Collaboration Checklist - wvde.us · Web viewAssign groups by mixing up the styles as much as possible. ... Sound and Waves: ... cleans up materials, and makes sure each group member

Project Based LearningThe Function of Trigonometric Functions

Math III

Project Title: The Function of Trigonometric Functions

Project Idea: You are a mathematician with a strong appreciation for the beauty of mathematics. You have found that you cannot share that appreciation with anyone other than another mathematician. Because you are so anxious to share your feelings about the beauty and wonder of mathematics, you are looking for a scheme to represent it in a musical way. Music seems to be a medium that most people can enjoy and understand at some level. You believe that if a person understands the music it will help them understand the mathematics. You and a team of mathematicians have decided to coauthor a book to showcase this relationship. In order to promote the book, you will build a homemade musical instrument and tune the instrument using trigonometric graphs. You will create a presentation to persuade publishing companies to publish your book. The presentation will include excerpts from your book relating the instrument you build to its mathematical connections.

Entry Event:Invite a piano tuner to speak to the students about the process he uses to tune pianos.View the famous video of the Tacoma Narrows Bridge to show wave motion: Tacoma Narrows Bridge Collapse (Sound Version) (Standard 4:3): Stillman Fires Collection; Tacoma Fire Department (Video) – Castle Films (Sound) - http://www.archive.org/details/SF121 Facilitate a discussion: Why Study Trigonometric Graphs?Teacher resources for this discussion: Graphs of Trigonometric Functions - http://www.intmath.com/Trigonometric-graphs/Trigo-graph-intro.php10 Everyday Reasons Why Trigonometry is important in your Life? - http://www.mathworksheetscenter.com/mathtips/trigonometry.html

West Virginia College- and Career Readiness Standards:

Objectives Directly Taught or Learned Through Inquiry/Discovery

Evidence of Student Mastery of Content

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

Proficient students clarify the meaning of real world problems and identify entry points to their solution. They choose appropriate tools and make sense of quantities and relationships in problem situations. Students use assumptions and previously-established results to construct arguments and explore them. They justify conclusions, communicate using clear definitions, and respond to arguments, deciding if the arguments make sense. They ask clarifying questions. Students reflect on solutions to decide if outcomes make sense. They discern a pattern or structure and notice if calculations are repeated, while looking for both general methods and shortcuts. As they monitor and evaluate their progress, they will change course if necessary.

M.3HS.30 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

The student meets the teacher set criteria on the CBR Investigation.

The student completes The Music Project at a level of success designated by the teacher

M.3HS.38 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

a. Graph square root, cube root and piecewise-defined functions including step functions and absolute value


The student completes the online investigations(1- 4) found at the following website: Graphs of Trigonometric

Created by Cheryl Reger, NBCT

http://www.mathworksheetscenter.com/mathtips/trigonometry.html

http://www.intmath.com/Trigonometric-graphs/Trigo-graph-intro.php

http://www.archive.org/details/SF121

functions.b. Graph exponential and logarithmic

functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline and amplitude. Instructional Note: Focus on applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.)

Functions - http://www.intmath.com/Trigonometric-graphs/Trigo-graph-intro.php

M.3HS.42 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Instructional Note: Use transformations of functions to find more optimum models as students consider increasingly more complex situations. Note the effect of multiple transformations on a single function and the common effect of each transformation across function types. Include functions defined only by graph.

The student meets the teacher set criteria on the following quiz: Quia - Trig Graph Info -http://www.quia.com/jq/10338.html

The student meets the teacher set criteria on the CBR Investigation.


Performance Objectives:

Know:Know how each parameter in a trigonometric equation affects the graphRecognize the parent trigonometric graphs,ƒ(x) = sin xƒ(x) = cos xƒ(x) = tan xƒ(x) = cot xƒ(x) = sec xƒ(x) = csc xRecognize data patterns that can be modeled by a trigonometric functionKnow the relationship between the trigonometric functions and their inversesKnow the definition of a periodic functionKnow the period of basic trigonometric functions

Do:Find a trigonometric equation that fits a set of data by adjusting the parametersIdentify a trigonometric equation when given a graph of the functionUse the graph of the function to make predictionsGraph trigonometric functions using changes in parametersGraph trigonometric functions given period, amplitude, and midlineGraph the inverses of trigonometric functionsFind the period of a function given the graphFind the period of a function given the equation

Driving Question: Can a musician and a mathematician live and work together in harmony?


http://www.quia.com/jq/10338.html



Assessment Plan:

Major Group ProductsTeam Group Roles and contractCBR InvestigationThe Music Project

Major Individual ProjectsActivity Sheet from Illuminations: Seeing Music - http://illuminations.nctm.org/LessonDetail.aspx?id=L686The Respond Sheet located at: SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com>Mathematics>Trigonometry > Inverse Functions > Web Inquiry 114

Assessment and Reflection:

Rubric(s) I will use: (Check all that apply.)

