Kent State University

Mathematics is the second module in the TWD unit. Mathematics should take place after the Social Studies module is finished and before the Science module starts.

The Math module uses the context of fairness of water distribution in the Tigris/Euphrates watershed to engage students in thinking about data literacy and proportionality. Students first engage in a hands-on activity to set the stage for learning about proportional reasoning. They then investigate per capita, unit rate (in the form of salinity), and percents. This culminates in an investigation into mathematical arguments that use proportional reasoning. Students are prepared for the Science and English Language Arts modules through exposure to the idea of salinity, and also by learning to evaluate and form mathematical arguments.

Preparing to Teach the Math Module

The Math module builds on the work the students have recently completed in the Social Studies module. Because of this, it will be helpful to acclimate yourself with the context of the Tigris/Euphrates watershed, as well as the brief overview of the Social Studies module.

In Social Studies students were asked to create an equitable water sharing treaty among Turkey, Syria, and Iraq. It is expected that most, or even all, students will have resorted to simple solutions, such as providing each country with 1/3 the water. However, this is not a truly equitable solution, as these countries are of different sizes, have different populations, and use water in different ways.  In this way the students are “prepared” to learn about proportional measures such as per capita. In order to fully leverage the social studies module, you should have a discussion with the social studies teacher(s) to determine what types of difficulties students had in creating their treaties, and the level of satisfaction students had with their treaties. This information will be helpful as the class revisits the social studies data and considers more complex ways of sharing water.

All worksheets and related materials are available on this website. Students can complete work electronically (make provisions for students saving files) or on paper (decide who will print out the materials). All the lessons in the module should be reviewed the week before its start to get a sense of the flow of the module; and each lesson should be carefully gone over the day before implementation.

Lesson 1 requires some special setup. An Internet connection and computer projection may be used to show the TWD website, to remind students of the overall context. In addition, each class will need to have 100 beans (or other tokens) divided into separate sets of 50 beans, 40 beans, and 10 beans.

Lesson 8 requires that the teacher has access to Excel to display a spreadsheet (students do not need Excel).

All lessons will require some way to project student worksheets. This can be done with a projector connected to a computer, or a document projector. Besides this, most of the lessons require only the teacher materials, the student worksheets found on this website, and student calculators (graphing calculators are not required).

	Content The Math module addresses the NCTM standards of Number, Measurement, Patterns, and Data Analysis through the study of per capita and percents. This module gives students insight into proportional and derived measures through the comparison of water allocation and related phenomena. Students also use charts and graphs, analyze and construct mathematical arguments, and identify appropriate and inappropriate use of data. More here ...
	Data Literacy In the Mathematics module students learn several important ideas in data literacy. They reinforce their skills in using charts and graphs, which were also the focus of social studies. Students explore how different measures can lead to different conclusions, and understand the importance of creating and using appropriate measures. Students also recognize when the data required to make a data-based argument is not available, a key component of recognizing when data are being misused in an argument. More here ...
	PFL The Math module is the learn part of PFL, and students come into math prepared to learn about proportionality. In social studies students attempted to create a “fair” water distribution in the Tigris/Euphrates watershed. The arguments created in Social Studies are typically underdeveloped, and not based on proportional measures. Students see the limitations of such arguments in Math class and are then motivated to create fair measures that take into account both population and the amount of available water. While students may still struggle as they attempt to create these measures in Math, there will be a time that they are told how to create a per capita measure. They then use similar measures in a variety of contexts. More here ...
	Argumentation The Mathematics module has students evaluate and create data-based arguments based on three aspects of argumentation: 1. Does the argument use accurate and factual data, and correct calculations using such data? 2. Does the argument use relevant data? and 3. Is the argument complete? This argumentation framework is the foundation for the development of persuasive arguments in the English Language Arts project. More here ...