Dr. Krista Holstein (kholstein@sms.edu)Ann Marie Davis (amdavis@sms.edu)

Saint Mary’s SchoolRaleigh, NC

Teamwork, Content,

and Growth

Mindset:Teaching

an Algebra/P

hysics Blended Course

Example Problems1. Harry and Draco were playing Quidditch. Harry started at one end of the field and flew 12 meters every 3

seconds. Draco started 28 meters from Harry and flew toward him at 9 meters every 3 seconds. a. Given this situation, show the other three representations (equations, tables, graphs) for both boys.

Draw both graphs on one set of axes on a sheet of graph paper. Be sure to label the axes and the lines clearly.

b. How far from the end of the field will Harry be after 3 seconds? Convert this value to centimeters. Convert this value to kilometers. Which unit is the most reasonable for this situation? Why?

c. What is Harry’s velocity? What is Draco’s velocity? d. Create the velocity-time graphs for both boys. Draw both graphs on one set of axes. Be sure to label

your axes and the lines clearly. e. Acceleration is the rate at which an object’s velocity changes over time. How would you describe Harry’s

motion in terms of velocity and acceleration?

Standards for #1: Multiple Representations of Linear Relationships Rate of Change Systems of Equations Solutions to Systems Represent motion on a position-time graph Analyze a graph of motion to determine if an object is moving at a constant or changing rate. Correctly use physics definitions and terminology and distinguish between common English words and words that

have a specific technical meaning in physics Proper use of units, symbols, prefixes, and notation. Use multiple representations (words, graphs, drawings, equations) of a physical situation and understand the

relationships among them.

2. In the Divergent Series, Tris chooses to join the Dauntless faction. Her first challenge is to run and jump on a speeding train with the other members of her group. Spoiler Alert: she makes it! Tris’ distance-time equation is y = x2 + 20, where x represents time (seconds) and y represents distance (meters). The train’s distance-time graph is shown at right.

a. Find the other representations for both Tris and the train (equations, graphs, tables). Draw the graph for Tris on the axes above.

b. Is Tris accelerating or not? Is the train accelerating or not? How do you know?

c. The platform ends after 125 meters. How close was she to reaching the end of the platform before she jumped on the train? Show all work and explain how you know.

Standards for #2: Quadratic Functions Use multiple representations (words, graphs, drawings, equations) of a physical situation and understand the relationships among them. Analyze a graph of motion to determine if an object is moving at a constant or changing rate. Correctly use physics definitions and terminology and distinguish between common English words and words that have a specific technical meaning in physics Proper use of units, symbols, prefixes, and notation. Use multiple representations (words, graphs, drawings, equations) of a physical situation and understand the relationships among them.

Systems of Equations and Projectile Motion Project

TASKYou and your team will analyze the motion of at least two objects that are interacting (while airborne). At minimum, you will:

Find an example of each situation: two linear relationships, and one linear and one quadratic relationship.

Collect data that yield linear or parabolic graphs Analyze the meaning of the graphs Find the equation for each line/curve and analyze the meaning of the values in the equation Find where the lines/curves intersect (providing evidence) and analyze the meaning of this point of

intersection Identify the forces that cause motion (including units)

PROJECT REQUIREMENTSYour team is expected to turn in the following by _______________.

A display of your work that will be visible to others in the school. Be creative! What can you create besides a poster? Make sure this display is:

Professional and pretty Organized and easy to follow

A hard copy of all your graphs, equations, work, etc. Each member of the team should have her handwriting on the work at some point.

Your team will present your results to the class on ________________. Your team will do a 5-10 minute presentation Each member of the team must speak

Each person will submit a word document in Canvas answering the following: What math and physics did you learn through this project? If you were to do the project again, what would you do differently? How did you, yourself, contribute to this project? Be as specific as possible. How did each of your team members contribute to this project? Be as specific as possible.

Each person will submit a self-assessment of the rubrics. Give yourself a score for each criteria in the following rubrics. For each section, provide an overall explanation for why you gave yourself the scores on that section. You do not need to provide an explanation for each performance area.

Project Drafts are _________________. You should have the following completed for the draft:

All data collected All graphs completed A plan for your display A plan for your presentation

TEAM ROLESResource Manager:

Get supplies for your team and make sure that your team cleans up. Make sure that everyone has shared all of their ideas and help the team decide when it needs outside

help. Call the teacher over for team questions.

Facilitator: Get your team started by having someone read the task out loud. Check that everyone understands what to work on. Make sure that everyone understands your team’s answer before you move on.

Recorder/Reporter: Make sure that each team member can see the work the team is discussing. Make sure that your team agrees about how to explain your ideas and each person has time to write

their answer. Make sure that each member of your team is able to share ideas.

Task Manager: Make sure that no one talks outside your team. Help keep your team on task and talking about math. Listen for statements and reasons.

