# STEM

## Science, Technology, Engineering, Mathematics

Mission: STEM at Trinity Hall is studied by a student-centered, inquiry-based interdisciplinary approach that encourages active participation, collaboration, and 21st century skills. Students are empowered to take ownership of the material, making connections on their own and sharing their insights (and questions) with the group. This move from a lecture-based model to a collaborative approach challenges students to become risk-takers and transforms their analytical and research skills, preparing them for a lifetime of problem-solving.

Core Beliefs: The Trinity Hall STEM Team adopts the following core beliefs:

- Scientific experimentation is a powerful tool to engage students in both the content and processes of science by providing a practical perspective and logical connection to theoretical concepts.
- Algebra skills are critical for modeling and problem-solving, and a deep, conceptual understanding of the algebra fundamentals is necessary to develop a solid foundation for all upper-level coursework.
- Geometry (in two and three dimensions) should be integrated across topics at all levels and include coordinate and transformational approaches.
- The study of discrete mathematics (including vectors, matrices, probability, combinatorics, and statistical data analysis) should be integrated into core courses.
- Computer and calculator-based activities, including basic coding, are fundamental to the experience of our courses.
- All concepts should be explored graphically, numerically, analytically, and verbally.
- Developing a wide range of problem-solving strategies is central to all courses so that students will welcome and be prepared for new challenges whose outcomes are unknown.

## Science:

**GRADE 9: Physics I**

This first-year physics course will focus on introducing students to the language of physics as well as the motion of bodies, both large and small. Models and graphical analysis are used to explain the phenomena of motion. Hands-on explorations using math and technology are incorporated to gain well-rounded knowledge of physics concepts. Students will accumulate data, construct graphs and develop mathematical models to describe the physical world. Lab activities are designed to develop skills in experimental design and data analysis.

**GRADE 10: Chemistry I**

This course will focus on developing an awareness of chemistry as an integral part of everyday lifeby building a proficiency in critical and creative thinking. Students will acquire a clear understanding of key chemistry concepts and skills, and master important processes and safety techniques through laboratory investigations. Inquiry-based methods for delivering content will enhance their learning of basic and advanced facts, formulas, and foundational principles of chemistry.

**GRADE 11/12: Biology I**

This course focuses on the universal processes and concepts that underlie all forms of life, from bacteria to humans. The use of modeling and guided inquiry helps students to explore and connect biological ideas with those in chemistry and physics and gives students a deep understanding of these universal and foundational biology concepts. Students will be challenged to explore how life works at the cellular and systemic level, to analyze the role of DNA in living things and the impact of biotechnology on our world, and to consider both the unity and diversity of organisms in the biosphere. Students will also gain the skills needed to be able to independently explore biological questions through well-designed controlled experiments, the use of specialized lab equipment, and critical thinking

**GRADE 11/12 Elective: AP Chemistry**

AP Chemistry builds upon Honors Chemistry in both breadth and depth, providing students with a college level chemistry course that follows the College Board’s curriculum. A focus is placed on understanding the evidence for chemical phenomena and the connections between themes (big ideas) to promote a solid understanding of the content. Our core methodologies are employed to ensure that students gain an understanding of the content in a way that allows them to apply their knowledge of chemistry to solve unfamiliar complex problems, preparing them for the AP exam and any future studies in chemistry.

**GRADES 11/12 Elective: AP Physics C **

This calculus-based college-level physics course challenges students to think about and model natural phenomena. Students will advance their understanding of kinematics, forces, and energy and discover new concepts in systems of particles and linear momentum, circular motion and rotation, oscillatory systems, and gravitation. Explorations will allow students to independently and collaboratively develop scientific reasoning to encounter and analyze complex scenarios using mathematical models, multiple representations, experimental design, and data analysis. Discussions and whiteboard presentations allow students to propose new ideas, present solutions, challenge misconceptions, ask productive questions of one another, and make connections among and across topics.

*Prerequisite/Corequisite: AP Calculus

**GRADE 12 Elective: AP Biology**

This course focuses on the universal processes and concepts that underlie all forms of life, from bacteria to humans. The use of modeling and guided inquiry helps students to explore and connect biological ideas with those in chemistry and physics and gives students a deep understanding of these universal and foundational biology concepts. Students will be challenged to explore how life works at the cellular and systemic level, to analyze the role of DNA in living things and the impact of biotechnology on our world, and to consider both the unity and diversity of organisms in the biosphere. Students will also gain the skills needed to be able to independently explore biological questions through well-designed controlled experiments, the use of specialized lab equipment, and critical thinking

**GRADE 12 Elective: AP Environmental Science**

*From College Board: *The AP Environmental Science course is designed to be the equivalent of a one-semester, introductory college course in environmental science, through which students engage with the scientific principles, concepts, and methodologies required to understand the interrelationships within the natural world. The course requires that students identify and analyze natural and human-made environmental problems, evaluate the relative risks associated with these problems, and examine alternative solutions for resolving or preventing them. Environmental science is interdisciplinary, embracing topics from geology, biology, environmental studies, environmental science, chemistry, and geography.

*Prerequisite: Honors Biology

**GRADE 12 Elective: Anatomy & Physiology **

This is an introductory course to human anatomy and physiology that complements what is learned in honors biology by examining how the foundations of biology come together in the human body. It aims to give students a better appreciation and understanding of the complexity of the human body that can benefit all students. We will examine the major body systems, how they contribute to homeostasis and how their functions are connected and coordinated to keep a person healthy as well as what can happen when this fails. Students will gain an understanding of the relationship between the structure and function of each of the body systems and their components through numerous dissections and hands-on activities.

