national debt project student handoutsschd.ws/hosted_files/2017ceaconvention/d2/national debt... ·...

National Debt ProjectStudent Handouts

pp. 1-2 Introduction

pp. 3-4 Part I: Overall Models

pp. 5-6 Part II: Democratic Models

pp. 7-8 Part III: Republican Models

pp. 9-10 Part IV: Analyzing Predictions

pp. 11-14 Part V: Democratic & Republican Analysis

pp. 15-16 Part VI: Group Presentation

pp. 17-18 Part VII: Conclusions & Reflections

pp. 19-20 Grading Rubric

pp. 21-26 Mathematical Modeling Notes

(Not included: Follow-up Article Review Assignments)

National Debt Project Name: ______________________________________

IntroductionThe following data related to the national debt of the United States comes from two reports on the government website https://www.treasurydirect.gov/govt/reports/pd/pd.htm. The 2001-2015 data came from the report Historical Debt Outstanding 2000-2015 and the 2016 data was taken from the Monthly Statement of the Public Debt for September 2016. Data on this table was rounded to the nearest million dollars.

Date Dollar Amount*09/30/2001 5,807,463,000,00009/30/2002 6,228,236,000,00009/30/2003 6,783,231,000,00009/30/2004 7,379,053,000,00009/30/2005 7,932,710,000,00009/30/2006 8,506,974,000,00009/30/2007 9,007,653,000,00009/30/2008 10,024,725,000,00009/30/2009 11,909,829,000,00009/30/2010 13,561,623,000,00009/30/2011 14,790,340,000,00009/30/2012 16,066,241,000,00009/30/2013 16,738,184,000,00009/30/2014 17,824,071,000,00009/30/2015 18,150,618,000,00009/30/2016 19,538,456,000,000

Over the next few weeks you are going to complete a guided analysis of these numbers. The project is broken into several parts – some completed as an individual and some completed in groups. You will turn in parts as you complete them to ensure that work in the initial parts is accurate before using that work in your analysis in the later parts.

A more detailed breakdown of the parts of the project is listed on the back side.

National Debt Project

Parts I - III:

You will create, graph and make predictions from linear, quadratic, and exponential models.

Part I: Overall Models based on the complete set of data (2001-2016)

Part II: “Democratic” Models based on the data from the years when President Obama was leading

the U.S. (2009-2016)

Part III: “Republican” Models based on the data from the years when President Bush was leading

the U.S. (2001-2008)

Part IV:

You will analyze the predictions from the Overall Models, Democratic Models, and Republican Models.

Part V:

You will analyze the data from both a Democratic perspective and a Republican perspective:

- find evidence to support the Democrats as the best party for controlling national debt

- find evidence to support the Republicans as the best party for controlling national debt

Part VI:

You will make a group presentation to support either the Democrats or the Republicans as the best party to

lead the United States for the purpose of controlling national debt. Groups will be assigned and half of the

class will be assigned the Democratic side and the other half of the class will be assigned the Republican side.

Part VII:

You will reflect on the following:

How do you evaluate which model is the most realistic model for predicting the national debt in the

future?

Is it sinful to make a report using numbers that you do not feel are realistic?

What does it mean to use mathematical analysis in God-honoring ways?

Part I: Overall Models Name: _______________________________

Date Dollar Amount Date Dollar Amount09/30/2001 5,807,463,000,000 09/30/2009 11,909,829,000,00009/30/2002 6,228,236,000,000 09/30/2010 13,561,623,000,00009/30/2003 6,783,231,000,000 09/30/2011 14,790,340,000,00009/30/2004 7,379,053,000,000 09/30/2012 16,066,241,000,00009/30/2005 7,932,710,000,000 09/30/2013 16,738,184,000,00009/30/2006 8,506,974,000,000 09/30/2014 17,824,071,000,00009/30/2007 9,007,653,000,000 09/30/2015 18,150,618,000,00009/30/2008 10,024,725,000,000 09/30/2016 19,538,456,000,000

1. Make a scatterplot using all the data from 2001-2016. On each axis start at 0 and count by ones – the x-axis will represent years after 2000 and the y-axis will represent the national debt in trillions of dollars.

