MakeYourVoteCount.doc

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Mathematics Senior Level Capstone Course Unit Overview

Title of Unit: Make Your Vote Count Unit Designers:

Kristin Vaughn, Page County Lisa Rosazza, Page County Tiffany Comer, Page County Pam Walker, Page County Laura Hansen, Culpeper County Editor: Diane Leighty, UVA-SCPS Office of Mathematics Outreach

Context: Our current electoral system awards all electoral votes to the plurality winner of that state. Students will investigate different methods of awarding electoral votes and test their new method on past elections. Students will recommend an alternative way to award electoral votes for selecting presidents. If students believe the current method of selecting the president is satisfactory then they must defend the current method and show how an alternative method would not be better. Number of Class

Hours: 15 Hours

Unit

Design: Problem Based Unit Other Subject Areas/

Disciplines Addressed:

Government, political science, history, government, economics, discrete mathematics

Driving Question: How should the United States Constitution award electoral votes in presidential elections? Mathematics Content

Addressed:

The following mathematics may arise based on students’ solution path: Fractions, ratio and proportion, percent, descriptive statistics, scatter-plots and correlations,

MPE Addressed:

Problem Solving Decision Making

Assumption of Prior

Knowledge: Fractions, percent, ratio and proportion; collecting; displaying, and analyzing data; graphing; standard deviation; normal curve; measures of central tendency;

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College and Career Readiness/21st Century Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A):

BIE Page 35-37

Collaboration E, A Research E, A

Communication (Oral and/or Written) E, A Technology E

Critical Thinking/Decision Making E Other: (Describe)

Major Products

and/or Performances: Group: Students will choose a method of awarding electoral votes, test it on past elections, and present their findings to a mock Senate.

Presentation Audience:

x Class

School Individual: Each person will use the Mathematicians

Journal to reflect at the end of each day.

Expert: Community

x Other: Mathematicians Journal

Launch: Event or experience used to engage the students interest and inquiry:

This 2-minute video of a news cast describes one proposed change to the electoral system. It also informs students on the nation’s voting process and why a change is desired.

http://www.ksl.com/?nid=960&sid=18116942

Evaluation: Formative Assessments

(During the Unit)

Interview Practice Presentations x

Mathematicians Journal x Notes x

Preliminary

Plans/Outlines/Prototypes

x Checklists

Rough Drafts x Concept maps

Field Tests Other:

Summative Assessment (End of Project)

Written Products, with a rubric x Peer Evaluation, with a rubric

x

Oral Presentation with a rubric x Self Evaluation, with a rubric

x

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Other Product(s) or

Performance(s), with a rubric x Other:

Resources Needed: On-site people, facilities:

The government teacher may be called upon for assistance or advice or to help present the problem to the class.

Equipment/Technology: Computers, graphing calculators, internet Materials:

Community Resources: Invite a local Senator to the class to share about the electoral system.

Reflection Methods: Individual, Group,

and/or Whole Class Mathematicians JournalWhole Class Discussions x Small/Focus GroupsFishbowl Discussions x

Survey Other:

Material Adapted From: Ideas and resources for this project were adapted from:

CoMap Math Modeling Forum site: http://www.mathmodels.org/problems/probview.php?probnum=20061

NCTM Illuminations; Getting Into the Electoral College http://illuminations.nctm.org/LessonDetail.aspx?id=U189

Alyson Pilawski, Purdue University WebQuest for algebra students http://questgarden.com/73/58/1/081118131802/process.htm

Template adapted from Buck Institute for Education: Project Based Learning for the 21st_Century

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U n i t M a p

P a g e 1

TITLE: Making Your Vote Count Time Frame: 1 day = 45 minutes Total: 4 wks

M O N D A Y T U E S D A Y W E D N E S D A Y T H U R S D A Y F R I D A Y

P R O J E C T W E E K O N E Engage Students:

Show Electoral College Video and lead class discussion on how the current presidential election works

- http://www.commoncraft.com/video/ electing-us-president

- http://www.schooltube.com/video/ ee1f3005a68bfe608934/Electoral-College

Explore and Brainstorm:

Introduce the problem and brainstorm as a class: - What do we know?