CollaborationCollaboration Checklist

X Written Communication

Critical Thinking & Problem SolvingThe Music Project

X Content Knowledge

Oral Communication OtherOther classroom assessments for learning: (Check all that apply)

Quizzes/ tests Practice presentationsPractice Presentation Checklist

X

Self-evaluationStudent Reflection Report

X NotesMusic Knowledge Rating Scale

X

Peer evaluationTeam Final Evaluation

X Checklists/observationsCollaboration Checklist

X

Online tests and examshttp://www.quia.com/jq/10338.html

X Concept maps

Reflections: (Check all that apply)

SurveyProject Debrief

X Focus Group

Discussion Task Management ChartTask Checklist

X

Journal Writing/ Learning Log Other

Map the Project:

Product: The Music Project

Knowledge and Skills Needed Already Have

Learned

Taught Before the Project

Taught During the Project

1. Graph the basic sine wave X2. Fit a function to a set of periodic data X3. Find the period, amplitude and frequency of a sine wave X4. Know how each parameter affects the graph X5. Find the note associated with a “sound generated” sine wave X6. Insert graphs from calculator to computer X7. Collect sound data with a microphone or other probe X8. Make predictions using multiple representations X9. Search and navigate the internet X10. Collaboration skills X11. Presentations skills X

Resources: School-based Individuals:Music and/or physics teacherCreated by Cheryl Reger, NBCT


http://www.sascurriculumpathways.com/

http://illuminations.nctm.org/LessonDetail.aspx?id=L686

Technology:Computers with Internet access and printer Computer algebra software Graphing calculators with graphlink cable Calculator based ranger or other device to detect motionMicrophone with appropriate connectionsCalculator Based Laboratory (CBL2)Word processing/spreadsheet/publishing software

Community: Piano tuner and/or musicians

Materials:Materials to construct a musical instrument or wind chimesInstrument to create sound (music)

Websites:Resource for forming collaborative groups: nsrfharmony.org -http://www.nsrfharmony.org/system/files/protocols/north_south_1.pdf

Resource for team building activities: Group Activities, Games, Exercises, & Initiatives - http://wilderdom.com/games/View the famous video of the Tacoma Narrows Bridge to show wave motion: Tacoma Narrows Bridge Collapse (Sound Version) (Standard 4:3): Stillman Fires Collection; Tacoma Fire Department (Video) – Castle Films (Sound) - http://www.archive.org/details/SF121 Resource for reasons to study trigonometric graphs: Graphs of Trigonometric Functions - http://www.intmath.com/Trigonometric-graphs/Trigo-graph-intro.phpResource for reasons to study trigonometry: 10 Everyday Reasons Why Trigonometry is important in your Life? - http://www.mathworksheetscenter.com/mathtips/trigonometry.html

Online quiz: Quia - Trig Graph Info - http://www.quia.com/jq/10338.html

Activity to connect mathematics and music: Illuminations: Seeing Music - http://illuminations.nctm.org/LessonDetail.aspx?id=L686

Activity on inverse functions: SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com>Mathematics>Trigonometry > Inverse Functions > Web Inquiry 114

Spaghetti activity: pbworks.com - http://octm2009spaghetti.pbworks.com/f/Trig+Graphs+and+Laws.pdf

Applet used to visualize what is happening in the spaghetti activity: Trigonometry-sine and cosine Do “the Wave” - http://catcode.com/trig/trig08.html

Begin to investigate variations in the basic sine and cosine graphs: SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com>Mathematics>Trigonometry> Circular Functions and Graphs > Web Lesson 520

Review the attributes of all of the basic trigonometric functions: Properties of the Six Trigonometric Functions - http://www.analyzemath.com/trigonometry/properties.html

Trigonometry graph resource: Free Trigonometry Tutorials and Problems - http://www.analyzemath.com/Trigonometry.html

