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Created byDanielle Rabina

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Quantifying Change: Mathematical Models for Social Justice

Grade 11Math2 days

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we, as data-driven advocates, use mathematical modeling to analyze the progress of a social justice cause and predict its future impact on society?

Essential Questions

Supporting questions that break down major concepts.

How do we determine which mathematical function (linear, exponential, quadratic, or logistic) best represents real-world trends in social justice?
What does the rate of change in our data reveal about the progress or stagnation of a specific social issue?
In what ways can mathematical models be used to predict future outcomes and inform policy or advocacy efforts?
How do we evaluate the reliability and bias of data sources when investigating sensitive social topics?
How can we use residuals and correlation coefficients to justify the validity of our mathematical arguments?
How can data visualization be designed to ethically and effectively communicate the urgency of a social cause?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Students will be able to select and justify the most appropriate mathematical function (linear, exponential, or quadratic) to model a real-world social justice dataset.
Students will interpret the slope, intercepts, and rate of change of their mathematical models in the specific context of their chosen social justice issue.
Students will utilize statistical tools, including correlation coefficients (r) and residual plots, to assess the validity and reliability of their mathematical models.
Students will construct data-driven predictions for the future of a social cause and communicate these findings through ethical data visualization.
Students will evaluate the bias and reliability of external data sources to ensure the integrity of their mathematical arguments.

Common Core State Standards for Mathematics

HSS.ID.B.6

Primary

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.Reason: This is the core of the project: students take social justice data, plot it, find a line/curve of best fit, and use that model to analyze the issue.

CCSS.MATH.PRACTICE.MP4

Primary

Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.Reason: The project explicitly asks students to act as 'data-driven advocates,' applying modeling to societal problems.

HSF.LE.A.1

Secondary

Distinguish between situations that can be modeled with linear functions and with exponential functions.Reason: One of the essential questions asks students to determine which function best represents the trend, requiring them to differentiate between growth patterns.

HSS.ID.C.7

Secondary

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.Reason: Students are asked to explain what the rate of change reveals about the progress or stagnation of their chosen cause.

HSS.ID.B.6.B

Supporting

Informally assess the fit of a function by plotting and analyzing residuals.Reason: Students use residuals to justify the validity of their mathematical arguments as part of their inquiry into model accuracy.

Entry Events

Events that will be used to introduce the project to students

The Invisible Thread: Uncovering Hidden Correlations

Students are shown a series of seemingly unrelated datasets (e.g., local zip codes' tree canopy coverage vs. asthma rates, or school funding vs. incarceration rates) and are asked to find the 'Invisible Thread.' They must choose a cause where they suspect a hidden correlation exists and use modeling to uncover whether one social variable is actually a leading indicator of another.

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Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.

Activity 1

The Social Justice Data Scout

In this foundational activity, students act as investigative journalists. They must choose a social justice cause (e.g., gender pay gap, incarceration rates by demographic, carbon emissions by country) and find a reliable dataset that spans at least 10-15 years. Crucially, they must evaluate their source's credibility and potential for bias, ensuring their mathematical arguments are built on a solid foundation.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Select a social justice topic from the provided list or propose your own for approval.

2. Research and locate a quantitative dataset that tracks at least two variables over a period of time (longitudinal data).

3. Perform a 'Bias Check' by researching the organization that provided the data and identifying their mission and funding sources.

4. Organize the raw data into a clean table with clearly labeled units for both the independent (x) and dependent (y) variables.

Final Product

What students will submit as the final product of the activityA 'Data Dossier' containing a raw data table, a link to the source, and a 250-word justification explaining why the source is reliable and what social justice 'Invisible Thread' they are investigating.

Alignment

How this activity aligns with the learning objectives & standardsAligns with Learning Goal: 'Students will evaluate the bias and reliability of external data sources' and MP4 (Model with mathematics). It addresses the 'Inquiry' phase of finding high-quality data.

Activity 2

The Invisible Thread Visualizer

Students transform their raw data into a visual representation. Using graphing software like Desmos or GeoGebra, they will create a scatter plot to identify the 'Invisible Thread.' They will describe the correlation (positive, negative, or none) and the strength of the relationship, making an initial hypothesis about which type of function (linear, exponential, or quadratic) might best fit the trend.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Input your raw data points into a graphing calculator or digital spreadsheet.

2. Scale the x and y axes appropriately to ensure the data is clearly visible and not distorted.

3. Analyze the shape of the data points: Does it look like a straight line, a curve that accelerates, or a parabola?

4. Write a hypothesis stating: 'I believe a [linear/exponential/quadratic] model will best fit this data because...'

Final Product

What students will submit as the final product of the activityA digital scatter plot with labeled axes and a 'Trend Hypothesis' paragraph describing the direction and strength of the correlation.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSS.ID.B.6 (Represent data on two quantitative variables on a scatter plot, and describe how the variables are related).

