# Measuring Human Rights: High School Mathematics Unit

In this unit, students will read and interpret primary sources to address the question, “How do we measure the attainment of human rights?” By exploring the Universal Declaration of Human Rights  (UDHR), the UN’s Guide to Indicators of Human Rights, and data from multiple databases, students will unpack the complexities of using indicators to measure human rights.

The unit focuses on the human right to have adequate food (Article 25). Students will examine two of the main indicators used to measure the degree to which this human right is attained in populations around the world: the prevalence (in %) of children <5 who are underweight, and the percent of adults with body mass index (BMI) <18.5. Students will compare these indicators with other development indicators including life expectancy, infant mortality, and GDP to assess the well being of populations.

Mathematical modeling and descriptive statistics are at the core of this unit. Students use class-generated data as well as data from the World Health Organization and the United Nations to analyze global situations, compare their predictions with real data, and use data to inform their understanding of global issues. To demonstrate their learning of both literacy and mathematics skills, students complete a final assessment in which they study and analyze the measurement of another right from the UDHR.

## Source List

### Anchor Source

The Universal Declaration of Human Rights

The Universal Declaration of Human Rights is a challenging text for high school students to read independently. The UDHL Preamble, when punctuated with commas as in its original publication, presents readers with a sentence of 321 words to read and decode. Even when the Preamble is broken into separate “Whereas” statements by inserting periods, the text still measures at 1710 Lexiles, well above the Grade 11-12 complexity band. Students will likely need guidance and modeling to derive meaning from this part of the primary source text. The particular article (#25) used for this unit measures at 1440L, and should be more accessible to students due to its length and clear language.

Notes about Use in This Unit:  The text is used in this unit to make connections between crucial concepts surrounding nutrition, ecological impacts of food choices, and food as a source of energy to the political concept of human rights, and specifically, the universal right to “a standard of living adequate for the health and well-being of himself and of his family, including food.” Note that students may need support in understanding what this document represents. Many students may not be familiar with the United Nations and its role in defining, monitoring and securing the “universal” rights of people all over the world. Since students will be familiar with the Bill of Rights, it may prove to be a helpful entry point into the subject of a political body ensuring rights of a people.

### Supporting Sources

Human Rights Indicators: A Guide to Measurement and Implementation

This comprehensive Guide presents many mathematical and graphic displays containing information about human rights indicators, as well as explanatory text at a fairly high reading level (the Introduction measures at 1490L). Students will likely read or interpret only selected sections of the 176 page guide, and may need support in interpreting its technical language.

Notes about Use in This Unit: This text presents many opportunities for students to think about the relationship of mathematics and statistical indicators to real world problems, in this case measuring the degree to which human rights indicators are being achieved. Students might be guided to read/interpret selected sections of the text, doing close reading of relevant quotations or explanations and/or studying mathematical displays or metadata sheets of key indicators such as Indicator 10 (p. 155), which relates to Article 25 of the UDHR. [Note: This metadata sheet measures at 1600L.] Primary Source Lesson 2 presents students with activities involving the reading and interpretation of selected text and displays from this comprehensive resource.

World Health Organization (WHO) Website

The comprehensive WHO website is continuously updated to provide information about health topics, data, publications and programs associated with WHO and its mission, as expressed in the “About WHO” introductory portal: “WHO is the directing and coordinating authority for health within the United Nations system. It is responsible for providing leadership on global health matters, shaping the health research agenda, setting norms and standards, articulating evidence-based policy options, providing technical support to countries and monitoring and assessing health trends.”

Notes about Use in This Unit: This website is accessed or referenced many times within the unit, as indicated by the multiple URL’s listed above. The website, as a primary source of information, provides an opportunity for students to learn about accessing and interpreting data through the Internet as provided by organizations such as WHO. Primary Source Lesson 3 presents activities involving orientation to and exploration of the WHO website; many of the Mathematics Lessons directly use or reference displays and data found through website links.

Text level varies across the site, but the complexity of the website and its many links suggests that students may need support in learning to navigate the site and interpret the vast repository of information it contains.

Specific WHO Pages and URLs Within the Unit

Global Health Observatory - Underweight in Children

Observatory Data Repository – Child Malnutrition

WHO Child Growth Standards

WHO Multicentre Growth Reference Study (MGRS)

Graph of Weight-for-age in Boys, Birth to Six Months

WHO Global Database on Body Mass Index (BMI) Overview

WHO Table of BMI for Adults % Underweight (BMI< 18.5)

Gapminder Website

List of Indicators in Gapminder World  - Search for “Malnutrition, weight for age (% of children under 5)” – Category: Health; Subcategory: Nutrition. Click on “Visualize” to generate interactive graphic display.

