The Very Spring and Root

An engineer's adventures in education (and other musings).

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Lesson Materials

Lesson Plan: Intro to Parallel Circuits

I’ve been wanting to upload more lesson plans and materials that I think worked well — like everything else, its just a matter of finding the time.

BACKGROUND

The attached are a lesson plan and a handout for how I did the introduction to parallel circuits. At this point in the unit, we had already covered the conceptual understanding of what voltage, current, and resistance area. We had already covered Ohm’s Law as well, both activity-based and mathematically.

I have removed the following from the lesson plan:

  • Mention of or planning for individual students. Normally, in addition to planning for all students in general, I am preparing for particular students who tend to need additional prodding to focus, often have clarification questions, or perhaps need additional language assistance. 
  • The section on planning for individual students with learning disabilities, since the plans would necessarily detail confidential information about my students.

 

My students had not done series circuits yet. The decision to start with parallel came after some thought — I wondered if there are good reasons why series circuits a usually taught first. I really couldn’t think of any that didn’t also have an analog on the parallel side. For example, in a series circuit, it is usually intuitive why the current is the same through all components (there is only one path for the charges to take).

However, understanding why the voltage drops in a series circuit have to add up to the total battery voltage (proportional to their resistances) requires more thought (and a good understanding of what voltage physically is). On the other hand, in a parallel circuit, the idea that the current in each branch should sum to the total entering and leaving the battery is easy to visually demonstrate. But why should the voltage across all components never change, no matter how many you add or remove (within reason)?

I figured it was six one way, half a dozen the other and went with parallel first for the novelty.

FILES

These are free to use, modify, and distribute. Please credit me and/or this blog if you use it for something, and I’d love to hear any revision suggestions for next year or reports on how it went with other students! 

Lesson3.1A-ParallelCircuits [pdf]

Lesson3.1A-Handout [pdf]

ANALYSIS

Students in general pieced the important concepts together well. One thing that surprised me was that one group seemed to be able to use the data they were getting in the lesson to validate an incorrect model of parallel circuits: that it was always the closest resistor to the battery that got the most current. I realized 1) that this was not a student idea that I had anticipated, and 2) that the setup of the lab allowed this alternative conception to be reinforced (note that the resistor with lower resistance is, in fact, closer to the battery on the circuit diagram).

I asked that group to test out their idea by swapping the resistor positions, telling them to predict what would happen first. They conferred and said that “it was probably about fifty-fifty” on whether or not their theory would be disproven by the new data. They were able to discover that the current depends only on the relative value of the resistances.

I then reframed the post-activity discussion to center on this student reasoning/discovery instead of my originally planned questions. In a way, this was serendipitous — I got students to demonstrate for their peers what real science looks like. We have an initial model that attempts to explain something we observe, we ask ourselves what we need to do to validate that model, we attempt validation, and then revise our model. That meta lesson was possibly more important in the long run than the actual content of parallel circuits.

The next day, we followed up with discussion, reading, and applying mathematical relations to what we learned in the exploratory activity.



Lesson Plan: Predictions With Conservation of Energy

by Nalin A. Ratnayake

Unit: Work and Energy, Component 2: Conservation of Energy
Date: January 15th, 2013
Day/Block: Day 4, Blocks A(3) / E(2) / F(6)
Time Available: E 58 min, A 58 min, F 65 min

Objective: You will be able to predict and analyze motion using the Law of Conservation of Energy.

Criteria for Success:

  1. Can I predict the final mechanical energy of an object in motion using energy conservation?
  2. Can I determine if and how an object’s mechanical energy has changed?
  3. Can I solve a physics problem using energy conservation?

Assessment: Handout and Exit Ticket
The handout will show qualitative understanding of Criteria for Success 1 and 2.
The short worksheet will show quantitative understanding of the Criterion for Success 3.

[10 min] Do Now

Please have a seat and work quietly on the Do Now.

A ball of mass 15.5 kg is released from rest at a point 1.2 m high.

1. If we ignore air resistance, what will be the velocity of the ball at the lowest point of motion?

2. If we assume that air resistance does -20 J of work on the ball as it falls, what will be the velocity at the lowest point of motion?

