# Measuring Human Rights: High School Mathematics Unit

**Note**: This lesson focuses again on the Body Mass Index (BMI) as one of the indicators used by the UN to evaluate the degree to which certain populations have adequate food. Be aware that many students may have low self-esteem due to their body weight. This lesson does not focus on issues of obesity and students will not be asked to measure their own weight or calculate their BMI. Rather, we will explore this issue from a population health perspective. The notion of standard weight for children and the classification for BMI are useful as indicators for evaluating populations, not individuals.

In the previous lessons, we focused on the weight of children under five years of age as an indicator for malnutrition (thus lack of adequate food for a population). In this lesson, we examine the BMI of adults in which BMI<18.5 is an indicator of underweight. The notion of BMI has several limitations, which are discussed in the lesson.

### Prior knowledge required

- Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

- Find solutions to a system of two linear equations in two variables.

### Learning Objectives

Students will be able to:

- Create a scatter plot from two quantitative variables
- Identify the independent and dependent variables
- Describe the relationship of the variables.

### Standards Addressed

*Math Content Standards*

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

*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.4 Model with mathematics.

- MP.7 Look for and make use of structure

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

## Instructional Approach

The prevalence of children <5 who are underweight and the proportion of adults with body mass index (BMI) <18.5 are two indicators that the United Nations uses to measure the degree to which the human right of having adequate food is met in a country.

- In this lesson we examine a data set which provides the percentage of people in different countries with BMI < 18.5, and then we compare the countries with the highest percentage of adults with BMI<18.5 to the percentage of children <5 in these countries who are underweight. (Basically we are comparing the two indicators.)

- By the end of this lesson, students are introduced to the emerging phenomenon in the developing world in which malnutrition shows up in two distinct forms: underweight and overweight populations. This phenomenon is called “the double burden of malnutrition”. Students are asked what kind of data they need in order to substantiate this claim. Through the investigation of data sets (adults with BMI< 18.5 and adults with BMI>25), students are asked to look for evidence in the data that substantiates this emerging phenomenon.

Start the class by projecting the map below (from the WHO website they have studied in Lesson 4). Ask students if they can tell you what this color-coded map is trying to explain. Pick a few students to volunteer. Ask students to give concrete examples using the information from the map.

While the map is projected, ask students to share observations about the distribution of underweight adults around the world.

http://apps.who.int/bmi/index.jsp

### Teacher Explanation

Currently, it is difficult - or maybe even impossible - to find a comprehensive data set that includes most countries adult underweight population that has BMI<18.5. (It is easier to find data that gives the percentage of country’s population considered to be obese).

The WHO’s data set includes data describing the percentage of adults with BMI<18.5 from 62 countries. Read aloud the caveat below (on the top of the map in italics) and briefly share that while we don’t have fully comparable data, it can still serve as a vehicle to show important trends happening in the world.

*The national BMI data displayed in this table are empirical and have been verified that they apply internationally recommended BMI cut-off points. However, it is important to note that the data presented are not directly comparable since they vary in terms of sampling procedures, age ranges and the year(s) of data collection.*

Ask each student to examine the data in Handout #1 and search for the ten countries that have the highest percentage of adults with BMI < 18.5.

**If tablets/computers/Internet are available**students can go directly to the World Health Organization Global Database on Body Mass Index at http://apps.who.int/bmi/index.jsp . Ask students to choose table format and the indicator: “BMI adults % underweight (<18.5)”. Ask students to choose the most recent data (under the left column “Most Recent”).