This website, overseen by statistician Hans Rosling, is dedicated to providing “a fact based world view” and Rosling’s mission to promote “sustainable global development and achievement of the United Nations Millennium Development Goals.” It is organized in tabs for Gapminder World, Data (presented in interesting interactive displays), Videos, Downloads, and tools/support For Teachers.

Notes about Use in This Unit: This website and displays data generated by its Gapminder World graphic interface is used directly in Mathematics Lesson 11 and might be used for further student research/exploration in conjunction with the final performance task. Text complexity varies across the site. Students will receive support in interpreting the interactive graphs during Primary Source Lesson 10 and Mathematics Lesson 11.

2012 World Population Data Sheet - Population Reference Bureau

This publication contains mostly tables and graphic displays, for some of which students may need orientation and support. The text that accompanies the data displays is fairly straightforward.

Notes about Use in This Unit: While not specifically referenced in any Mathematics lessons, this source provides a good general reference for understanding population trends (relative to the nutritional indicators and information studied) and for additional student research in conjunction with the final performance task.

## Standards Alignment

RI.1.11-12: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain.

RI.7.11-12: Integrate and evaluate multiple sources of information presented in different media or formats (e.g., visually, quantitatively) as well as in words in order to address a question or solve a problem.

Math Practice Standards:

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

MP.2 Reason abstractly and quantitatively.

MP.3. Construct viable arguments and critique the reasoning of others.

MP.4Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.7 Look for and make use of structure.

MP.8 Look for and express regularity in repeated reasoning.

Math Content Standards:

S.ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).

S.ID.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, Standard deviation) for two or more data sets.

S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.

S.ID.5.  Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

S.ID.6.  Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

## Developing Student Literacy

### Rationale

As a backdrop for their study of the unit’s essential question and the study of indicators and statistics related to UDHR Article 25 (and more specifically the right to adequate food/nutrition), students encounter a variety of primary sources, from the Universal Declaration of Human Rights itself, to publications and websites devoted to presenting indicators and statistics related to human populations and rights. Students are initially guided in the skills of reading and interpreting primary source text closely with the UDHR, and consider contextual information that helps them understand the historical and social context in which this primary document was developed and adopted by the United Nations. For each additional web or pdf based source, students are initially oriented to the primary source and its context, then practice close reading and information gathering skills with both text and statistical displays, initially guided by the teacher, then in pairs or teams, and finally with increasing independence.

Students are continuously expected to draw specific evidence from these sources to support observations or inferences they make, or to use in mathematical representations, modeling, or problem solving. Student demonstrate their skills of being able to read, interpret, and use information from primary sources throughout the unit, culminating in a final performance task in which they independently investigate the unit’s essential question in relationship to a selected Article from the UDHR.

### CCSS Areas of Focus

Reading Text Closely: Makes reading text(s) closely, examining textual evidence, and discerning deep meaning a central focus of instruction.

Explanation: For each primary source used in the unit, students initially orient themselves to the source and its context, then read/study selected information from that source closely, before using that information to solve mathematical problems or formulate conclusions that are supported by textual evidence and data.

Text­ Based Evidence: Facilitates rich and rigorous evidence ­based discussions and writing about common texts through a sequence of specific, thought­ provoking, and text­dependent questions (including, when applicable, questions about illustrations, charts, diagrams, audio/video, and media).

Explanation: Text-dependent questions are provided to guide close reading and discussion of each primary source – with an initial emphasis on interpreting complex text and then a focus on statistical charts and displays.

Writing from Sources: Routinely expects that students draw evidence from texts to produce clear and coherent writing that informs, explains, or makes an argument in various written forms (e.g., notes, summaries, short responses, or formal essays).

Explanation: Students engage in informal evidence-based writing in response to each primary source and its text-dependent questions, and more formally demonstrate their skills in interpreting and writing from primary sources in the culminating performance task.

Academic Vocabulary: Focuses on building students’ academic vocabulary in context throughout instruction.

Explanation: The primary emphasis is on academic vocabulary related to the study and use of statistics. Students also develop conceptual understanding of terms/ideas related to human rights and quantitative and qualitative indicators of those rights.

Building Disciplinary Knowledge: Provides opportunities for students to build knowledge about a topic or subject through analysis of a coherent selection of strategically sequenced, discipline-specific texts.

