Modeling Pooled-Sample Testing, Part I (Modeling Module)

COMAP presents a series of modules designed for teaching mathematics through the modeling of real-world phenomena. Most modules are suitable for use in high school classes, and some can be used in middle school, undergraduate courses, and in teacher education.

These modules are free to download and use in classrooms. Teachers have our permission to copy and distribute the student pages in their classes.

Each module in the series is built around several classroom activities. Each module includes student activity pages, teaching notes, and answers. Teaching notes and answers are in two-column format at the beginning of the module. Student activity pages are in full-page format at the end of the module.

Since technology plays a key role in mathematical modeling, most modules in this series offer opportunities to apply one or more forms of technology, such as graphing calculators and/or online graphing utilities, spreadsheets, and geometric utilities.

The context for this Modeling Module involves pooled-sample testing for diseases or drug usage in order to reduce costs and/or conserve resources used in testing. This is a two-part series. In Part I, students develop models for twosample pooled testing based on data they collect from simulations. In Part II, students develop two-sample, pooled-testing models from theory. Their theory-driven models confirm the form of the models developed in Part I. In addition, in Part II students develop models that involve pooling more than two samples. The materials for this Module are adapted from Testing 1, 2, 3, a unit in COMAP's secondary school core curriculum Mathematics: Modeling Our World (MMOW).

A Preparation Reading introduces the topic by describing several situations in which samples are pooled before testing for diseases or drug usage. One of the situations is the use of pooled-sample testing for COVID-19 in Massachusetts public schools. COVID testing in schools will serve as the main context for this module.

Prerequisites:

Students should be familiar with linear, quadratic, and exponential functions. They should have some experience assessing whether a model (linear, quadratic, or exponential model) is suitable for representing a particular dataset. In addition, students should be able to find the solutions to linear and quadratic inequalities (either using algebra or from graphs).

Students should be familiar with finding the average of a dataset. In this module, students will need to calculate weighted averages. If that is a new topic, you can introduce weighted averages in Activity 1 (See Lesson Notes, Activity 1, question 5).