClickHereToType



Data Table

	To be graphed on the X - Axis	To be graphed on the Y - Axis	Total Time as shown on Stopwatch (Note the auto-calculation for the time rolled will deal with the time being non-zero at the start when distance does equal zero) (s) +/- 0.3
	Time Rolled (Auto-calculated) [average] (s) +/- 0.2	Distance (m) +/- 0.05	Trial 1	Trial 2	Trial 3	Trial 4 (if necessary)
	#DIV/0!	0.00
	#DIV/0!
	#DIV/0!
	#DIV/0!
	#DIV/0!

What could go here?

What is going on here?

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Desmos Tips & Tricks

After entering your data . will allow you to zoom fit.

Use the slider to find your simplest best-fit model.

Delete mathematical models that do not fit your data

Undo last move

Distance = 2 * Time

Write your mathematical model here

DON’T!! y=2x DO!! Distance = 2 * Time

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Good Example of a Desmos Image

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Good Example of a Whiteboard

Time ball rolled for (s)

Distance ball rolled (m)

0.6 m high ramp

Distance = ____ × time × time

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Quality Control of Data and Graph
Orienting to the Data
Finding Similarities & Differences
Exploring the Pattern

— Walk the Triangle —

Make Sense of Pattern

in light of differences

Predicting the Future

Big Ideas to Consider for our Data Discussion

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Get similarities for each point on the triangle.
Get differences for each point on the triangle.
Use straightforward words of understanding before using technical terminology.
Launch a discussion using

the same input value.

Launch a discussion using

the same output value.

Analyze our Data

Ways to Explore the Triangle

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Understanding

Experience

(phenomenon)

Mathematical

Model

Graph

(Diagrammatic)

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Use private thinking and reasoning time.

Form A/B Partners.

A: explains their ideas

B: silently listens to understand A’s thinking

Reverse roles.

B: explains her/his ideas

A: silently listens to understand B’s thinking

A/B: discuss ways their ideas are the same and/or different

For triads and quads, continue until all partners have reported.

Listen and Compare - A/B Talk Cards

A1

A2

b3

b4

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Constant

Horizontal Line What always stays the same or What is not affected		Proportional & Linear Rate of Change or Slope
Quadratic Stretch or Curvature		Inversely Proportional What always stays the same

(c-value)

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Acceleration is the rate of change of your

velocity (m/s) per second.

So the unit is m/s /s

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The next few slides present two options for guiding students to discover c is actually = ½ acceleration.

However, our recommendation in light of time considerations is to tell or simply explain this to students using similar logic as below:

New equation but intuitive and possibly seen in middle school

substitute in definition

of average velocity

in the context of our experiment

initial velocity = 0 and final velocity was = acceleration * time

simplifying and gathering terms

gives us this equation

constant (c-value)

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Two options for guiding students to discover the specific value of the Constant (c-value) is

c = ½ acceleration.

Ball Drop with Motion Sensor

Trade-offs:

More structured.
Less time ~20 minutes.
Introduce students to sensor collected data.

Additional Analysis of Motion Data from Students’ own Experiment

Trade-offs:

More student centered.
More rigor ~ 40-60 Minutes (or can be selectively done by students who finish data collection quickly).
Next Level Desmos use, through finding the tangent line of a curve at multiple points.

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Guiding students to discover the specific value of the Constant (c-value) is A = ½ acceleration, with Ball Drop with Motion Sensor.

*link to Vernier Demonstration Guide Book

Use the automated sensor collected data of a dropped, free falling object to generate a distance vs time and velocity vs time graphs (acceleration vs time is additional low hanging differentiated).
Analyze the and discuss of what the slope on the velocity vs time graphs must be → this is the rate of change of the velocity, which is the definition of acceleration!
Wait! We thought the constant “c-value” was acceleration, nope! but it is close to it, in fact, comparing the numbers we see that A = ½ acceleration.
Added benefit, is that they get data to support that g = 9.8 m/s /s ~ 10 m/s /s

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Guiding students to discover the specific value of the Constant (c-value) is A = ½ acceleration, with Additional Analysis of Motion Data from Students own Experiment.