- What do we need to know?

- What are some first steps to get started? - What resources are available to get you

started? - What is fair?

-Math Journal to process information from the video and from interviewing 3 voting adults.

Explain:

Go over expectations for the groups and review the rubrics and handouts.

Make clear what final products and presentations are expected.

Students work with their group to begin planing. Math Journal: What do you know about the electoral system and what do you need to know in order to change it and make it better?

P R O J E C T W E E K T W O

Elaborate:

Work in groups and do research to understand and address the problem.

Each group meets with teacher and discusses two possible changes they may propose to the mock Senate.

While one group meets with the teacher, the other groups continue their research.

Groups must decide on 1 proposed change to the electoral college system and proceed to develop the mathematical model to test change with data from past elections.

Test proposed change on at least 3 past elections and keep detailed notes and records of election results.

U N I T C A L E N D A R page 2

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TITLE: Making Your Vote Count Time Frame: 1 day = 45 minutes Total: 4 wks

M O N D A Y T U E S D A Y W E D N E S D A Y T H U R S D A Y F R I D A Y

P R O J E C T W E E K T H R E E (Continued) Test proposed

change on several past elections and keep detailed records of election results.

Each group meets with teacher and brings rough draft of proposed change and supporting mathematical models.

Groups continue working on the mathematical models to support accepting or revising proposed change to the electoral college system.

Groups work on finalizing written paper, pictorial representations, and on writing, organizing and practicing oral presentation.

P R O J E C T W E E K F O U R Practice presentations with teacher.

Continue refining the group’s final written proposal with supporting documentation and oral presentation.

Groups turn in written proposal to mock senate and do their oral presentations.

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Virginia’s Senior Level Capstone Course Instructional Plan

Unit Title: Making Your Vote Count

Driving Question: How should the United States Constitution award electoral votes in presidential elections?

Problem: The constitution and its amendments have provided a subjective method for awarding electoral votes to states. Our current electoral system awards all state electoral votes to the plurality winner of that state no matter how close the state’s popular vote. Is this a fair method? Does your vote count? Is there a better method of determining who wins the election?

ENGAGE Introduce the problem

Number of hours _1.5__

The teacher will invite a local senator or government teacher to share how the electoral college system works. Or

The teacher will show a video explaining how the electoral system currently works. Several videos that explain the process are in the bulleted list below.

- http://www.commoncraft.com/video/electing-us-president

This video gives a School House rock version of the Electoral College. It is upbeat, catchy and may get your students interested in the project.

- http://www.schooltube.com/video/

ee1f3005a68bfe608934/Electoral-College This video describes one proposed change to the electoral system. It also informs students on the nation’s voting process and why a change is desired.

Teacher Notes:

Teachers can review one possible solution to the problem of awarding electoral votes to different states at

http://www.ksl.com/?nid=960&sid=18116942

Teachers can review information about the Electoral College at http://www.archives.gov/federal-register/electoral-college/faq. html#number. Teachers may then want to recommend this to students.

Students identify 3 voting adults to interview. They explain briefly to the adults how our presidents are selected. Then they should ask if they believe the method is fair and if not how they would like to see our present presidential election process changed. They then respond to the journal prompt.

Teacher note: The journal prompt is intended to get the

Mathematician Journal

Prompts

Students write about what they learned from the interviews and from the class discussion.

UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science

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students to begin thinking about other ways the election results could be determined.

EXPLORE Whole Class

Number of hours__1_

A whole class brainstorming session about the current

Electoral College model for elections and how a person’s vote counts. To prepare students to work in small groups teacher poses questions and records information generated by the students.

 What do we know about the current Electoral College process?

 What is fair?

 What else do we need to know?

 What are some first steps to get started?

 What resources are available to get you started?

Notes for teacher: Pose probing questions that will bring out the following.