RUBRICSThe rubrics on the following pages will be used to determine your grade.

Content Rubric Earned Assessment

Performance Area Entry Developing Proficiency Mastery

Self Teacher

Linear RelationshipsDetermine if a given equation represents a linear relationship.Quadratic FunctionsGraph a quadratic function by making a table of values. Describe the characteristics of the graph.Constant or Changing RateAnalyze a graph of motion to determine if an object is moving at a constant or changing rate.Position-Time GraphRepresent motion on a position-time graphRate of ChangeInvestigate slope in real-life situations (e.g., speed, motion).Slope and InterceptsWhen given a graph, interpret the meaning of the slope, x-intercept, and y-intercept.Definitions & TerminologyCorrectly use physics definitions and terminology and distinguish between common English words and words that have a specific technical meaning in physicsUnits, Symbols, Prefixes, and NotationProperly use of units, symbols, prefixes, and notation.Systems of EquationsSolve systems of equations by graphing, using the elimination method, and using the substitution method.Methods for Solving SystemsDetermine the most efficient and accurate method for solving a system of equations.

Comments:

Problem Solving Rubric Earned Assessment

Performance Area Entry Developing Proficiency Mastery Self TeacherCommunicationExplain the approach and solution to a problem in both written and verbal formsMultiple RepresentationsUse multiple representations (words, graphs, drawings, equations) of a physical situation and understand the relationships among them.Logical approachApproach the problem using logical methods

Comments:

Skills Rubric Earned AssessmentPerformance Area Entry Developing Proficiency Mastery Self Teacher

Persistence & Resilience

Leaves questions unanswered.Refuses to read challenging texts or gives up quickly and asks for outside interpretation in lieu of reading.Does not improve her work when assigned to do so.Frequently stops working when encountering moments of failure or critical feedback.Is paralyzed by mistakes, setbacks, or disappointment. Refuses to acknowledge responsibility for mistakes.Frequently uses a single, inflexible method for producing products.

Takes initial step(s) to begin problem-solving even when confused.Reads challenging texts just once and/or needs reading questions to engage with reading material.Partially attempts improvements to her work when assigned to do so.Usually perseveres in working when encountering moments of failure or critical feedback.Is honest about mistakes, setbacks, or disappointment and responds to suggestions for improvement. Fails to independently take further steps toward recovery. Sometimes lacks confidence and will only take risks when encouraged to do so.

Utilizes resources made available by the teacher to support problem-solving when confused. Re-reads and/or annotates challenging material without extensive directions on how to do so.Makes thoughtful improvements to her work when assigned to do so.Consistently perseveres in exploring ideas when encountering moments of failure or critical feedback.Begins to show capacity to independently recover from mistakes, setbacks, or disappointment in situations in which resilience is part of the learning process.Will initiate taking calculated risks; may need assistance to adapt plans in accordance with outcomes.

Independently identifies resources to support problem-solving when confused. Thoroughly engages with the text: summarizes for own learning, refers to or draws upon text in other classwork.Analyzes her work to determine how it could be improved regardless of whether she is assigned to do so.Models persistence by being courageous in sharing own failures and seeking critical feedback.Demonstrates resilience in the face of setbacks and disappointments by actively initiating recovery strategies.Is confident and able to take calculated risks and adapt plans in accordance with outcomes.

Self-Regulation & Reflection

Often identifies errors in the process, and how to fix them, incorrectly. Rarely analyzes and questions one’s own thinking, reasoning, and critical thinking dispositions with accuracy. Displays significant biases that prevent an objective perspective.Rarely questions and/or evaluates one’s own reasoning and cognitive skills; makes regular errors in reviewing performance.

Is beginning to show the ability to identify errors in the process, but needs support in correcting the problem or identifying a new course of action.Sometimes analyzes and questions one’s own thinking, reasoning, and critical thinking dispositions with accuracy. Sometimes identifies factors that affect one’s objectivity or rationality.Is beginning to review one’s own performance, but review shows errors in self-reflection.

Frequently identifies and corrects errors in the process.Often analyzes and questions one’s own thinking, reasoning, and critical thinking dispositions with accuracy. Often identifies factors that affect one’s objectivity or rationality. Knows own bias.Rarely makes significant errors in reviewing one’s own performance.

Nearly always accurately identifies all errors in the information or process. Always analyzes and evaluates one’s own cognitive skills with a view toward questioning and/or validating one’s reasoning and results.Accurately judges the extent to which one’s thinking is influenced by deficiencies in knowledge, stereotypes, prejudices, emotions, or any other factors that constrain one’s objectivity or rationality. Transcends bias to produce fair-minded thorough work.Designs reasonable procedures to

remedy or correct, if possible, any mistakes and their causes.

Work Creatively with Others

Almost always works in isolation; hesitant to communicate ideas and provide feedback to others.