Please round dollar amounts to three decimal places.

2. Make a linear model for this data.

a. What is the equation for the this model? ______________________________________

b. What is the value of r2 for this model? r2 = __________________

c. Accurately draw and label this model on the scatterplot.

d. Using this model make predictions for the national debt for 2020, 2025, and 2030

2020: _______________________________

2025: _______________________________

2030: _______________________________

3. Make a quadratic model for this data.

a. What is the equation for the quadratic model? ______________________________________

b. What is the value of R2 for this model? R2 = __________________



2020: _______________________________

2025: _______________________________

2030: _______________________________

4. Make an exponential model for this data.

a. What is the equation for the exponential model? ______________________________________

b. What is the value of R2 for this model? r2 = __________________



2020: _______________________________

2025: _______________________________

2030: _______________________________

Part II: Democratic Models Name: _______________________________Politically during this time, Democrat president Barak Obama led the country from the beginning of 2009 until the end of 2016. Therefore, looking at the data from a Democrat perspective can be done by looking at the “Democrat” years from 2009-2016.

Date Dollar Amount09/30/2009 11,909,829,000,00009/30/2010 13,561,623,000,00009/30/2011 14,790,340,000,00009/30/2012 16,066,241,000,00009/30/2013 16,738,184,000,00009/30/2014 17,824,071,000,00009/30/2015 18,150,618,000,00009/30/2016 19,538,456,000,000

1. Make a scatterplot using only the data from 2009-20016. On each axis start at 0 and count by ones – the x-axis will represent the years after 2000 and the y-axis will represent the national debt in trillions of dollars.







2020: _______________________________

2025: _______________________________

2030: _______________________________






2020: _______________________________

2025: _______________________________

2030: _______________________________






2020: _______________________________

2025: _______________________________

2030: _______________________________

Part III: Republican Models Name: _______________________________Politically during this time, Republican president George Bush led the country from the beginning of 2001 until the end of 2008. Therefore, looking at the data from a Republican perspective can be done by looking at the “Republican” years from 2001-2008.

Date Dollar Amount09/30/2001 5,807,463,000,00009/30/2002 6,228,236,000,00009/30/2003 6,783,231,000,00009/30/2004 7,379,053,000,00009/30/2005 7,932,710,000,00009/30/2006 8,506,974,000,00009/30/2007 9,007,653,000,00009/30/2008 10,024,725,000,000

1. Make a scatterplot using only the data from 2001-2008. On each axis start at 0 and count by ones – the x-axis will represent the years after 2000 and the y-axis will represent the national debt in trillions of dollars.







2020: _______________________________

2025: _______________________________

2030: _______________________________






2020: _______________________________

2025: _______________________________

2030: _______________________________






2020: _______________________________

2025: _______________________________

2030: _______________________________

Part IV: Analyzing Predictions Name: _______________________________

1. Complete these tables to summarize the predictions for the national debt for 2020, 2025, and 2030 for all of the models from Parts I, II, and III. Make sure to write the equation of the model below its title.

Model R2 2020 Prediction 2025 Prediction 2030 Prediction2001-2016 Linear

2001-2016 Quadratic

2001-2016 Exponential

Overall Data Models


2009-2016 Quadratic


Democratic Data Models


2001-2008 Quadratic


Republican Data Models

For questions 2 and 3 make sure to include the following details in your responses:1) Identify the model as Overall, Democratic or Republican2) Identify the model as linear, quadratic or exponential3) Include the dollar amount of the prediction (question 2) or value of R2 (question 3)

2. Based on the predictions from Parts I – III of this project:

a. Which model gives the best (lowest) prediction for the amount of the national debt in 2030?

b. Which model gives the worst (highest) prediction for the amount of national debt in 2030?