**Handout#1**

BMI Adults % underweight (<18.5)

Country | Most Recent % of Adults with BMI<18.5 | Country | Most Recent % of Adults with BMI<18.5 |

American Samoa | 0.1 | Kuwait | 2.5 |

Australia | 1 | Kyrgyzstan | 3.7 |

Austria | 2 | Lao People's Democratic Republic | 13.5 |

Barbados | 3.2 | Latvia | 3.5 |

Belgium | 3.8 | Lithuania | 2.4 |

Brazil | 4 | Madagascar | 19.2 |

Bulgaria | 3.9 | Malaysia | 9.6 |

Canada | 2.6 | Malta | 2.6 |

Chile | 0.8 | Mongolia | 4.9 |

China | 8 | Morocco | 5.3 |

Colombia | 3.9 | New Zealand | 1.3 |

Croatia | 0.2 | Norway | 5 |

Cuba | 7.3 | Pakistan | 31.2 |

Cyprus | 4.3 | Panama | 1 |

Czech Republic | 2.4 | Philippines | 12.3 |

Denmark | 2.2 | Poland | 2.2 |

Estonia | 4.6 | Portugal | 2.2 |

Fiji | 6.1 | Republic of Korea | 4.7 |

Finland | 2.4 | Romania | 3 |

France | 4.9 | Saudi Arabia | 7 |

Ghana | 16.4 | Singapore | 9.2 |

Hungary | 2 | Slovakia | 4.7 |

Iceland | 2.3 | South Africa | 8.6 |

India | 32.9 | Spain | 1.8 |

Iran (Islamic Republic of) | 5.7 | Sweden | 2 |

Ireland | 0.8 | Switzerland | 3.5 |

Ireland | 5.1 | Thailand | 19.2 |

Italy | 3.4 | Turkey | 3.5 |

Japan | 11.5 | United States of America | 2.4 |

Jordan | 3 | Vanuatu | 1.9 |

Kiribati | 0.5 | Viet Nam | 26.5 |

**Adapted from http://apps.who.int/bmi/index.jsp

Ask students to record the data set below (Handout #2) [REVIEWER’S NOTE: This instruction is unclear and needs further explanation.]

**Handout#2**

Country | % of BMI< 18.5 2004-2006 | Prediction of % underweight children aged <5 | % underweight children aged <5 | 1990-1995 |

India
| 32.9 | 43.5 | 59.5 | |

Pakistan
| 31.2 | 30.9 | 39 | |

Viet Nam
| 26.5 | 20.2 | 40.6 | |

Madagascar
| 19.2 | 36.8 | 40.9 | |

Thailand
| 19.2 | 7 | 16.3 | |

Ghana
| 16.4 | 14.3 | 25.1 | |

Lao People's Democratic Republic
| 13.5 | 31.6 | 39.8 | |

Philippines
| 12.3 | 20.7 | 29.2 | |

Japan
| 11.5 | 3.2 | 3.2 | |

Zimbabwe
| 9.9 | 10.1 | 11.7 |

Ask students to predict the (most recent) rates of underweight children in these countries.

Have students check the rates on WHO, complete the table, and write at least two reflections on their initial predictions. Probing questions:

*What surprised you about the data?**Is there a pattern in the discrepancies between your prediction and the World Health Organization data? (For example, were your estimations higher than the WHO numbers, or no apparent pattern, or lower?)*

Once students complete the handout, ask a few volunteers to share some of their observations with the whole class. Limit each student to one observation.

### Teacher Explanation

Share with students one possible observation:

In Thailand, there is a discrepancy between the percentage of adults who are underweight and children<5 who are underweight. According to the WHO’s data set, in Thailand 19.2% of adults are underweight (BMI<18.5) yet only 7% of the children<5 are underweight. Ask students to think of possible explanations for that discrepancy. In pop-corn style have a few students share their possible explanations.*

- Project the following data from the gapminder.org website that students studied in Lesson 10

Exact link: http://www.gapminder.org/world/ - children<5 underweightht

**** If tablets/computers/Internet are available, students can go directly to this site.**

- Select the indicator underweight children<5 for the Y axis, and Population aged 0-4 (which is same as<5) for the X axis. Start by looking at the year 2006 (which corresponds to the year of the WHO’s data). Explain to the students that the circles present countries, the size of circles present the size of countries, and the color corresponds to the geographical location (see map on side column). For example, in India (largest blue circle) 11% of the population is younger than 5, and around 44% of that population is underweight (see screen shot below).