1. Our presidential selection process may not select the president that the majority of the people want.

2. We know that if a candidate wins a state he/she receives all of the electoral votes.

3. We know that electoral votes were instituted during a time when the public was not well informed about the candidate. 4. As students consider fairness do they bring out fairness to an individual, to the population of a state, or other factors to consider.

5. Some ways that the selection process for president could be changed and how.

6. Teachers may want to provide the link to CNN One Page Student News: Electoral College to students

http://www.cnn.com/2008/LIVING/studentnews/07/22/one.sheet.ele ctoral.college/index.html

The journal prompts are to help students reflect on what they have heard or read and begin to identify what they see as a question to guide their research and their proposal.

Internet resources if students need additional help:  A Congressional Research Report: Presidential

Elections in the United States: A Primer

http://www.senate.gov/reference/resources/pdf/RL3052 7.pdf

 One page quick read on how the president is elected: http://www.enchantedlearning.com/vote/presidential_el ections.shtml

 Electoral College online calculator:

Prompts Based on what you currently know what do you see as the strengths and weaknesses of our current electoral system?

What additional information do you need to know in order to identify changes to improve the system?

At this point and what changes do you think would strengthen the system and make it fairer?

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http://www.archives.gov/federal-register/electoral-college/calculator.html

 Interactive map of U.S. shows results of past presidential elections http://www.270towin.com/  Electing U.S. President with rollover map showing

number of Electoral votes in each state

http://fog.ccsf.edu/~lfried/stories/election.html  Frequently asked questions about Electoral College

http://www.archives.gov/federal-register/electoral-college/faq.html

EXPLAIN Expectations for students work and working together

Number of Hours__1_

Provide students with HO# 1a and 1b, Make Your Vote Count. Review the situation and the expectations for the group’s work.

Inform students they need to consider the following:  What questions does the issue raise?

1. Is our current process fair? Why or why not? 2. Is there a better way to choose a president? 3. What other ways have people suggested or

used in the past?

4. Is it possible to devise a process that is always fair?

5. How would different processes affect past election outcomes?

6. What mathematical models can be used to describe the processes and what mathematics can be used to compare different processes? 7. Groups may develop other questions.

Teacher will review the rubrics and expectations with the students so that students know what is expected of them and areaware of deadlines.

Rubrics for grading are provided including: HO#2 Peer/Self-Evaluation form HO#3 Written Presentation Rubric

HO#4 Oral Presentation Rubric for TEACHER HO#5 Oral Presentation Rubric for AUDIENCE MEMBERS

What will students turn in along the way? (Formative Evaluations)

1. Action plan with the question they are using to guide their research and proposal. Identify what needs to be done, how will the work be shared, who will be responsible for various parts, what deadlines have been established along the way to

Prompts

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make sure the work is com be done and by whom

2. Preliminary notes and rough draft of proposal and practice oral presentation at scheduled meetings with the teacher.

3. Math journal each day at the end of class to reflect on what the group is thinking about, how you are thinking about the issue, questions that you are still thinking about, what other

information is needed to continue working on the proposal.

What is graded? (Summative Evaluation)

 Peer/Self Evaluation about how the group and individuals carried out their responsibilities. (HO #2)

 Written proposal with supporting documentation. (HO # 3 Rubric)

 Oral Presentation that is 10-15 minutes (HO #4 and HO #5 Rubric)

ELABORATE Students working in groups

Number of Hours___9__

Students work in groups using research to develop a written proposal with supporting documentation to address the issue and to develop an oral presentation to present their proposal.

 The group will develop an action plan and keep this in the group folder to monitor their own progress and to use in meetings with the teacher.

 Each individual will complete an entry in the Math Journal each day

 The group will meet three times with the teacher:

o 1st_{Meeting: Bring the groups action plan and} notes to the meeting. Be ready to discuss 2 possible alternatives the group has explored.

o 2nd_{Meeting: Bring a rough draft of proposed} change you group has identified and supporting mathematical models.

o 3rd Meeting: Final written proposal with

supporting documentation and be prepared do trial run of the oral presentation

Prompts

Each person will select from the general prompts to reflect on the day’s work and to record their thinking:

What became clearer for you today? What questions do you still have? What other

information do you think you need to find?