3. a. Explain what the value of R2 (or r2) indicates about a mathematical model.

b. Based on the value of R2 (or r2) which model is the most accurate? Explain why.

c. Based on the value of R2 (or r2) which model is the least accurate? Explain why.

Part V: Democratic & Republican Analysis Name: _______________________________

Democratic Analysis1. Of the three models you made in Part II, find the model that projects the least amount of national debt.

a. Equation of the model: _______________________________________________

b. Explain the meaning of the numbers used in the equation in the context of this problem.

2. For the model you selected in question #1:a. What is the value of R2? R2 = _________

b. How does the value of R2 in this model compare to the value of R2 in the other models?

3. The model you selected in question #1 was the model based on the years 2009-2016. Why would the years used matter when picking a mathematical model?

4. For the model you selected in question #1: What projections does it make for the national debt for 2020, 2025, and 2030?

2020 = _______________ 2025 = _______________ 2030 = _______________

5. Based on all the information you have gathered in questions #1 – 4 (and comparisons from Parts I – IV), what are three mathematical reasons that support that the model projecting the least amount of debt is the best model to use for making projections?

a.

b.

c.

6. Based on all the information you have gathered in questions #1 – 4 (and comparisons from Parts I – IV), what are three mathematical reasons that refute that the model projecting the least amount of debt is the best model to use for making projections?

a.

b.

c.

Republican Analysis1. Of the three models you made in Part III, find the model that projects the least amount of national debt.

a. Equation of the model: _______________________________________________

b. Explain the meaning of the numbers used in the equation in the context of this problem.

2. For the model you selected in question #1:

a. What is the value of R2? R2 = _________

b. How does the value of R2 in this model compare to the value of R2 in the other models?

3. The model you selected in question #1 was the model based on the years 2001-2008. Why would the years used matter when picking a mathematical model?

4. For the model you selected in question #1: What projections does it make for the national debt for 2020, 2025, and 2030?

2020 = _______________ 2025 = _______________ 2030 = _______________

5. Based on all the information you have gathered in questions #1 – 4 (and comparisons from Parts I – IV), what are three mathematical reasons that support that the model projecting the least amount of debt is the best model to use for making projections?

a.

b.

c.

6. Based on all the information you have gathered in questions #1 – 4 (and comparisons from Parts I – IV), what are three mathematical reasons that refute that the model projecting the least amount of debt is the best model to use for making projections?

a.

b.

c.

Part VI: Group Presentation Name: _______________________________

Directions: Part VI is making a group presentation with Google Slides to prepare for a debate regarding the national debt. Each person in your group should be in charge of one section of the project for (although you should all help each other on each part if needed).

The presentations will be given to a panel of students not in our class and/or teachers who will judge which political party provides a better argument concerning which party has been better at controlling national debt. The process for the debate will be:

1) The first party chosen presents Sections A, B and C (see below)2) The second party chosen presents Sections A, B and C (see below)3) The first party refutes the second party using Section D (see below)4) The second party refutes the first party using Section D (see below)

Your Group:

Group Members: _________________________________________

_________________________________________

_________________________________________

_________________________________________

Assigned Party: _________________________________________

Section A: Completed by: _______________________________________________

Make slides containing the following information:

1. A table of the national debt data (2001 – 2016)

2. Equations for the linear, quadratic, and exponential models including the values of R2.

3. Explanations / interpretations of the meaning of the numbers in the equations of the models.

4. A scatterplot showing the graphs of the data and each model (use Desmos.com).

5. Projections based on each model for 2020, 2025, and 2030.

Section B: Completed By: _______________________________________________

Make slides containing the following information:

1. A table of the national debt data for your party and explanation of why this is data represents your party.

2. Equations for the linear, quadratic, and exponential models including the values of R2.

3. Explanations / interpretations of the meaning of the numbers in the equations of the models.

4. A scatterplot showing the graphs of the data and each model (use Desmos.com).

5. Projections based on each model for 2020, 2025, and 2030.

Section C: Completed By: _______________________________________________

1. Provide an argument to support your party.

2. Support your case: Based on all the information you have gathered to this point, provide evidence to support the model that projects the least amount of debt for your political party is the best model. Include:

a. the equation of the model

b. the projections for 2020, 2025, and 2030

c. the three things you said supported this model from Part V of the project.