Vocabulary resource: Talking about Sound and Music - http://cnx.org/content/m12373/latest/Vocabulary resource: Google Books - http://books.google.com/ and enter “The Physics of Music”


http://books.google.com/

http://cnx.org/content/m12373/latest/

http://www.analyzemath.com/Trigonometry.html

http://www.analyzemath.com/trigonometry/properties.html


http://catcode.com/trig/trig08.html

http://octm2009spaghetti.pbworks.com/f/Trig+Graphs+and+Laws.pdf





http://www.mathworksheetscenter.com/mathtips/trigonometry.html


http://www.archive.org/details/SF121

http://wilderdom.com/games/

http://www.nsrfharmony.org/system/files/protocols/north_south_1.pdf

Data collection activity: Classroom Activities – Texas Instruments – US and Canada - https://education.ti.com/en/tisciencenspired/us/detail?id=1C88C70EA512453894D72DA9CD9452C0&t=9CCE22241F984128819ABD22248EDA90Resource for building instruments: Math, Science and Sound activities by Phil Tulga #09 - http://www.philtulga.com/MSSActivities.html#09Resource for building instruments: Greenriver.edu - http://www.instruction.greenriver.edu/projecttime/Music/AiM%20Module%20-%20Music.pdfResource for wind chimes: Make your own windchimes - http://www.phy.mtu.edu/~suits/windchime.htmlActivity to introduce inverse functions: Inverse trigonometric functions-Topics in trigonometry - http://www.themathpage.com/atrig/inverseTrig.htm

Manage the Process: See Trigonometric Graphing Storyboard.

The following description contains many opportunities for students to learn about graphing and the connections to the real world, in particular, music. In some cases, activities or tutorials might be eliminated for some or all students; however the suggested scaffolding is here if needed. If something is eliminated, the Task Checklist should be adjusted as well.

Week 1 Assign students to groups according to their personal style. The activity to determine this style can be found at nsrfharmony.org - http://www.nsrfharmony.org/system/files/protocols/north_south_1.pdf . Assign groups by mixing up the styles as much as possible. One of each style per group works well. After assigning groups, give them time to talk to each other about their individual style, strengths, and weaknesses. Students will take notes about members of the group and keep this as an artifact for the project. Plan other activities to help students see the importance and meaning of collaboration. Some team building activities can be found at Index to Group Activities, Games, Exercises, & Initiatives - http://wilderdom.com/games/ . Note: These activities may not be necessary if students in the class have experience working together in groups.

Launch the project by showing a video of the collapse of the Tacoma Narrows Bridge. This will motivate discussion about how trigonometric functions occur naturally. Teacher resources are listed in the entry event with more information about applications. Next invite a member of the community to discuss the process used to tune a piano. Distribute the project scenario and have groups complete a KWL. Discuss the goals of the project so that the learning targets are clear. Each group is expected to compose their own contract. They can use the internet as a resource to help them with ideas to include. After they determine the role of each student in the group, this should be included in the contract. Each student will sign the contract and it will be kept on file in the group folder.

Week 2Differentiation: What follows are two different ways to make the connection between the unit circle and the graphs of sine and cosine. The spaghetti activity would be more suited for the student who needs a hands-on experience to visualize this connection. The end product from this activity is a nice display to leave in the classroom while studying graphs. Spaghetti activity: pbworks.com - http://octm2009spaghetti.pbworks.com/f/Trig+Graphs+and+Laws.pdf (Lesson 1)Applet: Trigonometry-sine and cosine Do “the Wave” - http://catcode.com/trig/trig08.html used to visualize what is happening in the spaghetti activity:

The SAS Curriculum Pathways is an interactive online investigation and is more appropriate for the student who does not enjoy hands-on tasks. Since each has the same objective, students could be divided to meet this curriculum goal.SAS Curriculum Pathways Investigation:Why are Sine and Cosine called Circular Functions: SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com >Mathematics>Trigonometry> Circular Functions and Graphs > Web Lesson 520

Begin to investigate variations in the basic sine and cosine graphs:There are many resources online with good online investigations for this study. One such source is Graphs of Trigonometric Functions - http://www.intmath.com/Trigonometric-graphs/Trigo-graph-intro.php. The scaffolding of this topic on this website will be something like this:

Step 1: Investigate the amplitude of the sine and cosine functions: Choose #1 from the menu. At the end of this page students should complete the exercises and check their own answers to insure understanding.Step 2: Investigate the period of the sine and cosine functions: Choose #2 from the menu. At the end of this page students should read about frequency as related to electronics and look at the music example. Again there are exercises to complete to verify understanding.