Activity 3

The Model Architect

This is the core modeling phase. Students will perform regressions to find the mathematical equation that best represents their cause. They must go beyond the numbers to explain what the 'math' actually means for real people. For example, what does a slope of 0.5 mean for a city's homelessness rate? Is it growing linearly or exponentially?

Steps

Here is some basic scaffolding to help students complete the activity.

1. Run at least two different regression models (e.g., linear vs. exponential) to see which yields a better visual fit.

2. Select the most accurate model and write the full equation with defined variables.

3. Interpret the slope (rate of change): What does it tell us about the speed of progress or decline in this social cause?

4. Interpret the y-intercept: What does it represent in the context of the starting point of your data?

Final Product

What students will submit as the final product of the activityA 'Mathematical Blueprint' featuring the chosen regression equation and a 'Contextual Translation' guide for the slope and y-intercept.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSF.LE.A.1 (Distinguish between linear and exponential) and HSS.ID.C.7 (Interpret the slope and intercept in context).

Activity 4

The Validity Audit

Every good advocate must defend their arguments. In this activity, students 'audit' their own model to see if it is truly reliable. They will calculate the correlation coefficient (r) and generate a residual plot. They are looking for a random pattern in the residuals to confirm that their chosen function type was the correct choice.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Calculate and record the correlation coefficient (r) and the coefficient of determination (r-squared).

2. Generate a residual plot using your graphing software.

3. Analyze the residual plot: If there is a clear pattern (like a U-shape), your model might be the wrong type. If it is random noise, your model is a good fit.

4. Write a 'Defense Statement' explaining why your model is a statistically sound representation of the social issue.

Final Product

What students will submit as the final product of the activityA 'Model Validation Report' that includes a residual plot image and a paragraph justifying the model's accuracy using r-values and residual patterns.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSS.ID.B.6.B (Informally assess the fit of a function by plotting and analyzing residuals).

Activity 5

The Advocacy Oracle

In the final phase, students use their model as a tool for change. They will use their equation to predict where the social cause will be in 10, 20, and 50 years if the current trend continues. They will then create a compelling data visualization (infographic or slide) that communicates the urgency of their cause to a specific audience (policy makers, the public, or activists).

Steps

Here is some basic scaffolding to help students complete the activity.

1. Use your regression equation to solve for 'y' for future 'x' values (extrapolation).

2. Discuss the limitations of your prediction: Why might the model change? What external factors could intervene?

3. Design a visual infographic that highlights the most shocking or important data point from your model.

4. Write a 'Policy Recommendation' based on your mathematical findings (e.g., 'If we don't change X, the data shows Y will happen by 2040').

Final Product

What students will submit as the final product of the activityA 'Data-Driven Advocacy Poster' that combines the mathematical model, future predictions, and a call to action based on the 'rate of change' discovered.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSS.ID.B.6 (Use functions fitted to data to solve problems) and MP4 (Model with mathematics).

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Mathematical Modeling for Social Justice Rubric

Category 1

Foundational Data Literacy

Focuses on the student's ability to source, evaluate, and initially visualize complex social justice data.

Criterion 1

Data Scouting & Bias Analysis

Ability to select relevant social justice datasets and critically evaluate the credibility and potential bias of the source.

Exemplary

4 Points

Selects a highly relevant dataset spanning 15+ years; provides a sophisticated analysis of the source's mission, funding, and potential bias; clearly identifies a compelling 'Invisible Thread' connecting variables.

Proficient

3 Points

Selects a relevant dataset spanning 10-15 years; identifies the source's mission and funding; provides a clear justification for why the source is reliable and describes the 'Invisible Thread.'

Developing

2 Points

Selects a dataset with some relevance but may lack the 10-year span; provides a basic description of the source with limited analysis of bias or mission.

Beginning

1 Points

Dataset is incomplete, irrelevant, or lacks a clear source; little to no evaluation of bias or reliability is provided.

Criterion 2

Data Visualization & Hypothesis

Accuracy and clarity in creating scatter plots and formulating a mathematical hypothesis about the relationship between variables.

Exemplary

4 Points

Creates a flawless scatter plot with optimal scaling and precise labeling; hypothesis demonstrates advanced insight into function behavior (linear, exponential, quadratic) based on visual data trends.

Proficient

3 Points

Creates an accurate scatter plot with appropriate scaling and labels; hypothesis correctly identifies a likely function type based on the observed correlation.

Developing

2 Points

Scatter plot is mostly accurate but may have minor scaling or labeling errors; hypothesis identifies a function type but lacks strong visual justification.