Section D: By: ____________________________________________________

1. Provide an argument to refute what is supported by the other party.

2. Refute the case: Based on all the information you have gathered to this point, provide evidence to reject the model that projects the least amount of debt for the other political party. Include:

a. the equation of the model

b. the projections for 2020, 2025, and 2030

c. the three things you said refuted this model from Part V of the project.

Part VII: Conclusions & Reflections Name: ___________________________________

Directions: This part of your project is due by the end of your exam. You should complete this before

coming to your exam.

1. The mathematical models you completed in Parts I – VI of this project provided nine very different answers for the predictions of national debt. Based on the analysis you have done in the first six parts of this project, pick the three models that you feel are the most realistic.

Equation Based on years 2020 Prediction

2025 Prediction

2030 Prediction

2. How did you evaluate which model was the most realistic model for predicting the national debt in the future?

3. Extra Credit: Complete some additional research to find additional support for which model was the most realistic model. Make sure to cite sources for any articles/data you may find while conducting your research.

4. For the model that you selected as most realistic, can you prove that it is correct? For the model that you selected as least realistic, can you prove that it is incorrect? Explain why or why not.

5. If you made an official report on projections for the National Debt supporting a mathematical model that you felt was unrealistic, would that be considered sinful? Explain why or why not.

6. If you were in charge of creating a report for making projections about the National Debt, what are three things that you could do to make sure you made the report in a God-honoring way?

National Debt Project Name: _____________________________________________

Grading Rubric

1. Part I - turn in worksheet: Overall Graphs & Modelsa. Graphs for 2001-2016 _______ out of 5 points

b. Equations / R2 / Predictions for 2001-2016 _______ out of 5 points

2. Part II - turn in worksheet: Democratic Graphs & Modelsa. Graphs for 2009-2016 _______ out of 5 points


3. Part III - turn in worksheet: Republican Graphs & Modelsa. Graphs for 2001-2008 _______ out of 5 points


4. Part IV - turn in worksheet: Analyzing Predictions

a. Summary Table of Predictions _______ out of 3 points

d. Models with least/greatest amount of national debt _______ out of 3 points

e. Explanation of R2 _______ out of 4 points

5. Part V- turn in worksheet: Democratic & Republican Analysis

a. Democratic Analysis (questions #1-4) _______ out of 4 points

b. Three reasons to support the Democratic model with least debt _______ out of 3 points

c. Three reasons to refute the Democratic model with least debt _______ out of 3 points

d. Republican Analysis (questions #1-4) _______ out of 4 points

e. Three reasons to support the Republican model with least debt _______ out of 3 points

f. Three reasons to refute the Republican model with least debt _______ out of 3 points

6. Part VI – Group Presentation

a. Section A Slides (2001-2016)

1. Graphs / tables _______ out of 4 points

2. Equations and explanations _______ out of 4 points

3. Projections _______ out of 2 points

a. Section B Slides (2001-2008 or 2009-2016):