Explanation: The mathematical content emphasis is on statistics, building from Math Content Standard 1 (representing data) to Standard 6 (comparing data), while students also build interdisciplinary knowledge related to the concepts of human rights, indicators, and measurement of those rights. They become familiar with the UN’s UDHR and the World Health Organization (WHO) among other sources of information about world populations, by encountering a series of challenging and increasingly technical texts (websites) that progress from the UDHR, to the UN’s Guide to Human Rights Indicators, to various websites that present relevant data about health, nutrition, populations, and the measurement of indicators.

## Direct Learning Through Questions

### Essential Question

How do we measure the attainment of human rights?

This broad question forms a bridge between students’ study of primary sources about human rights and their study of indicators, measurement, and statistics. Students engage in teacher-led exploration of this question relative to UDHR Article 25 (health and nutrition), examining a range of statistics and models, then research how they might use similar primary sources, statistical information, and math practices to investigate the attainment of other human rights. This question should be derived from and related to the series of primary source texts students encounter and the text-dependent questions for those texts, and re-examined or re-thought as students’ understanding increases through the study of those texts and the information they provide.

### Supporting Questions

• Why do we measure whether people have attained human rights?
• What are indicators?
• What are human rights indicators? How are they determined and monitored?
• How are the two indicators (% of underweight children and % of underweight adults) used to measure the degree to which countries are reaching the human right to adequate food? (Article 25)
• How do we measure if a child is underweight? What is standard weight?
• How do we know if an adult is underweight?
• What is Body Mass Index?
• How do we use BMI to determine the well being of population?
• What is the “double burden of malnutrition”?
• How can we use data as evidence for the emergence of the “double burden”?
• How do development indicators relate to human rights indicators?
• How can we check the validity of claims?

## Integrate Learning Across Disciplines

The unit contains lessons that focus on literacy – the reading and interpretation of primary sources – as applied in the study of mathematics (specifically statistics). These lessons are designed to be taught by a math teacher in an applied mathematics context, or could be delivered collaboratively by Math and ELA teachers if they share a common group of students and instructional timeline. The content and concepts focused on in the unit (human rights, population, the United Nations, statistical indicators, health, nutrition) also suggest that the unit might be integrated with students’ learning in social studies (global studies or modern world history) and/or health and life science.

## Align Assessment with Instruction

Having studied primary sources, indicators, statistics, and math problems related to UDHR 25 (health and nutrition), students will identify another Article/Right from the UDHR and complete the following tasks:

• Explain the meaning and importance of that Article/Right, using specific textual evidence from the UDHR.
• Suggest ways in which the attainment of that Article/Right might be measured, and data that could be collected/analyzed to study how universally that right has been attained.
• Identify indicators that may have already been established (from the UN Indicators Guide, WHO database and/or other sources).
• Identify, display, and interpret relevant statistics derived from at least one of the primary sources (or a student-identified primary source).
• Identify two variables related to the Article/Right, compare those variables mathematically, and draw supported inferences from that comparison.
• Explain the process by which they have researched, studied, and “measured” the Article/Right, and how they have solved mathematical problems that have arisen.
• Respond to the unit’s essential question (and potentially supporting questions), using evidence from their research and mathematical study to support conclusions about both how and why the human right can and should be measured.

NOTE: This assessment can involve collaborative research and discussion, but students should be individually responsible for the final analyses and products they develop. Students might demonstrate their understanding through an informal written explanation, a more formal evidence-based argument, a speech or participation in a symposium, or a multi-media presentation, as appropriate to the classroom situation.

### Formative Assessment Strategies

Students respond to text-dependent questions for each of the primary sources they encounter, and use the questions as support for their text-based discussions. The teacher can periodically examine written responses to these questions (and/or observe responses in discussions) to see how well students are understanding information and applying close reading skills to both text and mathematical displays. Students demonstrate developing understanding of statistical concepts and thinking in each of the math exercises or problems they encounter in Math Lessons

## Consider Background Knowledge and Prerequisite Skills

### Prerequisite Learning

• Students should be somewhat skilled and independent in their ability to navigate complex, information-based websites.
• Students should understand what a primary source is, and why it is important to understand the context in which a primary source has been produced.
• Students should be able to identify key details or information in a text or display, and interpret that information accurately.
• Students should have background understanding of basic concepts of statistics such as mean, median, standard deviation, normal curve, box plot, scattergram, etc.
• Students should be able to locate and interpret data represented in tables, and do basic interpretation of graphic displays of statistical information.

### Pre-assessment of Readiness for Learning

Central to this unit are the abilities to interpret text and displays independently and to understand the concept of an “indicator.” In each Primary Source Lesson, students independently complete short written exercises that can serve as a pre-assessment of these skills and knowledge; similarly, the teacher can track the development of mathematical thinking and understanding through exercises within each of the Math Lessons. The teacher can then tailor instruction and assessment in succeeding lessons based on what these initial and ongoing informal assessments indicate.