Beginning

1 Points

Scatter plot is poorly constructed, distorted, or missing labels; hypothesis is missing or does not align with the visual data.

Category 2

Model Construction & Meaning

Evaluates the technical execution of the mathematical model and the ability to bridge math and reality.

Criterion 1

Regression Modeling

Success in performing regressions to find the best-fitting mathematical equation and justifying the choice of function.

Exemplary

4 Points

Expertly compares multiple regression models; selects the most accurate model with a sophisticated mathematical justification; variables are perfectly defined within a complete equation.

Proficient

3 Points

Runs at least two regression models; selects the best fit and provides a clear justification; writes a complete equation with defined variables.

Developing

2 Points

Performs a single regression; the equation is mostly correct but may lack variable definitions or a clear justification for the chosen model.

Beginning

1 Points

Regression model is inappropriate for the data or the equation is significantly incorrect or missing.

Criterion 2

Contextual Interpretation

Ability to translate mathematical parameters (slope/rate of change and y-intercept) into meaningful real-world context regarding social justice.

Exemplary

4 Points

Provides a profound interpretation of slope and intercept, connecting them to systemic issues; explains the human impact of the 'rate of change' with exceptional clarity.

Proficient

3 Points

Correctly interprets the slope as a rate of change and the y-intercept as a starting value within the specific context of the social cause.

Developing

2 Points

Identifies slope and intercept but the contextual explanation is generic or contains minor inaccuracies regarding the social issue.

Beginning

1 Points

Unable to explain the meaning of slope or intercept, or interpretation is mathematically and contextually incorrect.

Category 3

Validity and Rigor

Measures the student's ability to use statistical tools to defend the integrity of their mathematical arguments.

Criterion 1

Statistical Validation

Use of correlation coefficients (r) and residual plots to objectively assess the fit and reliability of the model.

Exemplary

4 Points

Provides a comprehensive audit; uses r-values and a sophisticated analysis of residual patterns (randomness vs. patterns) to prove the model's validity or suggest improvements.

Proficient

3 Points

Correctly calculates r-values and generates a residual plot; uses these tools to justify why the chosen model is a statistically sound representation.

Developing

2 Points

Calculates r-values but provides a limited or slightly confused analysis of the residual plot's implications for model fit.

Beginning

1 Points

Correlation or residuals are missing, incorrect, or not used to evaluate the model's validity.

Category 4

Data-Driven Advocacy

Assesses the final synthesis of data into a tool for social change and public awareness.

Criterion 1

Extrapolation & Limitations

Ability to use the model for future extrapolation and to recognize the limitations of mathematical predictions.

Exemplary

4 Points

Makes precise future predictions; provides a nuanced discussion of external variables and systemic factors that could limit or alter the model's accuracy over time.

Proficient

3 Points

Uses the equation to predict future outcomes at specific intervals (10, 20, 50 years); identifies at least two logical limitations or external factors.

Developing

2 Points

Attempts future predictions but may have calculation errors; identifies only one or very general limitations.

Beginning

1 Points

Predictions are missing or based on flawed math; fails to identify any limitations of the model.

Criterion 2

Communication & Advocacy

Creation of a compelling, ethical data visualization and a call to action based on mathematical findings.

Exemplary

4 Points

Designs an impactful, professional-grade infographic; provides a powerful policy recommendation that is directly and undeniably supported by the mathematical model.

Proficient

3 Points

Creates a clear and ethical data visualization; writes a logical policy recommendation based on the model's rate of change and future predictions.

Developing

2 Points

Visualization is basic or slightly cluttered; policy recommendation is present but only loosely connected to the mathematical evidence.

Beginning

1 Points

Visualization is misleading or poorly constructed; call to action is missing or lacks any mathematical basis.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning

Question 1

How did the process of finding the 'Invisible Thread' change your perspective on the role of mathematics in addressing real-world social justice issues?

Text

Required

Question 2

How confident do you feel in your ability to distinguish between linear, exponential, and quadratic trends when looking at a raw scatter plot?

Scale

Required

Question 3

During 'The Validity Audit,' which step do you feel was most important in ensuring your advocacy was ethically and mathematically sound?

Multiple choice

Required

Options

Conducting the 'Bias Check' on the data source

Calculating the correlation coefficient (r)

Analyzing the residual plots for patterns

Accounting for the limitations of extrapolation

Question 4

As a 'Data-Driven Advocate,' how do you plan to use mathematical modeling or data interpretation to evaluate claims you see in the news or social media in the future?

Text

Required

Question 5

Explain how your interpretation of the 'slope' or 'rate of change' helped you communicate the urgency of your chosen social justice cause in your final Advocacy Poster.

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Required