1. Graphs / tables _______ out of 4 points

2. Equations and explanations _______ out of 4 points

3. Projections _______ out of 2 points

c. Section C & D Slides

1. Model and projections for the model that is supported _______ out of 2 points

2. Reasons for supporting the given model _______ out of 3 points

d. Section D Slides

1. Model and projections for the model that is refuted _______ out of 2 points

2. Reasons for refuting the given model _______ out of 3 points

e. Oral Presentation

1. Section A (2001-2016):

Graphs / tables _______ out of 2 points

Equations and explanations _______ out of 2 points

Projections _______ out of 1 points

2. Section B (2001-2008 or 2009-2016):

Graphs / tables _______ out of 2 points

Equations and explanations _______ out of 2 points

Projections _______ out of 1 points

3. Section C

Model and projections for the model that is supported _______ out of 2 points

Reasons for supporting the given model _______ out of 3 points

4. Section D

Model and projections for the model that is refuted _______ out of 2 points

Reasons for refuting the given model _______ out of 3 points

7. Part VII – Conclusions & Reflections

a. Selecting the most realistic model _______ out of 2 points

b. Extra Credit research _______ out of 2 points

` c. Response to proving models correct or incorrect _______ out of 2 points

d. Response to supporting unrealistic models _______ out of 2 points

e. Response to creating God-honoring mathematics _______ out of 2 points

8. Final Grade

a. Total Score: ________ out of 120 points

b. Comments

Mathematical Modeling NotesPreparation & Clarification for National Debt Project

I. What is mathematical modeling?

A. Definition

1. Mathematical Model: Method of simulating real-life situations with mathematical equations to forecast their future behavior.

2. Parts of mathematical modeling:

a. Real-life situations

b. Mathematical equations

c. Forecast future behavior

B. What types of mathematical equations?

1. Linear

2. Quadratic

3. Exponential

C. ExampleHolly has recently joined her school’s bowling team. At the end of each week of the season her coach calculates the average score for each of the players. For the first five weeks of the season Holly has the following averages:

Week 1 2 3 4 5

Average 109 115 119 135 147

If Holly’s bowling season is 12 weeks long, what is a good prediction for her average score for the 12th week?

Start by making a scatterplot of the data and then include the graphs of the models as well

*** On the y-axis begin with y = 0 and count by 20 ***

Find the linear, quadratic, and exponential equations that best model this data and use them to make a prediction for Holly’s score in the 12th week of the season.

Linear:

Quadratic:

Exponential:

II. Evaluating Mathematical Models

A. Interpretation of the Equations

1. Linear Equations

2. Quadratic Equations

3. Exponential Equations

4. From our example in Part I

a. Linear

b. Quadratic

c. Exponential

B. Using R2

1. R2 is a statistical measure of how close the data are to the fitted regression model. It is also known as the coefficient of determination.

2. Definition: R2 is the percentage of the response variable variation that is explained by a regression model. So . . . R2 = Explained variation / Total variation

3. R2 gives a percentage of variation explained by the given model.a. That means R2 is always between 0 and 100% (or between 0 and 1)b. 0% or 0 indicates that the model explains none of the variability of the response data around its mean.c. 100% or 1 indicates that the model explains all the variability of the response data around its mean.

4. Diagram and comments to illustrate the main idea:

5. In general, the higher the R2, the better the model fits your data.

6. However . . .a. It is solely a . . .

b. It does not . . .

7. How do you find R2? We will always depend on our graphing calculator (must have Diagnostic turned on when using regression models).

8. From our example in I Part C . . .

Linear:

Quadratic:

Exponential:

C. Practical Domain and Range

1. Practical Domain –

2. Practical Range –

3. Both of these

a. Can be . . .

b. Should be . . .

c. But are also . . .


D. Consideration of Other Factors

1. Objective Factors

a. Multiple Variables

b. Additional Research

2. Subjective Factors

a. Supporting a certain point of view (bias)

b. Determining which factors to include and exclude


E. Reflection

1. A lot of subjective decisions are part of mathematical modeling.

2. Each decision can be made in an honest or a manipulative manner.

3. Christians need to use discernment when working with mathematical models to . . .

a. Determine if they are mathematically correct

b. Determine if they have been created in an honest, God-glorifying manner or in a manipulative, sinful manner.

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