Share out. Specific questions to ask students: Can you step me through how you found the velocity? How do you know much initial mechanical energy the ball has? How do you know that the total mechanical energy will remain constant? Where does the kinetic energy of the ball come from?  What does the work done by friction do to the mechanical energy of the ball?

[2 min] Framing the Day

The scenario we will be looking at today will be very similar to the Do Now… only more dangerous!

Objective: You will be able to predict and analyze motion using the Law of Conservation of Energy.

Criteria for Success:

  1. Can I predict what will happen to the mechanical energy of an object by using energy conservation?
  2. Can I determine if and how an object’s mechanical energy has changed?
  3. Can I solve a physics problem about the motion of an object using energy conservation?

Can someone please raise his or her hand and explain what we are doing today?
Can someone please raise his or her hand and remind us how we will know if we are successful today?

[35 min] Will Professor Lewin Survive?

Note: The following activity will be outlined on a handout / graphic organizer.

We are handing out a worksheet. These will be collected today at the end of the period. Please take a couple of minutes to read the first two sections, labeled “Video” and “Directions”.

VIDEO
Professor Walter Lewin is going to put his life on the line to prove the law of the conservation of energy. He will release a 15.5 kg pendulum bob from his chin, and wait to see what happens when the ball swings back at his face! Will the ball smash his face in? Or will the laws of physics protect him? We will find out….
Can someone please raise their hand to volunteer to read the first paragraph for us?

Directions

  • We will be watching a video that goes along with this handout. Do not move ahead. Some questions we will do as a class, some as a table, and others individually.
  • Write your answers in complete sentences wherever possible. This helps organize your thinking and gives you better study materials later for quizzes and tests.

Can someone please raise their hand and tell us, what is one direction we should follow today? Why should we do that?
Can someone please raise their hand and tell us, what is another direction we should follow today? Why should we do that?

Play the video of Walter Lewin putting his life on the line to prove Conservation of Energy.

Stop the video at 2:54.  (Right after “…this will be my last lecture.”)

PREDICTIONS

Answer question 1 individually on your worksheet now.
1. What kind(s) of mechanical energy does the ball have right now and how do you know?
Quick share, check for agreement or disagreement and why.

Take a couple of minutes to work with your table group on the first column of the table (question 2).
After each column, ask a student to share out what their group answered. Questions to ask: Why do you think that the mechanical energy will increase/decrease? Why will this make the height higher/lower? What does positive/negative work do to the mechanical energy of the pendulum? How will we know if the mechanical energy is higher/lower?

Repeat for questions 3 and 4.

2. Prof. Lewin does not push the ball and we assume no air resistance 3. Prof. Lewin does not push the ball but we include air resistance 4. Prof. Lewin accidentally pushes the ball as he lets go
What kind of work will be done on the ball (positive / negative / none)?
What will happen to the total mechanical energy of the ball (increase / decrease / constant)?
What will be the height of the ball when it swings back to Prof. Lewin (higher / lower / same)?
Will Professor Lewin be safe (yes / no)?

Add this diagram to the slide to be clear about what I mean by “height”:

Answer question 5 on your worksheet individually.
5. Make your prediction: What will happen to the mechanical energy of the ball? How will you know if your prediction is right or wrong?

Play the rest of the video.

Show a side by side of the before (at the time of release) and after (1 cycle):

Ask the class:
I was careful to stop the video exactly when the ball reached its maximum height on the return swing. Is he at the same position or not? What do you notice about the ball’s position?

At this point there should be at least 20 min remaining in the period.

ANALYSIS
Answer the following question individually:
6. What happened to the mechanical energy of the ball, and how do you know?  What evidence tells you so?

DISCUSSION
Possible questions:What happened to the mechanical energy of the ball, and what evidence do you have? Was there work done on the ball? If so, by what force and was it positive or negative work? How can we explain what happened using the Law of Conservation of Energy? As students answer, ask for agreement or disagreement and why.

CONFER
In a couple of minutes, I’m going to ask you to answer question 7 individually. But before we do that. you have 2 minutes to check with your partner and make sure you agree on what happened. This is your only chance to confer before answering question 7 on your own.