EVALUATE Groups submit all products and make oral

Groups present their proposal to an audience.

 Students complete peer and self-evaluations.

HO #2 Peer/Self-Evaluation form: Make Your Vote Count

Prompts Select another UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science

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presentations

Number of Hours_ 2

 Provide students with rubrics for any written work, presentation, product produced by the group. Rubric for Written Work: HO #3 Make Your Vote Count Written Presentation Rubric Audience

 Provide audience with observation criteria/rubrics Rubric for Audience Members watching oral presentation: HO #5 Make Your Vote Count Oral Presentation Rubric Audience

Rubric for Teacher watching oral presentation: HO # 4 Make Your Vote Count Oral Presentation Rubric Teacher

group’s

presentation and compare their proposal with your group’s proposal. Discuss the merits of each proposal.

Discuss why you think your proposal is better.

Map the Unit Make Your Vote Count

Task: The constitution and its amendments have provided a subjective method for awarding electoral votes to states. Our current electoral system awards all state electoral votes to the plurality winner of that state no matter how close the state’s popular vote UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science

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Working with your group you will use different methods of mathematical processes to investigate the current mathematical model for awarding the state electoral votes. Then your group will create a mathematical model for at least one alternative method that is better than the current electoral system. Carefully describe your model and test its

application with the data from the 1992 election provided with this handout and two other elections. Finally, justify why the new model is better than the current model or why the current model is better.

KNOWLEDGE AND SKILLS NEEDED

(The solution path groups take will determine the mathematics needed to develop their models. The list below is an indication of what may emerge)

Assumed already learned

Students will self-assess

Will be learned during the unit

1.

Ratio and proportions, proportional reasoning

x

2.

Decision making

x x

3. Measures of central tendency, scatter plots and correlations,

x

4. Tables, charts, graphs x

5. Excel spread sheets and word processing

x

6. Fractions, decimals, percents x What project tools will student’s use?

 Know/need to know lists  Daily goal sheet

X Mathematician’s Journals X Briefs/Memos

X Task lists/Action Plan  Planning Calendar

□ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________

HO #1a

Make Your Vote Count!

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The Problem:

The constitution and it’s amendments have provided a subjective method for awarding electoral votes to states. Our current electoral system awards all state electoral votes to the plurality winner of that state no matter how close the state’s popular vote. Is this a fair method? Does your vote count? Is there a better method of determining who wins the election?

Working with your group you will use different methods of mathematical processes to investigate the current mathematical model for awarding the state electoral votes. Then your group will create a mathematical model for at least one alternative method that is better than the current electoral system. Carefully describe your model and test the model with the data from the 1992 election provided with this handout and two other elections. Finally, justify why the new model is better than the current model or why the current model is better.

You will have three weeks to work with your group to develop your proposal with supporting evidence and to present your findings.

Expectations:

 Your group needs to develop a question to guide your research and your proposal. Once your group has determined what needs to be done develop an action plan with goals and tasks for how to work on the problem and how to develop the final products. Develop a table to show this plan which will include what needs to be done, who is the responsible person/persons, and the due dates.

 The group will meet three times with the teacher:

o 1st_{Meeting: Bring the groups action plan and notes to the meeting. Be ready to discuss 2} possible alternatives the group has explored.

o 2nd_{Meeting: Bring a rough draft of proposed change you group has identified and} supporting mathematical models.

o 3rd_{Meeting: Final written proposal with supporting documentation and be prepared to} trial run of the oral presentation.

 Evaluation

o Peer/Self Evaluation about how the group and individuals carried out their responsibilities. (HO #2)

o Written proposal with supporting documentation. (HO # 3 Rubric)

o Oral Presentation that is 10 – 15 minutes (HO #4 and HO #5 Rubric)

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HO #1b

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HO # 2 Make Your Vote Count: Peer/Self-Evaluation

The following is a list of statements to be answered about yourself and each of your group members. Think carefully about assigning rating values for each of the statements.