Use the Tangent Tool linked in the Student and Teacher Calendar to find slope (velocity) at several different times.
Then plot this data in that same Desmos using the blank table below.
Next guide a discussion of what the slope on the velocity vs time graphs must be → this is the rate of change of the velocity, which is the definition of acceleration!
Wait! We thought the constant “c-value” was acceleration, nope! but it is close to it, in fact, comparing the numbers we see that A = ½ acceleration.

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Skeleton of a Conclusion:

with Reasoning about the Constant, the Pattern, and General Equation

Prediction

Confidence with Justification

+ Research Extension Question

Claim

Evidence

Mathematical Model

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Skeleton of a Conclusion:

Claim

1) Name the system being studied. 2) Identify the independent variable and dependent variable. 3) Describe the relationship (pattern) between the variables tested.

Evidence

1) Explain how the collection of data shows the pattern (relationship) in the claim.

2) Select two specific data points to use to demonstrate that the data follows the pattern.

Mathematical Model with Reasoning

1) State the mathematical model in its specific form with a numerical constant (c-value).

2) Explain what the constant (c-value) represents about the system in the real world.

3) Explain how the pattern (relationship) makes sense for the observations of the real world .

4) Restate the mathematical model in its general form using all words.

Prediction

1) State the value of the independent variable presented at the beginning of the experiment in the wild guess question.

2) Predict how the dependent variable of the system would behave according to the mathematical model.

Justification

1) Provide a level of confidence in the prediction for the future behavior of the system. 2) See the language in the “Determining Confidence in a Prediction” table below to justify the chosen confidence level.

+ Research Extension Question:

Use your experience with this investigation to create a thoughtful or interesting follow up experiment.

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Exemplar Conclusion from Packing Marbles Experiment:

After investigating the packing behavior of marbles, I conclude that there is a quadratic relationship between the Independent variable: diameter of the container and the dependent variable: number of marbles. My evidence for this claim is that all of my data fits on a single best-fit curve that is quadratic. This means that when the diameters doubled from 10 to 20 cm, the number of marbles quadruples from 30 to 120 marbles.

The marble and container system can be mathematically modeled as:

Number of Marbles = 0.3 * Diameter ²,

where 0.3 marbles/cm² is the “packability” of the marbles. This means that each cm² of area within the container fits 0.3 large marbles. This quadratic patterns makes sense because doubling the diameter both doubles how wide and doubles how tall the container is, so the area and marbles quadruple. Generally, we could state that the

Number of Marbles = (Marble Packability) * Diameter * Diameter.

Using this model, I predict for a container with diameter 14.3 cm, 61 marbles will fit. My confidence in this prediction is only medium-high, since the prediction is inside our data range but the best-fit curve hits near the edges of many of my data points.

Now that I know something about how objects are packed together to maximize the use of space, I wonder: How does the shape of an object affect its packability?

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Toolbox of Big Ideas

Physics

1 - Inquiry & Patterns

2 - Texting & Driving

4 - Engineer a Shoe

5 - Waves & Technology

Fold

Here

3 - Engineering & Energy

6 - Electricity, Power Production, & Climate Science

7 - Space & the Universe

* - Professionalism in STEM

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When

time doubles

distance quadruples

d = ½at²

t	d
0	0
1	1
2	4
5	25

t₁ → d = 1

t₂ → d = 4

distance = ½ acceleration ∗ time²

t

d

Popular Choral response: Some things in this world, like rolling a ball down a ramp, when you double the time, two things happen, you give it double the time roll and double the time to speed up, so the distance quadruples, so pattern for constant acceleration is Quadratic.

Suggested Hand Motion: shake two fingers during “two things happen” and mime unfolding the square wider and higher during “the output gets twice as wide and twice as high, so the output quadruples, so we call this pattern quadratic.“

Suggested demonstration: roll a ball down the ramp for 1 second (or a count of “one - one thousand”) and catch the ball, then pace out quadrupling that distance, mark it, and reroll the ball for 2 seconds (or two counts of “one - one thousand”) and observe how the doubling the time, quadruples the distance rolled.