Week 3




http://catcode.com/trig/trig08.html

http://octm2009spaghetti.pbworks.com/f/Trig+Graphs+and+Laws.pdf

http://wilderdom.com/games/

http://www.nsrfharmony.org/system/files/protocols/north_south_1.pdf

http://www.themathpage.com/atrig/inverseTrig.htm

http://www.phy.mtu.edu/~suits/windchime.html

http://www.instruction.greenriver.edu/projecttime/Music/AiM%20Module%20-%20Music.pdf


http://www.philtulga.com/MSSActivities.html#09

https://education.ti.com/en/tisciencenspired/us/detail?id=1C88C70EA512453894D72DA9CD9452C0&t=9CCE22241F984128819ABD22248EDA90


Step 3: Investigate phase shift of the sine and cosine functions: Choose #3 from the menu. Students should complete the exercises and check for understanding.Step 4: Continue by investigating the graphs of the tangent, cotangent, secant, and cosecant trigonometric functions. Choose #4 from the menu.

Differentiation: It may be necessary for some students to review the attributes of all of the basic trigonometric functions and a good resource for this is: Properties of the Six Trigonometric Functions - http://www.analyzemath.com/trigonometry/properties.html

Additional resources: Free Trigonometry Tutorials and Problems - http://www.analyzemath.com/Trigonometry.html Understanding can be reinforced and/or assessed by using the Families of Graphs Investigation. This can be done using graphing calculators or computer algebra software.

Week 4Introduce some type of computer interface to collect data and look at its graph. One way to do this is with a motion detector (CBR) linked to a graphing calculator. Working in their teams, students will find a way to generate data (using motion) that has a sinusoidal shape. Follow directions in the CBR Investigation that is provided. While students are experimenting with this, others may need extra practice graphing. When ready, use the Online Mini Quiz, Quia - Trig Graph Info - http://www.quia.com/jq/10338.html to assess student knowledge.

Week 5Connect sine waves to musical harmony and dissonance:(Begin with the Preactivity questions) and work on the “Seeing Music” Activity at the following website:Illuminations: Seeing Music - http://illuminations.nctm.org/LessonDetail.aspx?id=L686

The primary focus of The Music Project is to highlight connections between trigonometry and music. Groups will need time to collaborate as each member carries out their tasks. Students should also be working on the Music Knowledge Rating Scale. Differentiate by providing some resources for students who need help finding definitions:

Resource #1: Talking about Sound and Music - http://cnx.org/content/m12373/latest/Resource #2: Google Books - http://books.google.com/ and enter “The Physics of Music”

If available, you can use Sketchpad 5 sound generator to evaluate the function and find the equation of the sinusoid. This is a scaffolding activity in preparation of the data collection.Using a microphone and a computer interface or graphing calculator, investigate the properties of the sine wave. Generate the data by using a tuning fork, electric keyboard, or other musical instrument. Analyze the properties of the sound by considering the period, amplitude, and frequency. This is the process groups will use to tune their products for the final project. A variety of equipment and software can be used for this activity. One such choice has detailed instructions provided at the following web resource:Classroom Activities – Texas Instruments – US and Canada - https://education.ti.com/en/tisciencenspired/us/detail?id=1C88C70EA512453894D72DA9CD9452C0&t=9CCE22241F984128819ABD22248EDA90 Or at education.ti.com, browse by subject: Science : Physics : Sound and Waves: Activity “Physics: Vernier - Sound Waves and Beats”. Here you will find a step by step description of the process and a list of necessary equipment. For the final product (The Music Project) groups may choose from the following:Choice #1: Build a musical instrument made of tubes and use it to play a tune.Choice #2: Build a set of wind chimes and play a tune with it.Choice #3: Play a tune with glasses or water bottles.Each note on the instrument will be tuned by following the above procedure. These sine waves, as well as equations to fit them, will be included as part of the presentation to promote the book the team is authoring. You may want to share this information with the students when you launch the project.Resources for making an instrument:Math, Science and Sound activities by Phil Tulga #09 - http://www.philtulga.com/MSSActivities.html#09Greenriver.edu - http://www.instruction.greenriver.edu/projecttime/Music/AiM%20Module%20-%20Music.pdfWind chime resources:Make your own wind chimes - http://www.phy.mtu.edu/~suits/windchime.html