1- Strongly Agree 2- Agree 3- Neutral 4- Disagree 5- Strongly Disagree

Self: Teammate: Teammate: Teammate:

Was dependable in attending class

Willing to accept assigned tasks

Contributed positively to group discussion

Completed work on time or made alternative arrangements

Helped others with their work when needed

Did work accurately and completely

Worked well with other group members

Overall was a valuable member of the team

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HO #3

Make Your Vote Count: Written Proposal

and Supporting Documentation Rubric

CATEGORY 4 3 2 1

Mathematical Concepts

Uses appropriate mathematics to support the proposal and demonstrates thorough understanding of the underlying

mathematical concepts

Uses appropriate

mathematics to support the proposal and shows some understanding of the underlying mathematical concepts.

Uses some appropriate mathematics to support the proposal and shows weak understanding of the underlying mathematical concepts.

Uses insufficient or inappropriate

mathematics to support the proposal or shows limited to no

understanding of the underlying concepts.

Mathematical Reasoning

Uses rigorous and refined mathematical reasoning.

Uses effective

mathematical reasoning

Uses weak mathematical reasoning.

Uses little or inappropriate mathematical reasoning.

Written Explanation

Explanation of what was done, how the decision was made is detailed and clear. Provides supporting mathematical models with explanations of how they support the proposal.

Explanation of what was done, how the decision was made is clear but may lack sufficient details. Provides supporting mathematical models to support the decision but may lack sufficient explanation of how they support the proposal.

Explanation of what was done but it is difficult to understand. Provides some supporting mathematical models but there is no explanation or vague explanation of how they support the proposal.

Explanation is missing several components and difficult to understand. Weak or no mathematical models are presented to support the proposal.

Diagrams and Sketches

Graphs, tables, diagrams and/or sketches are clear and greatly add to the reader’s understanding of the procedure(s).

Graphs, tables, diagrams and/or sketches are clear and easy to understand.

Graphs, tables, diagrams and/or sketches are somewhat difficult to understand.

Graphs, tables, diagrams and/or sketches are difficult to understand or are not used.

Mathematical Terminology and Notation

Correct terminology and notation are always used, making it easy to understand what was done.

Correct terminology and notation are usually used, making it fairly easy to understand what was done.

Correct terminology and notation are used, but it is sometimes not easy to understand what was done.

There is little use, or a lot of inappropriate use, of terminology and notation.

Grammar, Punctuation, and writing structure

The paper consistently uses correct grammar, punctuation, spelling and writing structure. Well organized and subheadings are used to improve the readability.

The paper has 2 –3 errors in grammar, punctuation, spelling and writing structure. Organized and some subheadings are used to improve the readability.

The paper has 4 – 5 errors in grammar, punctuation, spelling and writing structure. Somewhat organized and few subheadings are used to improve the readability.

The paper has more than 5 errors in grammar, punctuation, spelling and writing structure. Not well organized and if subheadings are used may not improve the readability.

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HO #4 Make Your Vote Count - Oral Presentation Rubric for TEACHER

Group

Collaboration

Each group member has an active part in the oral presentation, in the answering of questions asked by audience members, and/or in group collaboration.

Lacks participation by each group member in one of the following areas: the oral

presentation, in the answering of questions asked by audience members, and/or in group collaboration

Lacks participation by each group member in two of the following areas: the oral

presentation, in the answering of questions asked by audience members, and/or in group collaboration

Lacks participation by each group member in

participation in the following areas: the oral presentation, in the answering of questions asked by audience members, and in group collaboration

Speaks Clearly Speaks clearly and distinctly all (100-95%) the time, and mispronounces no words.

Speaks clearly and distinctly all (100-95%) the time, but mispronounces one word.

Speaks clearly and distinctly most ( 94-85%) of the time.

Mispronounces no more than two words.

Speech is not clear or distinct due to mumbles or cannot be understood OR mispronounces more than two words.

Content Shows a full

understanding of the proposal and the supporting mathematics model.