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When

time doubles

velocity doubles

t	v
0	0
1	5
2	10
5	25

v = at

t₁ → d = 1

t₂ → d = 4

velocity = acceleration ∗ time

v

t

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Let's Predict the Future

Wild Guess: How far will this ball bearing roll on this angled ramp in ___ seconds?

Wild Guess or Data Informed?

Fist to Five: I get what we mean when we say “we ask a question, take some measurements, utilize mathematics to find a pattern, and then we predict the future.”

Science Works!

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Check In:�You Should Be able to Answer:

Focus Question

How do we create a mathematical model for the simplest constant acceleration?

Language Focus

Be able to express those patterns graphically, mathematically, visually, and verbally.

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
System Analysis	We used system analysis to defined and operationalized the problem. This included breaking the situation into: distracted, reacting, and braking. We also ran mini-experiments to get data-informed times of distraction and reaction.	This framework allows us to figure out the next steps to estimating how far a car will travel while texting and driving.
Finding Models	We used our prior knowledge of the model distance = velocity * time for distance while distracted and distance while reacting. We found the deceleration due to breaking. We found the mathematical model for the time of braking. We found the model for constant acceleration from rest.	This allows us to get the distances while distracted and reacting from the inputs of time and velocity. Also, now we can get the time of braking from the inputs of initial velocity, final velocity, and deceleration of brakes. We are one step closer to getting the distance while braking.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Using the cross-cutting concepts and scientific practices cards, choose one of each, within the two options, and explain how it applies to our investigation.

A - Patterns; Cause and Effect; Scale, Proportion, and Quantity; Systems and System Models; Energy & Matter; Structure and Function; Stability and change.

B - Asking Questions and Defining Problems; Developing and Using Models; Planning and Carrying Out Investigations; Analyzing and Interpreting Data; Using Mathematics and Computational Thinking; Constructing Explanations and Designing Solutions; Engaging in Argument from Evidence; Obtaining, Evaluating, and Communicating Information

Exit Ticket

A1

A2

b3

b4

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Some of you brought up that the pattern with constant acceleration might be exponential

How should we determine if it is exponential or quadratic?

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Some of you brought up that the pattern with constant acceleration might be exponential

How should we determine if it is exponential or quadratic?

Yes! Let’s look at the data and try to fit each pattern to the data!

DESMOS link here.

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Texting & Driving - Day 4

Agenda:

Jump back to finish

Investigating Constant Acceleration from Rest

Review System Analysis

for Next Steps

Due This Class

The Ultimate Graph Challenge 2

Due Next Class

Looking at the patterns in Olympic Performances

Warm-up Question:

Connecting our lab to our project: What factors might affect the braking acceleration of a car?

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Why Study Braking Systems?

Ad-free link below YouTube Link below

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That story had it slightly wrong, that truck was engineered to do that: Volvo’s Emergency Braking System

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Jump back to finish Investigating Constant Acceleration from Rest

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Texting & Driving - Day 5

Agenda:

Quiz on Constant

Acceleration

Putting it all together with

Computational Thinking

Due Next Class

Watch Wolfram's TED talk about the value of Computational Thinking

Due This Class

Patterns in Olympic Performances

�

Warm-up Question:

A student collects two different data sets. One for a ball rolling down a ramp and one for a ball rolling across the floor. Explain the difference between how the ball is moving represented by the solid line vs the dotted line. Use the claim, evidence, reasoning format.

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Warm-Up Question

Two student collect data for the set up above. One collects data for the ball rolling down a ramp and the other collects data for while the ball is rolling across the floor. Explain the difference between how the ball is moving represented by the solid line vs the dotted line. Use the claim, evidence, reasoning format.

Key words: distance, time, rate of change, constant, increasing, velocity, acceleration.

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4 Square Group Share

Students have an opportunity to quick write / problem solve as a group on one sheet of paper.
Each student writes a response to a prompt in one corner - simultaneously.
Subsequent students add their responses.
They share out to the group, then as a group decide on the consensus response to write in the center.

