# 2020 Sessions and Slides

# 2020 Sessions

# Descriptions and Slides

### Pythagoras, Music, and the Mathematics of Harmony, Greta Mills, Oxbridge Academy

How can we use mathematics to create sound? In this session we will look at the difference between Pythagorean tuning and equal temperament, creating a 12-tone scale using simple ratios. Exponential and trigonometric functions can be combined to synthesize the sound of a xylophone—will you be able to hear the difference?

https://drive.google.com/file/d/0B3jbuzH_9GyMZVlJXzExLVFuOEtnd3MxWmtKS3NpS1htZVU4/view?usp=sharing

### What I learned about teaching math from teaching flying (and vice-versa), Philip Rash, NCSSM

How is teaching someone how to fly an airplane similar to teaching someone mathematics? As I've discovered in the past year and a half (since earning my flight instructor certificate), they have more in common than you might realize! In this session I'll briefly overview the process involved in earning a pilot certificate and share some reflections on the similarities between flight instruction and teaching mathematics.

### Where in the World is San Diego? Ryan Pietropaolo, NCSSM

This session will utilize concepts of arc length, radian measure, and basic trigonometry to solve questions relating to earth measurements. For example, “Describe the points on the earth’s surface that can be seen from a space station that is 100 miles above the North Pole” and “What is the Earth’s rotational speed at a site whose latitude in θ degrees?”. This is a great opportunity to introduce Trigonometry applications that are literally, out of this world.

### Mathematics with Python, Mahmoud Harding, NCSSM

Participants will learn how to use Python to enhance learning. Examples will include, data visualization, regression models, and explorations in set theory and probability.

https://drive.google.com/file/d/13pTx5w14FApjN3VOIgUzxYqeo8rODQ38/view?usp=sharing

### Introduction to Desmos Activities, Nick Koberstein and Christine Belledin, NCSSM

Did you know that Desmos can do more than just graphing? In this session we will explore ways to use Desmos Activities to enhance learning in your classroom. We will share activities that range in content from Algebra to Calculus and Statistics, demonstrate how to edit and improve activities already available, and show how the teacher tools can help guide and promote student engagement. For a more advanced session, join us for Taking Desmos to the Next “Layer” where we focus on creating new Desmos Activities.

### Taking Desmos to the Next “Layer," Christine Belledin and Nick Koberstein, NCSSM

If you are using Desmos Activities in the classroom and want to learn to create your own activities or improve those that you already use, this session is for you! We will highlight some of the tools available to you including the Computational Layer and discuss best practices for creating engaging and effective activities. Examples will range in content from Algebra to Calculus and Statistics. Bring your laptop and you’ll leave this session ready to build your own collection of activities!

### Reaching Beyond Algebra II, Exploring Non-Traditional Mathematics Topics, Tamar Avineri and Ashley Loftis, NCSSM

In this active learning session, we will focus on topics that may appear in courses beyond Algebra II, such as set theory, number theory and logic. We will spend the majority of our time working collaboratively on relevant tasks pertaining to these topics, and participants will walk away with resources they can implement in their classrooms. These topics can be found in the new North Carolina Discrete Mathematics course, launching in 2020, but participants outside of North Carolina are also very much encouraged to attend.

### Applications of Taylor Polynomials and Taylor Series , Dan Teague, NCSSM

The section in BC Calculus on Taylor series is one of the most challenging to teach. The concepts are very different from what has come before and, since it is at the end of the course, there is no opportunity to apply the ideas to see why they are important (application of Taylor series is not a part of the AP exam). In this presentation, we will see applications of Taylor series to mathematical modeling, differential equations, numerical analysis, number theory, combinatorics, and network theory.

https://drive.google.com/file/d/0B3jbuzH_9GyMRG5fSTVIZTM2eklGOEVRdlR2MHBIQ1Q1X244/view?usp=sharing

https://drive.google.com/file/d/0B3jbuzH_9GyMYUpFekJsTnRxRGlBMm9ZbjlBMGN1NDIyQU93/view?usp=sharing

### What is an Artificial Neural Network? Dan Teague, NCSSM

It seems that every day brings a new application of artificial neural networks, of “learning machines” and artificial intelligence, that are increasingly supporting modern life. From self-driving cars, to identification of snow leopards, to diagnosing disease from odors, inspecting foods, speech recognition, and a vast array of other areas, neural networks are there (most commonly without our knowledge). So, what makes them work? How, and in what way, can a computer program learn? This presentation is a basic introduction to some of the big ideas and fairly simple mathematics that is the foundation of neural networks.

https://drive.google.com/file/d/0B3jbuzH_9GyMTXVLQVRRSnlfdnpYTTJuejlqel9VN1hObTVN/view?usp=sharing

### Who's Doping? Optimizing the Number of Blood Tests, Maria Hernandez, NCSSM

Engage your students with a (COMAP) modeling problem that connects math concepts from Algebra to Multi-Variable Calculus. Suppose that you have a large population you wish to test for a certain characteristic in their blood or urine (for example, testing all NCAA athletes for steroid use or all US military personnel for a particular disease). Since the number of individuals to be tested is quite large, we can expect that the cost of testing will also be large. How can we reduce the number of tests needed and thereby reduce the costs?

### Biocalculus: Crossing the Discipline Divide, Cheryl Gann, NCSSM

NCSSM is currently developing a semester-long non-AP calculus course that will focus on biological applications. The emphasis in this course is on understanding many of the big ideas of calculus through discovery labs and the use of technology, with less emphasis on algebraic manipulation. In this session we will look at an outline of the course as well as sample problems and projects focusing on mathematical modeling of biological systems. The problems shared would also fit well in a more traditional calculus course.