Works collaboratively with others. Is beginning to communicate ideas and feedback to others effectively, but sometimes struggles to make connections between or to build upon others’ ideas to generate new and unique insights.

Works collaboratively with others. Communicates ideas and feedback to others effectively; often makes connections between and builds upon others’ ideas to generate new and unique insights.

Displays a sophisticated level of openness and responsiveness to new and diverse perspectives; incorporates group input and feedback into the work.

Idea Generation

Generates few ideas that are limited in diversity and are often vague and loosely related to the creative challenge at hand. Shows an understanding of the concept of precedents, but fails to research whether ideas offered are new ideas.Participates in limited amounts of brainstorming; raises few open-ended, “what if” questions during the idea generation process.Represents a single, often inflexible, perspective in pursuing ideas.

Communicates some new ideas, but the volume is not sufficient to spark a creative process. Offers ideas that are somewhat diverse and reasonably clear, though they may not be detailed or expanded enough to show a relationship to the creative challenge at hand.Is beginning to show willingness to challenge and go beyond one’s underlying assumptions or beliefs when exploring ideas and solutions.Engages minimally with ideas generated by others.

Generates a sufficient volume of new ideas. Offers ideas that are broad in their diversity; ideas are clearly articulated and closely related to the creative challenge at hand.Displays sufficient willingness to challenge and go beyond one’s underlying assumptions/beliefs when exploring ideas and solutions.Is curious about new ideas and concepts. Actively seeks out ideas other than her own.

Takes an imaginative approach to idea generation. Finds useful and relevant information that others did not find from sources that others did not think of using. Asks sophisticated, open-ended questions that lead to the generation of original ideas.Demonstrates high levels of curiosity, imagination, and tenacity in exploring new concepts and ideas.

Comments:

Responsibility Rubric Earned Assessment

Performance Area Entry Developing Proficiency Master

ySelf Teacher

ResponsibilityWork is complete and turned in on time.

Comments:

Quadratic Equations ProjectTASKYou will explore the graphs and the solutions of quadratic equations in various contexts and create a display of your findings that will be visible to other students. You will work in groups of three or four students.

Collect data for a falling object In Logger Pro, create the following graphs with fitted curves and equations:

o Position vs. timeo Gravitational potential energy vs. time o Kinetic energy vs. time

Find the roots for your quadratic equations Write an explanation of what the roots mean in terms of the original problem context Develop a story for your falling object that was graphed in Logger Pro

o Find the roots and explain their meaning in terms of your storyo Explain why the distance between points is increasing over time

Create your display

PROJECT REQUIREMENTSTurn in the following on ____________

A display of your work (one per team) that will be visible to others in the school. Be creative! What can you create besides a poster or PowerPoint? Make sure this display:

o Is professional, pretty, and creativeo Is organized and easy to followo Includes the group’s function, graph, and story:

The graphs from Logger Pro (with fitted curve and equation) At least one screenshot from the data collection The mathematics used to find the roots A story for your falling object including:

An explanation of the root(s) in terms of your story An explanation for why the distance between points is increasing over time Story should explain the changes in energy that occur as the object falls

A word document (one per person) reflecting on your project experience. This information should be presented in paragraph form, but you may include a bulleted list or a table if necessary. Make sure this document:

o Is organized, professional, and easy to followo Includes an explanation of:

Your favorite part(s) of the project What you learned (e.g., mathematical content, physics content, group work dynamics,

etc.) The difficulties you had (e.g., completing the mathematical computations, developing a

story, using technology, etc.) and how you overcame these difficultieso Is submitted to Canvas by __________

Corrections & RetakesFor assignments (homework, problem sets, etc.), you may earn full points back by completing corrections. Here is the procedure:

1. Read through all feedback on the assignment and/or Canvas2. ON A SEPARATE SHEET OF PAPER:

a. Write your name and the name of the assignment on the top.b. Redo any questions that were incorrect.c. Write an explanation for each question that you redid. For example, what was incorrect about

it? How do you know? What will you do to ensure you don't make that mistake again?3. Attach this sheet of paper to your original assignment and turn it in.

For assessments (tests, quizzes, etc.), you will need to RETAKE the assessment to earn back full points. Here is the procedure:

1. Complete the "Request to Retake" form. This includes:a. Writing a reflectionb. Attending tutorialc. Completing all related homeworkd. Completing corrections (see steps #2-4 below)

2. Read through all feedback on the assignment and/or Canvas3. ON A SEPARATE SHEET OF PAPER:

a. Write your name and the name of the assignment on the top.b. Redo any questions that were incorrect.c. Write an explanation for each question that you redid. For example, what was incorrect about

it? How do you know? What will you do to ensure you don't make that mistake again?4. Attach this sheet of paper to your original assignment and turn it in.5. Schedule a time with you teacher to complete the re-assessment.