Week 6Introduce inverse trigonometric functions and use the following two activities:Inverse trigonometric functions-Topics in trigonometry - http://www.themathpage.com/atrig/inverseTrig.htm (tutorial)SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com>Mathematics>Trigonometry > Inverse Functions > Web Inquiry 114Some students can be working on these activities while others are working on the project, then rotate.Created by Cheryl Reger, NBCT


http://www.themathpage.com/atrig/inverseTrig.htm

http://www.phy.mtu.edu/~suits/windchime.html


http://www.philtulga.com/MSSActivities.html#09

http://education.ti.com/educationportal/activityexchange/BrowseBySubject.do?cid=US&brsOpenNode=bt1.o(103)

http://education.ti.com/educationportal/activityexchange/BrowseBySubject.do?cid=US



http://books.google.com/

http://cnx.org/content/m12373/latest/



http://www.analyzemath.com/Trigonometry.html

http://www.analyzemath.com/trigonometry/properties.html

Feedback from the Practice Presentation Checklist can help teams improve their final product. After final projects are presented, students will complete the Student Reflection Report, Team Final Evaluation, and Project Debrief.

Project Evaluation: Feedback from the Practice Presentation Checklist can help teams improve their final product.After final projects are presented, students will complete the Student Reflection Report, Team Final Evaluation, and Project Debrief.

Key Words: contextual situationsfunction transformationsinverse functions, key featuresmath and musicmodeling with trigonometric functionssound wavestrig functionstrig graphs


Trigonometric Graphing Storyboard

Week 1

Form groups

Team building activities ==>

Launch the project

Goals ==>KWL

Team roles

Team contract

Week 2

Spaghetti activity and/orSAS Curriculum Pathways Investigation: Why are Sine and Cosine ==>Called Circular Functions

Internet investigation of the amplitude of the sine and cosine functions.

==>Distribute Music Knowledge Rating Scale

Internet investigation of the period of the sine and cosine functions.

Week 3

Internet investigation of phase shift of the sine and cosine functions. ==>

Internet investigation of the graphs of the tangent, cotangent, secant, and cosecant trigonometric functions. ==>

Families of Graphs Investigation

Progress check with each team

Week 4

CBR Investigation

==>Test: Online Mini Quiz

Complete CBR Investigation

==>Choose the musical instrument for the group project.

Use a microphone and a computer interface to analyze sound.

Revisit KWL and revise

Week 5

“Seeing Music” Illuminations Activity

==>Work on the Music Knowledge Rating Scale

Continue research to develop musical instruments.

==>Work on music related activities: “Music in the Air”

Continue research on music vocabulary and connections to mathematics.

Begin to build musical instruments.

Week 6

Prepare presentation of the projectIntroduce inverse functions: ==>Tutorial at themathpage.com andSAS Web Inquiry 114

Peer review of projects

Begin making final ==> presentations

Peer evaluation

Project reflection


What do we know? What do we need to know? What should wedo to learn more?

KWL


Team Group Roles

Members of the group will assume the following roles. The responsibilities of each role include, but are not limited to the following:

Team leader: The team leader keeps all members of the group on task and keeps a task management chart. They make sure that each member participates fully and shows respect for one another.

Recorder: The recorder maintains the group work folder, writes out solutions to problems, and facilitates the preparation of materials for presentations.

Reporter: The reporter reports progress to the group, class, and instructor. They facilitate any oral presentations required for the project.

Process director: The process director maintains the ground rules, monitors time, cleans up materials, and makes sure each group member is mastering concepts.

Floater (in groups of five): The floater assists the leader or other group members as needed. They will substitute for any absent member and assume their duties.

Participant: All members of the group are expected to participate fully. As a participant, they will take part in all activities of the group and keep a journal.

Team Expectations

Each member of the group is expected to pull their weight as part of the group. To prevent any member of the group from receiving a lower grade as a result of group learning, you will compose a group contract that every member will sign. Use the Internet to research contracts that could help you with some ideas. Be sure to include behaviors you expect from each individual as well as the group as a whole. Each member must sign the contract and designate which of the above roles they will be assuming.


Collaboration Checklist

Not at all 1

Sometimes 2

Often3

Displays a positive attitude

Participates in discussion

Stays on task/uses time wisely

Organizes results/completes tasks

Engages in cooperative behavior

Comments _____________________________________________________________

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________


Families of Graphs Investigation

1. Graph the function y = sin x. Explain why it is a function.

2. Graph each of the following groups of functions and describe how the change alters the graph of the parent function y = sin x.