Now, answer question 7  on your own.
7. Write out a short story of what happened to Prof. Lewin’s swinging pendulum. You must answer the following questions in your story: Was work done on the ball and by what force?  What did this work do to the mechanical energy of the ball? What did we observe that told us what happened to the mechanical energy of the ball?

[5 min] Exit Ticket

Professor Lewin released a 15.5 kg pendulum from 1.20 m high. We carefully measure the height of the ball when it swings back towards him, and determine that the ball only went 1.05 m high when it came back. How much work was done by air resistance on the ball?

Collect student work. If running out of time, ask co resident to help photograph worksheets and exit tickets of case study students as a worst case fallback option.

52 min total:  ~5 min of buffer
If need be, the CONFER section of the plan can be eliminated without impact to the cognitive demand or student sense-making in the lesson.



Lesson Plan: Conservation of Energy using a Music Video

Lesson 2.2: Exploring Conservation of Energy

Unit: Work and Energy, Component 2 – Conservation of Energy
Date: January 10th, 2013
Day/Block: Day 1 –  A/E/F
Time Available: A 58min / E 48min / F 65min

Objective:
You will be able to design and analyze a Rube Goldberg Machine using the Law of Conservation of Energy.

Criteria for Success:
Can I design my own machine that transfers mechanical energy between objects through work?

Can I use the Law of Conservation of Energy to explain how my design transfers energy?

Assessment:
Handout with machine design and analysis questions.

Agenda:

[10 min] DoNow:

The complicated chain of events in the music video is called a “Rube Goldberg Machine”. These machines use many transfers of energy between a whole lot of objects in order to do a very simple task.

Invent your own small (2 objects) Rube Goldberg machine. How would you use one object to make another object do something else? Where is there work and energy? How does one object transfer energy to another?

Example:

[10 min] Discussion: Music Video

Show OK Go’s music video for “This Too Shall Pass”: (4 min)

Note: Watching the video was assigned as homework the previous night, along with the following guided questions: Where do you see work? Where do you see energy being transferred from one form to another? Write down at least 1 example (note the video time), and make sure to explain what object is doing work on what other object, what kind of energy is being transferred, and how you know.

Talk to a partner next to you and share 1 example of work and energy being transferred from one object to another. I will ask several students to share an observation that their partner noticed, and explain to me what object is having work done on it and what kinds of energy are involved.

Possible questions to ask:
What did you see? Be specific, tell me what happened to the object that makes you think there was work done. What kinds of energy do you think that the object has?  How do you know that the object has that kind of energy?

Record student observations on the whiteboard.

[15 min] In-Depth Analysis: Tire

Show video clip of the tire section twice (7 second clip starting at 1:03). Ask students to write down exactly what they see happening to the tire. Have students share their observations, and assemble a record of the tire’s journey on the board to refer to later.  (Make sure that the bucket hitting the tire is included.)  Hand out the worksheet for scaffolded analysis of the tire scenario.

Refer to your handout. Take 30 seconds to answer the first question by yourself. Ask one student to share what they wrote with the class.
1. At the beginning of the scenario, does the tire already have mechanical energy? If so, what form(s) is it in, and how do you know?

Take two minutes to answer questions 2 and 3 with a partner.  Ask one or two pairs to share, depending on time.
2. During the scenario, is work done on the tire by any other object?  Is this work positive or negative, and how do you know?
3. What happens to the tire’s total mechanical energy when the work is done to it?

Take four minutes to answer questions 4 and 5 with a partner. Ask one or two pairs to share, depending on time.
4. Describe what happens to the tire’s GPE, KE, and total ME as it goes through the scenario.
5.  What happens to the tire’s mechanical energy at the end of the scenario?

[15 min] Creative Activity: Design and Analyze

Turn over your handout. Now you have a chance to design your own Rube Goldberg machine! Draw your machine in the space provided, and use the Tire Analysis as a guide to answer the analysis questions below. The questions are due tomorrow for stamps. If you don’t finish in class, please complete the analysis questions as homework.

6. Draw your own piece of this Rube Goldberg Machine that uses 1 object. You must include at least 1 transfer of energy from one object to another.