## Provide Support While Building Toward Independence

### Strategies for Supporting All Students in Building Independence

The progression of this unit, both for developing primary source reading skills and mathematical understanding, is designed to provide initial support and scaffolding as students interpret sources and use statistics to study information drawn from those sources. Primary Source Lesson 1 (The UDHR) presents opportunities for the teacher to model close reading and oversee guided practice while students work in teams to unpack the meaning of short sections of the UDHR. Students use these same skills – more independently – in Primary Source Lesson 3, then apply them when they encounter web-based text and data displays in Lessons 4 and 10. To complete the final performance task project, students must go back and re-access and re-read these sources, now independently, and apply their developing close reading skills to find and interpret information to support an analysis of a second human right.

Similarly in mathematics, students first are guided in reviewing and using basic statistical representations such as box plots in Math Lesson 2, then move through guided use and interpretation of more advanced statistical calculations and representations in Lessons 5-9, eventually doing statistical comparisons in Lesson 11. Throughout, students work in pairs before doing individual assignments, and are increasingly asked to make predictions and/or develop inferences on their own. In the final performance task, students must decide on their own which data to use in their studies of a human right, and which statistics to apply in representing, analyzing, and interpreting that data. Thus, students are being asked to apply independently the math concepts and skills they have learned and practiced during the unit.

The texts used in this unit, particularly the UDHR, present complex reading challenges for all hiigh school students, much less those who are not native speakers/readers or who are not reading at the upper high school level. However, there are a wealth of online resources available to support students who will have difficulty accessing the text(s). As indicated in the instructional notes for Lesson 1, students can be assigned simpler sections of the UDHR Preamble or Articles, and/or can read a simplified, alternate version of the UDHR Articles found at the Youth for Human Rights website: http://www.youthforhumanrights.org/what-are-human-rights/universal-declaration-of-human-rights/articles-1-15.html

For more visual learners, background knowledge and support can be provided by using one or more of the many YouTube videos that have been developed to present and interpret the UDHR, some of which use animation and other visually interesting means of conveying meaning. [Search YouTube for “Universal Declaration of Human Rights.”]

When working with websites and databases, students may need additional support to navigate sites and to understand how data is organized in various displays. While the unit presents instruction for all students in understanding the layout of tables and matrices, some students may need additional instruction/review and the use of scaffolding such as graphic organizers that illustrate how horizontal and vertical axes organize information – both ideas and numbers - into cells.

Finally, when some students get to the final performance task – intended to be a demonstration of how well they can independently interpret primary sources and use statistics – they may need some additional guidance and/or modifications. Students can be directed to more simple Articles of the UDHR, can return to data already used in class activities, can mirror the work done on handouts in class exercises, and/or can use the data and calculations already studied by the entire class as a basis for their final analysis and report. These students might also be given alternate formats for presenting their learning, such as simpler written assignments and/or visual or multi-media presentations.

The unit already presents challenging text and data sources for such students to read and analyze, but also offers many opportunities for differentiation and advanced work. Advanced students can take on the more challenging sections of the UDHR and can do independent research to find additional sources of information about various human rights and their measurement. When presenting and analyzing the data they find to support their study of a human right in the final performance task, advanced students might be directed to use more sophisticated statistical methods (i.e., comparative statistics) to study relationships among variables.

## Unit Outline and Lesson Sequence

Lesson Intro (OPTIONAL*): Interpreting Primary Sources – The Universal Declaration of Human Rights

Lesson #1: Mathematics – Measuring Human Rights

Lesson #Pre 2A (OPTIONAL): Interpreting Primary Sources – Human Rights Indicators: A Guide to Measurement and Implementation

Lesson #Pre 2B (OPTIONAL): Interpreting Primary Sources – World Health Organization (WHO) Website

Lesson #2: Mathematics – Educated Estimate: The Number of Underweight Children in the World

Lesson #3: Mathematics – Underweight Children, Multiple Estimates: Compare and Contrast 3 Methods of Representing Data

Lesson #4: Mathematics – Underweight: Standards and Deviations

Lesson #5: Mathematics – Underweight, Normal Weight: How do we know?

Lesson #6: Mathematics – Recording and Interpreting Data (BMI)

Lesson #Pre 7 (OPTIONAL): Interpreting Primary Sources – Gapminder Website

Lesson #7: Mathematics – Comparing Indicators and Data – Underweight Children and Adult BMI

Lesson #8: Final Performance Task – A Measure of Our Human Rights

*Note: The optional lessons were created by Odell Education