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A1

A2

b3

b4

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Quiz on Constant Acceleration

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
System Analysis	We used system analysis to defined and operationalized the problem. This included breaking the situation into: distracted, reacting, and braking. We also ran mini-experiments to get data-informed times of distraction and reaction.	This framework allows us to figure out the next steps to estimating how far a car will travel while texting and driving.
Finding Models	We found the model for distance while distracted and reacting was distance = velocity * time. We found the deceleration due to breaking. We found the model for constant acceleration from rest.	These models allow us to quickly customize and predict the distances involved in texting and driving.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Where are we Going?

Remember our System Analysis.

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
Finding Models	We found the right model for constant velocity. We found the deceleration do to breaking. We found the model for constant acceleration from rest.	These models allow us to quickly customize and predict the distances involved in texting and driving.
Computational Thinking	Use computational reasoning to develop a mathematical model for complex motion	We can use it to build a program to estimate the distance a car travels while braking.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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By the End of this Exploration �You Should Be able to Answer:

Focus Question

How do we create a mathematical model for complex motion?

Language Focus

Be able to express those patterns graphically, mathematically, visually, and verbally.

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Motion is Relative

The Mythbusters were asked is it possible to shoot a soccer ball out of a cannon that is mounted on the back of a truck that is going 50 mph and make the ball “stand still” from the perspective of being on the sidewalk?

What do you think? Is that possible?

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Looped Video

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Check-In Question:

Imagine you are on a field trip with your teacher. On the bus ride your teacher asks you to throw a basketball. A student who was left behind is on the sidewalk, would the student see the basketball going in air the same speed, faster, or slower than the bus?

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What happens when you are accelerating and already moving?

What will the pattern be for the frisbee as you begin to throw it (accelerate it) on a moving bus?

Think. Pair. Share.

With words, pictures or equations.

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Use private thinking and reasoning time.

Form A/B Partners.

A: explains their ideas

B: silently listens to understand A’s thinking

B: carefully re-voices A’s ideas without judging, adapting, or commenting on correctness of ideas

A: clarifies as needed

Reverse roles.

B: explains their ideas

A: silently listens to understand B’s thinking

A: carefully re-voices B’s ideas without judging, adapting, or commenting on correctness of the ideas

B: clarifies as needed

A/B: discuss ways their ideas are the same and/or different

Revoice and Compare

A1

A2

b3

b4

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Open 2CT - Student Version - Computational Thinking for Texting and Driving

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Google sheet: Data for Motion Data Tables

Determine the pattern for complex motion.
Take a peek at the computer code to get that columns output.
Try the next tab at the bottom of the screen.
What did you figure out by yourself?

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Velocity of ball in Bus = a t_f

Velocity of ball in Bus = a t₁

Final Velocity = Initial Velocity + acceleration ∗ time

t	v
0	10
1	15
2	20
5	35

Velocity of Bus = V_initial

time = 0

time = t₁

time = t_f

Velocity of Bus = V_initial

V_final= V_initial+ a∗t

Velocity of Bus = V_initial

+

=

v

t

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Let’s put what we learned into the System Analysis

Time of Braking =

V_final - V_initial

acceleration

Just one last thing!

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Total Distance = Velocity_initial ∗ time + ½ acceleration ∗ time²

distance on ramp = ½ at²

t	d
0	0
1	10
2	30
5	150

d

t

0

25

50

75

100

125

1

2

3

4

5

Distance of Bus = vt₁

d_o

d₁

d_f

Total Distance ball has gone

Distance of Bus = vt_f

D = V_i∗ t + ½ a∗t²

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Check In: �You Should Be able to Answer:

Focus Question

How do we create a mathematical model for complex motion?

Language Focus

Be able to express those patterns graphically, mathematically, visually, and verbally.

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Time of Braking =

v_final - v_initial

acceleration

Distance while Braking =

v_i t + ½ a t²

We have our System Analysis Completed!