7. What is your main object in this scenario? :

8. Describe what happens to your object’s GPE, KE, and total ME as it goes through the scenario beginning to end..

9. Where is work done on your object or by your object? How does this work change your object’s total mechanical energy?

10. Explain how your machine obeys the Law of Conservation of Energy, MEi + W = MEf.



Lesson Plan: Exploring Newton’s 3rd Law in Sports

EXPLORING NEWTON’S 3rd LAW IN SPORTS

Unit: Dynamics
Date: November 19th, 2012
Day/Block: Day 3 / A Block
Time Available: 65 min

Teacher Prep:

  • Ensure prerequisite knowledge of: introduction to Newton’s 3rd Law
  • Make slides (including one for Objective and Criteria for Success)
  • Print and copy exit tickets
  • Rehearse lesson and do the work of the students

Lesson Objective:
You will be able to identify action-reaction force pairs and make predictions about motion using Newton’s Third Law.

Criteria for Success:
You will be able to explain what Newton’s 3rd Law says about forces.
You will be able to use Newton’s 3rd Law to predict what forces will act on an object in physical scenarios.

Assessment:
Exit ticket.

Agenda:

[5 min] Do Now


Newton’s 3rd Law tells us that all forces come in action-reaction pairs. List the action-reaction force pairs that you can think of on the red football player. (Hint: Mr. Ratnayake sees at least 4). Draw a free body diagram of the red football player.

[1 min] Making Explicit the Content of the Lesson

Hang on to what you did for the Do Now. We will be returning to it later on in the lesson.

Lesson Objective: You will be able to identify action-reaction force pairs and make predictions about motion using Newton’s Third Law.

Criteria for Success:
You will be able to explain what Newton’s 3rd Law says about forces.
You will be able to use Newton’s 3rd Law to predict what forces will act on an object in physical scenarios.

* Ask students to revoice the objective and CfS.

[10 min] Mini-Lecture 1: Review of Newton’s 3rd Law

[7 min for lecture] Review the main points of the third law.

  • There is no such thing as a single force — forces always come in action-reaction pairs.
  • Action-reaction pairs are the same kind of force acting on different objects.
  • Action-reaction pair have equal magnitude forces acting in opposite directions.

* Ask students, what do you think I mean by “same kind of force”? (Gravity, perpendicular contact force, parallel contact force, etc).
* Ask students, what do you think I mean by “magnitude”? (Strength of the force, size of the force, the value of the number, etc).

[3min for processing time] Take 2 minutes to check with a partner next to you. Look back at your list of action-reaction pairs from the Do Now. Do the pairs on your list fit what we just wrote down about Newton’s 3rd Law? I will ask someone to tell me about what their partner wrote.

* Ask students to name a force pair that their partner wrote down, and why they think it fits the description of an action reaction pair.  Draw the force pairs on the football player.

[10 min] Mini-Lecture 2: Review of Free Body Diagrams.

[5 min for lecture] A Free Body Diagram of an object only shows the forces acting on that object.
Free Body Diagrams do not include the forces that the object itself applies on other things.

Ask yourself: if I were this object, which forces would I feel acting on me?

Block on a surface example. There are two action-reaction pairs:

  1. gravity from the earth on the block, with gravity from the block on the earth
  2. contact force from the block to the surface, with contact force from the surface to the block

Which of these forces do you think the block is feeling? (normal force and weight). Draw FBD.

[2 min for processing time] Take 1 minute to check with a partner next to you. Look back at your free body diagrams from the Do Now. Does your partner’s FBD of the football player obey the rules of a free body diagram?

[3 min for closure on the Do Now] * Have a student draw the free body diagram for the red football player. Use questions for students to correct it if necessary.

[1 min] Instructions for Scenarios

Take 1 minute to read the directions for this next segment. I will call on a student to explain what we are doing for the class.

  • You will be given a scenario and several questions for discussion in your table group.
  • I will call on someone for each part of the discussion questions.
  • If they represent their group well, the whole group gets a stamp.

*Ask students: What are we going to be doing?

[15 min] Scenario 1: Serena Williams — Tennis

[15 min total, 8 min to discuss with group and work out the scenario, 7 min for discussion]

Tennis star Serena Williams uses Newton’s Laws to get the tennis ball to move.