A. y = 2sin x Describe y = c sin x where c > 0

y = sin xy = 3sin x

B. y = -sin x Describe y = c sin x where c < 0y = -2sin x

y = - sin x

C. y = sin 2x Describe y = sin cx y = sin 3x

y = sin x

D. y = sin x + 2 Describe y = sin x + cy = sin x + 3

y = sin x -

E. y = sin(x – 2) Describe y = sin(x + c)y = sin(x + 3)y = sin(x - )

Note: Graph from –6.28 to 6.28


CBR Investigation

1. Use the CBR (motion detector) to generate a sine wave on the calculator.2. After getting an acceptable curve:

Find the average amplitude Find the average period Find the vertical translation and/or phase shift Find the equation that models your data

Link the calculator to the computer and get the graph (on the clipboard) of:1) data graph2) both graphs together

Paste each graph into a word document

Use the equation editor to type your equation. List the period, amplitude, vertical shift, and phase shift. Write several sentences describing what you did to get your graph to be sinusoidal. Put everyone’s name on the paper and save it in your group folder.


The Music Project

You are a mathematician with a strong appreciation for the beauty of mathematics. You have found that you cannot share that appreciation with anyone other than another mathematician. Because you are so anxious to share your feelings about the beauty and wonder of mathematics, you are looking for a scheme to represent it in a musical way. Music seems to be a medium that most people can enjoy and understand at some level. You believe that if a person understands the music it will help them understand the mathematics. You and a team of mathematicians have decided to coauthor a book to showcase this relationship. In order to promote the book, you will build a homemade musical instrument and tune the instrument using trigonometric graphs. You will create a presentation to persuade publishing companies to publish your book. The presentation will include excerpts from your book relating the instrument you build to its mathematical connections.


Mathematical Reasoning

and Problem Solving Graphs Modeling

Mathematical Concepts

Technology Neatness and Organization

20% 20% 20% 20% 10% 10%

4

Our musical instrument contains a minimum of 5 notes that can be used to play a tune accurately.

Our presentation includes accurate trigonometric graphs that represent the actual sound of each note our instrument plays.

Our presentation includes accurate equations that model the graphs of each note our instrument plays.

Our presentation includes a detailed explanation, using correct mathematical terminology, of the relationship between each graph and its corresponding note.

Our final product shows evidence that advanced features of multiple technology tools and electronic resources were used.

Our work is presented in a neat, clear, organized fashion that is easy to understand.

3

Our musical instrument contains less than 5 notes but they are all tuned accurately.

Our presentation includes accurate trigonometric graphs that represent the actual sound of 3 or 4 notes our instrument plays.

Our presentation includes somewhat accurate equations that model the graphs of each note our instrument plays.

Our presentation shows substantial understanding of the relationship between the graph and the musical note.

Our final product shows effective use of several technology tools and electronic resources.

Our work is presented in a neat and organized fashion that is usually easy to understand.

2

Our musical instrument contains a minimum of 5 notes but they are not tuned accurately.

Our presentation includes partially accurate trigonometric graphs that represent the actual sound of some of the notes our instrument plays.

Our presentation includes somewhat accurate equations that model the graphs of 3 or 4 notes our instrument plays.

Our presentation shows some understanding of the relationship between the graph and the musical note.

Our final product shows some evidence of effective use of technology tools and electronic resources.

Our work is presented in an organized fashion but may be hard to understand at times.

1

Our musical instrument contains less than 5 notes and they are not tuned accurately.

Our presentation includes inaccurate graphs or few graphs for the notes our instrument plays.

The graphs in our presentation are inaccurate or incomplete.

Our presentation shows very limited understanding of the underlying concepts needed to find the note from the graph.

Our product shows little evidence of effective use of technology tools and electronic resources.

Our work appears sloppy and unorganized. It is hard to know what information goes together.

The Music Project Rubric


Music Knowledge Rating ScaleAs you learn the definition write the definition under “What It Means.”

