# Measuring Human Rights: High School Mathematics Unit

### Learning Objectives

Students will be able to:

- Compare and Contrast Three Methods of Representing Data

- Represent data appropriately using frequency tables, histograms, and box plots.

- Draw conclusions from the data displayed.

- Analyze data provided in various plot forms and draw conclusions from the data displayed

- Identify similarities and differences in shape, center and spread of various data sets across and within specific representations.

### Standards Addressed

**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.

**Math Practice Standards **

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

**MP.4**Model with mathematics.

**MP.5**Use appropriate tools strategically.

## Instructional Approach

### Teacher Introduction:

- Ask students to imagine a class of 400 students doing the same exercise (of putting up post its on the number line). What do they think would happen? (Total chaos)

- Remind students that one way to organize this data is by creating “bins” (also known as ‘class’). In our case, we will take a range and divide it into equal intervals. In our case, we will divide the number line into 6 equal intervals (in millions) 1-25, 26-50, 51-75, 76-100, 101-125, 126-150.

- Distribute Handout #3

- Project (or draw) a frequency distribution table with 5 population bins (classes) on the board and ask students to raise their hands if their estimate falls within the first bin (class). Make a tally mark for each student who raises his or her hand. Repeat this process for the rest of the ranges. Ask students to copy the results on the corresponding table in Handout #3.

**Handout #3 With Example (Red)**

Number of children (<5) in the world who are underweight (in millions) | Frequency (number of students vote) | Cumulative Frequency (Answers in green) |

1-25 | ||

25-50 | ||

51-75 | ||

76-100 | ||

101-125 | ||

126-150 |

**Handout #3 With Example (Red and Green)**

Number of children (<5) in the world who are underweight (in millions) | Frequency (number of students vote) (in red example of filled table) | Cumulative Frequency (Answers in green) |

1-25 | II (2) | 2 |

25-50 | IIII (4) | 6 |

51-75 | IIIIIII (7) | 13 |

76-100 | IIIIIIIII (9) | 22 |

101-125 | II (2) | 24 |

126-150 | IIIIII (6) | 30 |

### Individual Work

Begin filling the cumulative column on the board and ask students to complete the cumulative frequency column in Handout #3.

- Once students complete the table ask them to individually complete the questions in the handouts (15 minutes), and then review answers as a class before going to next process (10 minutes).

- Use the table and create a histogram that matches the frequency table. (If needed, give students a refresher handout on how to create a histogram)
- Which of these representation(s) (e.g. frequency table, histogram, and box plot) shows the most popular estimation in the class? Why?
- Which representation do you think shows students’ estimations most accurately? Why?
- Optional if time permits: Can you make up data for another class, which will be different from your class’s data set but result in the same box plot and histogram? If your answer is ‘yes’, show the data set. If your answer is ‘no’ explain why.

### Small Group Work

- Divide students into pairs or trios, hand out Class Mix Up cards to each group

- Tell students that four (optional: six) more classes participated in this activity. Each class produced a card with a histogram and a card with a box plot that represent their classroom data. Unfortunately you mixed up the cards. The group’s task is to match each histogram card with the appropriate box plot card. Tell students that each group will be asked to justify their matching choices to the rest of the class. (Give each group set of 8 cards containing 4 box plots and 4 histograms, or a set of 12 cards with 6 histograms and 6 box plots)

- Once all group members agree on the 4 matches (pairs), ask them to glue matching solutions on a poster.

- Post and conduct a gallery walk and ask students to look for commonalities and differences across the posters.

- Once the class reconvenes, using a projector, present the histograms and box plots and ask volunteers from various groups to explain why they matched their cards as they did.

- Encourage the rest of the students to respectfully challenge and counter answers.

- Ask students if they can tell the number of students for each match. Do they have enough information? How do you know?

**Handout #4**

**Class Mix Up Cards: Match Box Plots with Histograms**

### Teacher Explanation

According to the World Health Organization 15.7% of all children who are under the age of 5 in the world are underweight. As we discussed in the previous lesson, in 2012 it was estimated there were 642 million children in the world under the age of 5. Given this number, ask students to calculate the number of children under 5 in the world that are underweight. (Approximately 101 million)

### Conclusion

Conclude the class with discussion of the following questions:

*Which representation would you use to determine the number of individual students who had the closest estimation? (box plot, frequency table, or histogram)*

*How does our class’ estimation compare the other (6) classes? Which class came the closest (within the bin) to the actual number of children <5 in the world who are underweight (101 million)?*

**Homework**: The focus of the next class is on the first indicator: Prevalence of underweight and stunted children under five years of age. Ask students to think about 3 ways to determine if children are underweight.

### Differentiation and Supports

**Adaptations**

- Struggling: During small group work students can work with the first 3 pairs of cards only.
- Struggling: During the matching card game, direct students to focus on one aspect at a time. Begin with students figuring out how many students are in each class.
- Advanced: Can you make up data for another class, which will be different from your class’s data set but result in the same box plot and histogram? If your answer is ‘yes’, show the data set. If your answer is ‘no’ explain why.
- Advanced: Create additional set of cards for the card game and share it with class.

**Supports**

- While students engage in the group task, teacher can work with a small group of students on the same task. Explicitly demonstrating how he/she goes about marching the cards.

**Note:***The lesson is dealing with the notion of body weight (e.g. prevalence of underweight in children and BMI in adults). Be aware of many students who may have low self-esteem due to body weight. In the first part of the lesson we are focusing on children under five years of age (the UN indicator). In the second part we are looking at adults BMI and the focus is on BMI<18.5 as a function of underweight. The notion of BMI has several limitations, which we will discuss in the lesson. In addition, both, the notion of standard weight for children and the classification for BMI are useful as indicators for evaluating populations. NOT individuals.*

### Assessment

Handout #3 will provide assessment data on student learning.

Observations of Class Mix Up Activity.