  • Describe the action-reaction force pair that acts to accelerate the tennis ball. What are the forces? In which direction do they act? On what does each force at?
  • Draw a free body diagram of the tennis ball. In which direction is the net force on the tennis ball? Predict what will happen to the tennis ball and racket, using Newton’s Laws.

[15 min] Scenario 2: Ron Weasley — Quidditch

[12 min total, 7 min to think-pair-share, 5 min for discussion]

Quidditch keeper Ron Weasley blocks a quaffle coming in from the left of the image.

  • Describe the action-reaction force pair that acts to block the quaffle at the time of impact. What are the forces? In which direction do they act? On what does each force at?
  • Draw the FBD for the quaffle and the FBD for Ron. In which direction is the net force and acceleration for the quaffle? What about for Ron?
  • Which will accelerate more, the quaffle or Ron? If Ron and the quaffle both experience an equal force from the impact, why are their accelerations different?

 

[7 min] Exit Ticket

How can you tell if two forces are an action-reaction pair according to Newton’s 3rd Law?

An archery target stops an arrow on impact. The arrow experiences high acceleration to go from a fast speed to at-rest very quickly. Do the arrow and the target experience the same force from the impact? Do the arrow and the target experience the same acceleration? Why or why not?

64 min total:  ~1 min of buffer

Pacing: If necessary due to unexpected time constraint, one of the scenarios can be cut out and the other extended slightly.



Lesson Plan: Introduction to Newton’s Second Law of Motion

[7 min] Do Now

Review from 1st Law, introduce 2nd Law:

In which of these cases do we have balanced forces? Explain why.

  • A cat is moving with constant velocity towards his date.
  • A car is moving with constant acceleration to pick up more physics homework.
  • A cow is at rest, taking a nap.
  • An apple is hanging from a tree.

Share out and discuss. Bridge the transition between Newton’s First Law and the idea of net force into Newton’s Second Law.

[1 min] Making Clear the Objective

Objective: You will derive the relationship between force and acceleration from simulated experimental data.
Criteria for Success: Graphs of data will show proof of Newton’s 2nd Law of Motion.

[12 min] Simulation: Newton’s Second Law

We will be using the simulation of Newton’s 2nd Law located at: http://phet.colorado.edu/en/simulation/forces-1d

Set: show horizontal force, show total force.
Turn friction off.
Turn on graphs for acceleration and velocity.

Use students to run simulation and call out the data for their classmates to record.

We will be using a simulation. For each trial, record the following:

  • mass of the object
  • force applied to the object
  • acceleration of the object

Run the simulation for the dog (25 kg) with three forces: 50 N, 100 N, 200 N. Ask the students to make a prediction before the last one. Make sure to reset the simulation and graphs before each trial.

Run the simulation  for the textbook (10 kg) with the same three forces.

 

[15 min] Graphing the Data

Turn and Talk:
What was the independent variable and why?
What was the dependent variable and why?
What was the main control variable and why?

What do we put on the y-axis? What do we put on the x-axis?
The independent variable of our experiment always goes on the x-axis (Force). The dependent variable of our experiment always goes on the y-axis (Acceleration).

Work with your partner:
Draw 2 graphs. Don’t forget units and labels!

  • Acceleration vs force variable for the dog
  • Acceleration vs force variable for textbook

 

[15 min] Analyzing the Data

We seem to have found a correlation between two variables, force and acceleration. Let’s see if we can define a relationship between them.

Find the slope of each graph and write it next to the plot.
Find the inverse of the slope for each graph and write it next to the plot.

Think-Pair-Share:
Do we see any patterns? Does the slope look like a variable we recognize? How would I write the equation of this line?

a = 1/m F   →   F = m a

[2 min] Summarize Findings

Newton’s 2nd Law of Motion:
The acceleration of an object is directly proportional to the net force acting on the object. The acceleration will be in the same direction as the net force. The acceleration is resisted by the mass of the object.

F = m a

Estimated Instructional Time: 52 min

 

[6 min] Exit Ticket


The catapult on an aircraft carrier can can accelerate a fighter jet from rest to 56 m/s in just 2.8 s. If the fighter jet has a mass of 13,000 kg, what is the force required?




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