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A1

A2

A1

A2

A	Share your ideas I think…… Something that reminded me of this is……. Evidence I have is…...	1 minute
B	Share your ideas I think…… Something that reminded me of this is……. Evidence I have is…...	1 minute
A	Borrow Ideas: Tell B which ideas they shared that you would like to use in the next round to clarify or support your explanation Something you said that really helped me was….	20 seconds
B	Borrow Ideas: Tell A which ideas they shared that you would like to use in the next round to clarify or support your explanation I thought it was interesting when you said…..	20 seconds

Use private thinking and reasoning time. Then line up and:

Stronger and Clearer

Then, A’s rotate one and repeat stronger and clearer.

b3

b4

b3

b4

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
Finding Models	We found the right model for constant velocity. We found the deceleration do to breaking. We found the model for constant acceleration from rest.	These models allow us to quickly customize and predict the distances involved in texting and driving.
Computational Thinking	Use computational reasoning to develop a mathematical model for complex motion	We can use it to build a program to estimate the distance a car travels while braking.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Texting & Driving - Day 6

Agenda:

Putting it all together with

Computational Thinking

Programming Simulation

Iterate it to handle more complex scenarios

Due This Class

Programming our simulation

Due Next Class

Using science to enhance a social discussion

Warm-up Question:

Let’s try some generic practice with coding in spreadsheets:

What will this code display?

=(B2+A1)/B1

	A	B	C
1	4	5	5
2	9	6	7

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By the End of this Computational Thinking �You Should Be able to Answer:

Focus Question

How do we code a simulation of texting and driving in a spreadsheet (an app) for a real-world scenario?

Language Focus

Use the language of spreadsheet coding to achieve your vision.

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2Tutorial1 - Creating Your Diagram

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2Tutorial2 - Coding Distance while Distracted

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2Tutorial3 - Coding Distance while Reacting

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2Tutorial4 - Coding Distance while Braking

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2Tutorial5 - Full Tutorial for Coding Your Spreadsheet for Texting and Driving

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Check In: �You Should Be able to Answer:

Focus Question

Language Focus

How do we code a simulation of texting and driving in a spreadsheet (an app) for a real-world scenario?

Use the language of spreadsheet coding to achieve your vision.

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
Computational Thinking	Use computational reasoning to develop a mathematical model for complex motion. We coded a simulation of texting and driving into a spreadsheet.	We can use it to build a program to estimate the distance a car travels while braking. This allows us to have a data-informed prediction about the distances a car travels that we can easily modify for different scenarios.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Texting & Driving - Day 7

Agenda:

Finish Programming Simulation

Iterate it to handle more complex scenarios

Claim/Evidence/Reasoning

*If you finish early: Think all coding is on a screen? Check out this Science Friday.

Due This Class

Wolfram's TED talk about Computational Thinking

�

Upcoming Events

Assessment: Enhance a Social Discussion with STEM

Warm-up Question:

Open up your google sheet from last time.

What is one useful thing about spreadsheets?

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By the End of this Computational Thinking �You Should Be able to Answer:

Focus Question

How do we iterate our app for a more complex real-world scenario?

Language Focus

Use the language of coding to achieve your vision.

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Circling Back to Iterate our Simulation to Handle all of the more Complex Situations we Brainstormed on Day 1

What about if you are tired?
What if it is raining?
What if you read and then reply?
What if you drift into oncoming traffic? →
What else...

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How do we think scientifically about this scenario of texting and driving -- Signal to Noise Winner

https://www.youtube.com/watch?v=3uCROILNCVE

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Check In: �You Should Be able to Answer:

Focus Question

Language Focus

How do we iterate our app for a more complex real-world scenario?

Use the language of coding to achieve your vision.

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By the End of this Activity �You Should Be able to Answer:

Focus Question

How do we use STEM to enhance a social discussion?

Language Focus

How do we write a scientific argument?

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Is texting and driving potentially hazardous versus alert driving?

