These teaching materials were were developed in close collaboration with high-school teachers. The materials are self-contained modules that can be used in high school curriculum. The generous support of the National Science Foundation DMS-1845406 made these modules possible. If you do use them in your classes, I'd love to hear about your experience! Please send me an email at asaibab AT ncsu DOT edu.

## Materials from 2021 Workshop

The materials from this year focussed on Network Science and Graph Theory.

### 1. Social Networks

In this module, students will learn the basics of network science and how to apply them to social networks. Students will start by learning a general overview of the vocabulary of network science and graphs. In the next lesson, students will learn or review information on graph theory, matrices, and adjacency matrices by participating in engaging Desmos activities. After students have established an understanding of the background information they will investigate the Friendship Paradox by calculating a weighted average for a small network. Finally, students will learn about the Small World Effect by participating in interesting games and calculating the average geodesic distance for small networks.

- Google document.
- PDF document.
- Desmos activities Intro to Graph Theory, Adjacency Matrices and Networks.
- Octave Extension.

### 2. Networks and Spread of Diseases

In this module, students will learn about disease spread and how mathematics is able to model this spread throughout a population. First, students will be given an introduction to network science and graphs. In the following lesson, they will be shown a simple exponential model that can be represented using a geometric series or logarithms. Next, students will be introduced to the SIR Model, which represents disease spread through transition graphs and matrix vector equations. Finally, students will explore disease spread through a variety of networks using random, small-world, scale-free, and complete networks via computer simulation.

- Google document.
- PDF document.
- Desmos activities Intro to Graph Theory, Adjacency Matrices and Networks, Markov Chains.
- Excel Sheet for SIR Model.
- Octave Extension.

## Materials from 2020 Workshop

The materials from this year focussed on Matrices and Linear Algebra.

### 1. The mathematics of ranking

In this module, students will engage in activities that apply their knowledge of matrices to the study of ranking. Specifically, students will study Colley’s Method of Ranking in various contexts and apply it to a problem that they design in a culminating assignment. The module begins with lessons on elementary matrix operations and then continues with an introduction to the Method through a lesson plan, guided notes, and a problem set. The lesson is followed by a class activity to collect data and apply Colley’s Method to that data. The module concludes with a group project in which students work with real-world data to apply their knowledge and communicate their understanding in writing.

### 2. Image Processing

In this all-inclusive module students will learn how to use matrices and vectors to manipulate and edit images. The students will be provided with their own image editing activity where they will create their own classroom "Instagram feed." There is also an extension activity that incorporates some basic Python programming into this module.

### 3. X-Ray Imaging, Mathematics, and Puzzles

In this module, students will learn about x-ray imaging and how mathematics plays a role in generating the images that we obtain using x-ray devices. First, students will be given lessons on matrix operations including adding, multiplying, and Gaussian Elimination. Students will participate in several games/puzzles such as Kakuro and Nonograms. The strategy used in these games parallel the mathematical techniques used in generating images from x-ray devices. The students will read an article that ties x-ray imaging to mathematics and participate in a discussion.