- Ask students to share any observations and/or patterns they see in the chart. (Possible answers: the countries with the highest population of children<5 are in Africa (dark blue dots): the yellow countries (north/south America) have relative lower % of children underweight)

- After sharing a few observations, click on the Play button (bottom left) and display the simulation. As you are watching, explain this is an view over time of the relation between these two variables. Show this 2-3 times.

- Go back to the example of Thailand, and reiterate that in Thailand 19.2% of adults are underweight (BMI<18.5) yet only 7% of the children<5 are underweight. Tell students that together you are going to further explore the data about Thailand and develop an explanation for this change.

- On the right column select Thailand. Be explicit about how you go about the process.

- Start the simulation. Repeat the simulation 3 times (it is a 2 second simulation).

- Freeze the screen on the situation in Thailand in 2006 (see below).

### Individual Work:

Distribute Handout #3

- In the first part of the handout students are asked to use the information from the gapminder chart (a screen shot of different scenarios according to years included in the chart) and suggest way(s) to explain the discrepancy between the current % of adults underweight and % of children<5 underweight in Thailand. Make sure students record their ideas on the handout.

### Small Group Work:

- Divide the class into pairs or trios.

- Ask students to share their individual work and together refine their explanation for this discrepancy between adult and child populations.

- Continue working together on Handout #3 (see group section).

**Handout #3**

### Part A: Individual Work

Complete the table below and graph the data.

Year | X | Y |

1987 | 10 | 17 |

1990 | ||

2000 | ||

2003 | ||

2006 | ||

2013 |

What happens over time to the % of children<5 in Thailand?

What happens over time to the % of underweight children in Thailand?

Describe your answers to questions two and three using math vocabulary. (For example: Positive correlation, positive association)

If this trend continues, what would you expect the % of population aged 0-4 to be in 2013?

If this trend continues, what would you expect the % of underweight children to be in 2013?

Use the information from the charts above and the graph from question one to provide a possible explanation for the discrepancy between the current percentage of adults underweight and percentage of children<5 underweight in Thailand. Record your suggestions on the space below. Be clear about the information you use and its connection to resolving the discrepancy. Use mathematical vocabulary whenever you can as part of your explanation.

### Part B: Small Group Work

Each student in the group shares an explanation from part A. Encourage students to listen carefully to each other, ask clarifying questions and respectfully listen to their peers’ explanations.

The task of each group is to build on each other’s ideas and construct, as a group, an improved explanation for the discrepancy between the current percentage of adults underweight and percentage of children<5 underweight in Thailand.

Compare your solutions to questions 1-6 in part A with each other.

If you got different answers to any of these questions discuss these and as a group decide the best answers for these questions. Listen carefully to each other’s explanations and only change your answer if you are convinced there is a better one.

Take turns sharing your possible explanation for the discrepancy between the current percentage of adults underweight and percentage of children<5 underweight in Thailand. Question #7).

Build on each other’s ideas and as a group come up with an improved explanation. Record your group explanation on a flip chart. Make sure to provide some evidence from the data for your group explanation.

Be prepared to present and defend your group explanation to the whole class.

### All Class Discussion and Closure:

- Have a student reporter from each group share the group’s explanation and post flip charts on wall so students can view, compare and contrast.

- Ask students which explanation(s) make the most sense to them and why.

- If time permits, form pairs and ask students to share with each other one thing they learned today. Have a few students share their reflections with the class.

- Let students know that we will continue to use math to understand more about trends (which are patterns that show increases and decreases over time, as they saw on gapminder) as a way to better understand the degree to which countries are achieving the human right to have adequate food.

### Assessment

Student learning, and readiness for the summative performance assessment task, can be checked by reviewing work on Handouts 2 &3, and by observations made during discussions.