Modeling Pooled-Sample Testing, Part I

The context for this Modeling Pull-Out 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 Modeling Pull-Out 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 Pull-Out.

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 Pull-Out, 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).