### Math CSI: Solving Crimes and Engaging Students, Veronica Vazquez, NCSSM

In this session you will explore two activities in which students are asked to solve fictional murders by taking some measurements and making some calculations. In one, students use Newton's Law of Cooling to determine a time of death and possibly exonerate one or more suspects. In another, students use similar triangles and proportions (or right triangle trigonometry) to locate the position of suspect at the time of the murder and collect evidence from the scene.

https://drive.google.com/file/d/0B3jbuzH_9GyMNE5TTWZzMTlmU3BLMXlteXdVRzR0emJGeVFz/view?usp=sharing

https://drive.google.com/file/d/0B3jbuzH_9GyMZjVfR0czNFNzbVAzSHZQejNxSmE3S2FOOHBF/view?usp=sharing

https://drive.google.com/file/d/0B3jbuzH_9GyMbDdtY0tFaUU3VHYzM3RrU2ZIeEp4RU45R0U0/view?usp=sharing

https://drive.google.com/file/d/0B3jbuzH_9GyMSkxPcHpWT0tYNlVXVXUxbm5zQW54MWpab3VJ/view?usp=sharing

https://drive.google.com/file/d/1ST9yeJz6FhcUycokBmNFyPPCT-9TlxS0/view?usp=sharing

### When Should You Replace Your Car? A Modeling Problem for Precalculus Students, Floyd Bullard, NCSSM

In this session we'll look at the particular problem that's in the title and one possible solution will be shared. But the main subject of the session will be finding "entrance ramps" to mathematical modeling for students with different levels of previous experience. The scaffolding that we give to less experienced students reflects just the sort of thinking process we want our more experienced students to go through unprompted.

https://drive.google.com/drive/folders/1a0HQr8QM5U-zT-7VA_BjCcXa0yuhS39K

### Mathematical Expeditions in Polar Science, Lynn Foshee Reed, Maggie L. Walker Governor's School

There are multidisciplinary challenges facing our planet, and polar science provides particularly interesting contexts to engage students. The session will focus on a mathematics lesson based on shrinking Arctic sea ice extent. If time permits, additional lessons on measuring the discharge of a melt water stream and using geometric models to calculate the mass of blubber from field measurements of a Weddell seal.

https://drive.google.com/file/d/0B3jbuzH_9GyMSm9zMjRiYXRJemp5dVZPSW1uWVczOVZwcWM4/view?usp=sharing

https://drive.google.com/file/d/0B3jbuzH_9GyMdGk1dmJROFpvcmZTQVNWamc2Mkdqd1EzTXZz/view?usp=sharing

https://drive.google.com/file/d/0B3jbuzH_9GyMTTJwWWxpZFdUdXE0dlJlZm9URnZHNVEzTFM4/view?usp=sharing

https://drive.google.com/file/d/0B3jbuzH_9GyMT3hsZWoza0NqZFhKWHZUWTRscW1UakotX2dj/view?usp=sharing

### Bridging Communities of Practice: The Role of Mathematics Educators in Advocacy, Discourse, & Capacity Building, Tracie McLemore Salinas Appalachian State University

Mathematics education is foundational to recent pushes in twenty-first century thinking and growing a STEM economy, yet as a community, we are not necessarily equipped to engage in conversations and actions that impact policy and practice. In this talk, we take an educational change perspective to the role of mathematics educators and mathematics teacher educators and how we can become better advocates, influencers, and capacity builders for mathematics teaching and learning.

### Pat, Alex and Sam's Financial Adventure, Annalee Salcedo, Cate School

Pat, Alex, and Sam are triplets who land the same job with the same salary and the same yearly bonus. But each decides to invest their money differently. Who is better off when it comes time to retire? We will explore this classic modeling problem using current tools like Excel/Google Sheets and Desmos and watch excerpts of student "video write-ups" of this project to see what choices they made during the modeling process. Participants will leave the session with fully worked up teacher notes and student handouts that are classroom ready. Math content includes exponential growth, arithmetic sequences, geometric series.

### Mathematical Language Routines: Cultivating Conversation in High School Classrooms, Jennifer Wilson, Illustrative Mathematics

Math language routines simultaneously support students in language development and sense-making of mathematical content. During this session, we will experience math language routines to see how they support communication, understanding, and community building.

### Discrete Math: Let's Develop Algorithmic Thinking Through Real World Problems, Ginger Rhodes, University of North Carolina at Wilmington

Computers have changed our world in significant ways, including how we explore and solve mathematics problems. Discrete mathematics provides a foundation for understanding computer science. In discrete mathematics we develop and compare algorithms. At the core of solving problems with computers are algorithms. In this session we will examine the real-world problems in discrete mathematics that provide opportunities to develop algorithmic thinking.

### Using CODAP for Data-Intensive Statistics Lessons in Advanced High School Classes, Hollylynne Lee, North Carolina State University.

Bring your laptop or tablet for a hands-on session to learn to use advanced features of CODAP to teach advanced modeling and statistics topics. CODAP is a free web-based data tool that can integrate easily into your classroom.

### CodeR4Math: Power up student modelers with R, Ben Galluzzo, Clarkson University

The CodeR4Math (Computing with R for Mathematical Modeling) project develops classroom ready math modeling activities that support computing needs that are often discovered while engaging in real world problem solving. Bring your laptops to this session in which we’ll use web-based R to create, visualize, and analyze math models. We’ll also view sample student work and investigate how to use CodeR4Math tools to build classroom specific lessons.