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Task	What did we do? What practices, tools of science, and actions did we use to advance towards solving the problem.	How does it connect?
Computational Thinking	Use computational reasoning to understand complex motion and build a simple program to estimate the distance a car travels during a texting and driving incident	This allows us to have a data-informed prediction about the distances a car travels that we can easily modify for different scenarios
Arguing from Evidence	We used claim evidence reasoning, where the evidence was from our own programmed simulation, to create an argument about the dangers of texting and driving.	We create one thoughtful answer to how can we use STEM to enhance a social discussion.

Calendar of Learning Sequence

Project Based Learning - Keeping our “eyes on the prize”

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Claim: Write a sentence stating if texting and driving is potentially hazardous.

Your claim is a sentence that answers the original question.

Usually one sentence in length
Accurate, specific, and completely answers the question.

Possible Sentence Frames:

After analyzing ___, I conclude …
I believe that ___.

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Evidence: Use data (actual numbers and screenshots of your simulation) from your simulation that supports your claim about if texting and driving is hazardous.

The evidence is all the data that supports the claim.

Evidence must be sufficient and relevant to the claim. Not all data is considered relevant.
Have several pieces of data to back up your claim.

Possible Sentence Frames:

My evidence for this claim is …
The claim is supported by …
___ shows that ___.

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Reasoning: Write a statement that explains how your evidence leads to your claim about if texting and driving is potentially hazardous.

Reasoning is the explanation that connects your claim to the evidence that supports it.

Shows why the data you chose counts as evidence

Possible Sentence Frames:

I observed that ___, which shows ___ because …
___ suggests that ___ because …
The evidence strongly points to ___.
In ___, we see ___, whereas in ___, we see ___.
___ argues that ___.
___ supports my position because …
___ allows me to infer ___ because …
Considering these two pieces of evidence together, it can be seen that ...

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After investigating and programming a simulation for texting and driving, I conclude that distracted driving is much more hazardous than alert driving. I have two pieces of evidence for this claim. Evidence piece #1, is a screenshot of my simulation for an alert driver, driving 15 m/s and having a reaction time of 0.5 s, and it shows an alert driver will travel 31 m. Evidence piece #2, is a screenshot of my simulation for a distracted driver, driving 15 m/s, having a reaction time of 0.5 s, and a distracted time of 3.0 s, and my simulation show the distracted driver will travel 76 m. Considering these two pieces of evidence together it can be seen that even at this low speed a distracted driver will travel 45 more meters -- that is over twice as far as an alert driver and could be the difference of an awful accident and a close call where everyone is safe.

Screenshot #1 - Alert Driver

Screenshot #2 - Distracted Driver - note the pink highlight showing the 45 m travelled while distracted.

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After investigating and programming a simulation for texting and driving, I conclude that distracted driving is much more hazardous than alert driving. My evidence is the comparison of the distances involved for an alert driver versus a distracted driver. Evidence piece #1, is a screenshot of my simulation for an alert driver, driving 15 m/s and having a reaction time of 0.5 s, and an acceleration of - 8 m/s/s. It shows an alert driver will travel 22 m. Evidence piece #2, is a screenshot of my simulation for a distracted driver, driving 15 m/s, having a reaction time of 0.5 s, an acceleration of - 8 m/s/s, and a distracted time of 3.0 s. It shows the distracted driver will travel 67 m. Considering these two pieces of evidence together it can be seen that even at this low speed a distracted driver will travel 45 more meters -- that is over twice as far as an alert driver and could be the difference of an awful accident and a close call where everyone is safe.

Screenshot #1 - Alert Driver

Screenshot #2 - Distracted Driver - note the pink highlight showing the 45 m travelled while distracted.

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Screenshot 2

Screenshot 1

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Check In: �You Should Be able to Answer:

Focus Question

How do we use STEM to enhance a social discussion?

Language Focus

How do we write a scientific argument?

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Assessment: Enhance a Social Discussion with STEM

*If you finish early: Think all coding is on a screen? Check out this Science Friday.

Due Next Class

Optional: Check Out and Make Sense of the Visuals about our Columbia River

Upcoming Event

New Unit on Energy & Engineering

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End

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