Shows a good understanding of the proposal and the supporting mathematics model...

Shows a good understanding of parts the proposal and the some supporting mathematics model.

Shows little understanding of the proposal and/or the supporting mathematics model.

Vocabulary Uses vocabulary appropriate for the audience. Extends audience

vocabulary by defining words that might be new to most of the audience.

Uses vocabulary appropriate for the audience. Includes 1-2 words that might be new to most of the

audience, but does not define them.

Uses vocabulary appropriate for the audience. Does not include any

vocabulary that might be new to the audience.

Uses several (5 or more) words or phrases that are not understood by the audience.

Preparedness Group is Group seems pretty Group is somewhat Group is UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science

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completely prepared and has obviously

rehearsed.

well prepared but might have needed a more rehearsals.

prepared, but it is clear there was little or insufficient rehearsal

unprepared.

Stays on Topic Stays on topic all (100%) of the time.

Stays on topic most (99-90%) of the time.

Stays on topic some (89%-75%) of the time.

Topic was unclear to the listener.

Time-Limit Presentation is 10-15 minutes long.

Presentation is 8-10 minutes long.

Presentation is 7-8 minutes long.

Presentation is less than 7 minutes OR more than 15 minutes.

Enthusiasm Voice, facial expressions and body language generate a strong interest throughout the presentation. Voice, facial expressions and body language sometimes generate a strong interest and enthusiasm during the presentation.

Voice, facial expressions and body language are used to try to generate

enthusiasm, but seem unnatural or forced.

Voice, facial expressions or body language where lacking and did not generate much interest in the presentation.

Mathematical Explanation

Group clearly and specifically explains mathematical approach with supporting details and accurately answers questions asked by audience.

Group gives a general explanation of mathematical approach but lacks a few details and accurately answers most questions asked by audience.

Group gives a brief and insufficient explanation of mathematical approach lacking details and answers some of the

questions asked by audience.

Group gives a limited explanation of mathematical approach lacking supporting details and answers few questions

accurately asked by audience.

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HO #5 Make Your Vote Count - Oral Presentation Rubric for AUDIENCE MEMBERS

Speaks Clearly

Speaks clearly and distinctly all (100-95%) the time, and mispronounces no words.

Speaks clearly and distinctly all (100-95%) the time, but mispronounces one word.

Speaks clearly and distinctly most ( 94-85%) of the time. Mispronounces no more than one word.

Often mumbles or can not be understood OR mispronounces more than one word.

Vocabulary Uses vocabulary appropriate for the audience. Extends audience vocabulary by defining words that might be new to most of the audience.

Uses vocabulary appropriate for the audience. Includes 1-2 words that might be new to most of the audience, but does not define them.

Uses vocabulary appropriate for the audience. Does not include any

vocabulary that might be new to the

audience.

Uses several (5 or more) words or phrases that are not understood by the audience.

Preparedness Group is completely prepared and has obviously rehearsed.

Group seems pretty well prepared but might have needed a more rehearsals.

Group is somewhat prepared, but it is clear there was little or insufficient rehearsal

Group is unprepared.

Stays on Topic

Stays on topic all (100%) of the time.

Stays on topic most (99-90%) of the time.

Stays on topic some (89%-75%) of the time.

Topic was unclear to the listener.

Enthusiasm Voice, facial

expressions and body language generate a strong interest throughout the presentation.

Voice, facial

expressions and body language sometimes generate a strong interest and

enthusiasm during the presentation.

Voice, facial

expressions and body language are used to try to generate enthusiasm, but seem unnatural or forced.

Voice, facial expressions or body language where lacking and did not generate much interest in the presentation.

Mathematical Explanation

Group clearly and specifically explains mathematical approach with supporting details and accurately answers questions asked by audience.

Group gives a general explanation of mathematical approach but lacks a few details and accurately answers most questions asked by audience.

Group gives a brief and insufficient explanation of mathematical approach lacking details and answers some of the questions asked by audience.

Group gives a limited explanation of mathematical approach lacking supporting details and answers few questions accurately asked by audience.