WordKnow It

WellHave Seen or Heard It

Have No

ClueWhat It Means

amplitude

consonance

crest

decibel

dynamics

frequency

harmonics

harmony vs dissonance

hertz

music

octave

period


periodic motion

pitch

simple harmonic motion

sound wave

trough

wave length


Individual Task Checklist

o Team summary of individual styles, strengths, and weaknesses

o SAS Web Lesson 520 or Spaghetti Graph

o Online exercises from intmath.com (#1-4)

o Families of Graphs Investigation

o Online Mini Quiz

o Illuminations “Seeing Music” Activity Sheet

o Music Knowledge Rating Scale

o Inverse tutorial located at themathpage.com

o Respond sheet from SAS Web Inquiry 114

o Peer evaluation

o Student reflection report

o Project Debrief

o Other artifacts

Group Task Checklist

o Team contract

o KWL

o CBR Investigation

o Team notes

o Peer review confirmation (who did what)

o Final Music Product

o Group Presentation of Music Project


Practice Presentation Checklist

Compelling Evidence

Little Evidence No Evidence

Spelling and grammar in product(s)

Use of technology

Process clearly explained

Shares data gathered

Includes well designed graphs

Supports graphs with equations

Comments _____________________________________________________________________________

_________________________________________________________________________

_____________________________________________________________________________


Student Reflection

Not at all Sometimes OftenI listened to the ideas of others

I offered suggestions

I worked on the project at home

I stayed on task

I met deadlines

I encouraged and complimented others

I did my best work

I enjoyed the project

I cooperated with my group

Some ways we worked well were

_____________________________________________________________________________

_________________________________________________________________________

We could have worked better by

_____________________________________________________________________________

_________________________________________________________________________

I am proud of this project because

_____________________________________________________________________________

_________________________________________________________________________

This project could have been better if I had

_____________________________________________________________________________

_____________________________________________________________________________


Team Final EvaluationThe Music Project

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

How well do you think you met the requirements of the project?

Component

Level

CommentsYour

Estimate ActualCombined research with mathematical reasoning to create a musical instrument that accurately plays at least 5 notes.

20

Presented the project usingboth equations and graphs.

20

Analyzed the graphs to create notes that play a tune.

20

Explained, with correct mathematical terminology, the process used to determine each note.

20

Demonstrated skill in the use of multiple technology tools and resources.

10

Created a neat, clear, organized presentation.

10

Total 100


Rate yourself and your colleagues using the following levels: A: Accomplished (unusually good) C: Competent (consistent) E: Emerging (inconsistent, but evident) N: Novice (not evident)

How well did you work with your team?

Component

Level

CommentsYour

Estimate ActualWork distribution and task completion 10

Participation in the problem-solving process and discussion

20

Cooperative behavior 20

Total 50

WORK DISTRIBUTION GRAPH: As you think about the project, make a circle graph that shows the percentage you think each of your team members contributed.


As you reflect on this project, rate each person in your team?

Team LeaderPerson responsible:

Component

Level

CommentsYour

Estimate ActualKeeps all members of the group on task

10

Makes sure that each member participates fully

10

Makes sure that each member shows respect for one another

10

Participates fully 10

Takes part in all activities of the group 10

Keeps a journal and a task management chart

10

Pulls their weight as part of the group 10

Meets the requirements included in the group contract

30

Total 100


RecorderPerson responsible:

Component

Level

CommentsYour

Estimate ActualMaintains the group work folder 10

Writes out solutions to problems 10

Facilitates the preparation of materials for presentations

10




10



30

Total 100


ReporterPerson responsible:

Component

Level

CommentsYour

Estimate ActualReports progress to the group 10

Reports progress to the class and/or instructor

10

Facilitates any oral presentations required for the project

10




10



30

Total 100


Process directorPerson responsible:

Component

Level

CommentsYour

Estimate ActualMaintains the ground rules and monitors time

10

Cleans up materials 10

Makes sure each group member is mastering concepts

10




10



30

Total 100


FloaterPerson responsible:

Component

Level

CommentsYour

Estimate ActualAssists the leader or other group members as needed

20

Substitutes for any absent member and assumes their duties

10




10



30

Total 100


Project Debrief: The Function of Trigonometric Functions

Name _____________________________________

Reflection is an important part of any project. Please answer the following questions in a thoughtful manner. Be specific with your comments.

What are some things you learned during the project?

Was there a part of the project you liked or did not like? Explain.

What could be added or dropped to make the project better?

Was enough time allocated for each task in the project? Give details.

Are there any assignments you still don’t understand?

Other comments?


Documents

Collaboration Checklist - wvde.us · Web viewAssign groups by mixing up the styles as much as possible. ... Sound and Waves: ... cleans up materials, and makes sure each group member