National Debt Project
Student Handouts
pp. 1-2Introduction
pp. 3-4Part I: Overall Models
pp. 5-6Part II: Democratic Models
pp. 7-8Part III: Republican Models
pp. 9-10Part IV: Analyzing Predictions
pp. 11-14Part V: Democratic & Republican Analysis
pp. 15-16Part VI: Group Presentation
pp. 17-18Part VII: Conclusions & Reflections
pp. 19-20Grading Rubric
pp. 21-26Mathematical Modeling Notes
(Not included: Follow-up Article Review Assignments)
National Debt ProjectName: ______
Introduction
The following data related to the national debt of the United States comes from two reports on the government website 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 / 5,807,463,000,000
09/30/2002 / 6,228,236,000,000
09/30/2003 / 6,783,231,000,000
09/30/2004 / 7,379,053,000,000
09/30/2005 / 7,932,710,000,000
09/30/2006 / 8,506,974,000,000
09/30/2007 / 9,007,653,000,000
09/30/2008 / 10,024,725,000,000
09/30/2009 / 11,909,829,000,000
09/30/2010 / 13,561,623,000,000
09/30/2011 / 14,790,340,000,000
09/30/2012 / 16,066,241,000,000
09/30/2013 / 16,738,184,000,000
09/30/2014 / 17,824,071,000,000
09/30/2015 / 18,150,618,000,000
09/30/2016 / 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 ModelsName: ______
Date / Dollar Amount / Date / Dollar Amount09/30/2001 / 5,807,463,000,000 / 09/30/2009 / 11,909,829,000,000
09/30/2002 / 6,228,236,000,000 / 09/30/2010 / 13,561,623,000,000
09/30/2003 / 6,783,231,000,000 / 09/30/2011 / 14,790,340,000,000
09/30/2004 / 7,379,053,000,000 / 09/30/2012 / 16,066,241,000,000
09/30/2005 / 7,932,710,000,000 / 09/30/2013 / 16,738,184,000,000
09/30/2006 / 8,506,974,000,000 / 09/30/2014 / 17,824,071,000,000
09/30/2007 / 9,007,653,000,000 / 09/30/2015 / 18,150,618,000,000
09/30/2008 / 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 alinear 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 =______
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:______
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 =______
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:______
Part II: Democratic ModelsName: ______
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 / 11,909,829,000,000
09/30/2010 / 13,561,623,000,000
09/30/2011 / 14,790,340,000,000
09/30/2012 / 16,066,241,000,000
09/30/2013 / 16,738,184,000,000
09/30/2014 / 17,824,071,000,000
09/30/2015 / 18,150,618,000,000
09/30/2016 / 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.
Please round dollar amounts to three decimal places.
2. Make alinear 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 =______
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:______
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 =______
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:______
Part III: RepublicanModelsName: ______
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 / 5,807,463,000,000
09/30/2002 / 6,228,236,000,000
09/30/2003 / 6,783,231,000,000
09/30/2004 / 7,379,053,000,000
09/30/2005 / 7,932,710,000,000
09/30/2006 / 8,506,974,000,000
09/30/2007 / 9,007,653,000,000
09/30/2008 / 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.
Please round dollar amounts to three decimal places.
2. Make alinear 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 =______
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:______
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 =______
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:______
Part IV: Analyzing PredictionsName: ______
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
Model / R2 / 2020 Prediction / 2025 Prediction / 2030 Prediction2009-2016 Linear
2009-2016 Quadratic
2009-2016 Exponential
Democratic Data Models
Model / R2 / 2020 Prediction / 2025 Prediction / 2030 Prediction2001-2008 Linear
2001-2008 Quadratic
2001-2008 Exponential
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 Republican
2) Identify the model as linear, quadratic or exponential
3) 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 AnalysisName: ______
Democratic Analysis
1. Of the threemodels you made in Part II, find the model that projects the least amount of national debt.
- Equation of the model: ______
- 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 thatsupport 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 Analysis
1. Of the three models you made in Part III, find the model that projects the least amount of national debt.
- Equation of the model: ______
- 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 PresentationName: ______
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. thethree 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. thethree 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 Prediction2. 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 ProjectName: ______
Grading Rubric
1. Part I - turn in worksheet: Overall Graphs & Models
a. 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 & Models
a. Graphs for 2009-2016______out of 5 points
b. Equations / R2 / Predictions for 2009-2016______out of 5 points
3. Part III - turn in worksheet: Republican Graphs & Models
a. Graphs for 2001-2008______out of 5 points
b. Equations / R2 / Predictions 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. SectionB 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 Notes
Preparation & 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. Example
Holly 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 / 5Average / 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 ***