## Engineering:

### GRADE 9: Engineering I: Creative Design Process

This introductory course is designed to promote an understanding and appreciation of the engineering design process by giving the students the opportunity to develop skills and understanding of key concepts in design through activity-based and project-based learning. Using a teamwork approach, students will build their interpersonal skills while acquiring skills in research and analysis, communication methods, global and human impacts, and technical documentation.

### GRADE 10: Engineering II: Creative Design Theory

The second-year course will help students understand the field of engineering from a more detailed perspective, exploring how engineers use scientific principles to solve problems. Using activities, projects and problems, students model how engineers use math, science and technology in an engineering problem-solving process to benefit people. The course also addresses concerns about social and political consequences of technological change.

### GRADE 11: Engineering III: Innovative Design Technology

The third-year course is based on a model of learning that incorporates knowledge, research skills and design principles in problem-solving contexts. Students work in teams to design and develop an original solution to a valid open-ended technical problem by applying the engineering design process. At the same time it provides details about materials and processes, and develops secondary level knowledge and skills in mathematics, science, and technology.

### GRADE 12: Advanced Engineering

The final year of engineering is a specialized course designed to introduce students to the high-tech, innovative nature of modern manufacturing. Computer-aided manufacturing processes, product design, robotics, and automation are the core elements to this final course with project-based work using three-dimensional solid modeling software for problem solving. This capstone course will culminate in a major technical project that will incorporate experts from the field and a final presentation to an external panel.

### GRADE 11/12 Elective: Robotics

These comprehensive STEM electives allow students to progress from building and operating autonomous machines that execute tasks to their own robotics designs that interact with the environment in complex ways. Applying their knowledge of the engineering design process, electronics, programming, and mechanics, students will explore, build, code, and assess collaborative and individual designs to improve capability. Students will also learn how to use feedback from sensors, applied mathematics and measurement to program their robot to navigate distinct pathways. Valuable skills in problem-solving, iteration, innovation, and systems thinking will be honed in a fun and competitive setting.

## Mathematics

### GRADE 9: Mathematics I

This integrated course develops facilities in working with numbers, tables, equations and inequalities (linear and quadratic), coordinate geometry, exponents and radicals. The focus is on solving word problems and reading carefully, and thus the building of algebra and geometry skills arises naturally from context, instead of from drill-and-practice. Students learn how to use the TI-Nspire CX CAS graphing calculator as a problem-solving tool. In addition, students undertake various projects and hands-on labs (including ones in coordination with Grade 9 Physics) that require them to collect data, make conjectures, and draw conclusions.

### GRADE 9/10: Mathematics II

The second-year course is an intensive in geometry and Algebra 2 topics, focused on how geometry interplays with algebra. Students investigate lines, polygons, and vectors. Right-triangle trigonometry is developed, as are circles and parabolas. Linear motion is explored, leading to the use of parametric functions (requiring the frequent use of computers and graphing calculators). A dynamic vision of geometry is further encouraged by viewing similarity and congruence through transformations.

*Prerequisite: Successful completion of Mathematics I or by teacher placement

### GRADE 10/11: Mathematics III

This integrated pre-calculus course enables students to expand their view of algebra and geometry to include nonlinear motion and functions. The investigation encompasses circular motion and the trigonometric functions that describe it, ellipses and hyperbolas, exponential and logarithmic functions, dot products and matrices, and geometry on the surface of the Earth. Approximation behavior, especially instantaneous rates of change and slopes of nonlinear graphs, will end the course and lead to calculus.

*Prerequisite: Successful completion of Mathematics II or by teacher placement.

### GRADE 12 Elective: Mathematics IV: College Algebra and Statistics

This course is designed to strengthen and increase the understanding and application of algebraic and trigonometric concepts as well as introduce statistics. Students will continue to expand upon their knowledge of linear, quadratic, absolute value, logarithmic, exponential, and trigonometric functions to model authentic scenarios and problem solve. Students will also learn the major concepts and tools for collecting, analyzing and drawing conclusions from data to interpret results, provide written explanations, find patterns, and make decisions. The main objective is to provide students with the foundations in mathematics and statistics mostly used in a wide variety of disciplines.

### GRADE 12 Elective: Statistics

This course will introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. The fundamental purpose of this course is to explore the fundamental concepts of probability and statistics through exercises that require students to interpret results, provide written explanations, find patterns, and make decisions. The main objective is to provide students with the foundations of statistical inference mostly used in a wide variety of disciplines. The critical areas deepen and extend understanding of how to summarize, represent, and interpret data, and how to interpret linear models. In addition, students will be able to understand and evaluate random processes underlying statistical experiments, make inferences and justify conclusions from sample surveys, experiments, and observational studies, and use rules of probabilities to compute probabilities and evaluate outcomes.

### GRADE 11/12 Elective: Calculus

This course is a slower introduction to the main ideas in calculus. It strengthens students' understanding of functions so they are ready to explore rates of change, limits and continuity, differential calculus, and basic integration. Students will work within contexts to explore concepts, make connections, and use multiple representations to solve problems centered with a focus on their applications. Each class, students will collaborate to present their discoveries, thoughts, and proposed solutions and the subsequent discussions will develop both the theory and mathematical tools.

### GRADE 11/12 Elective: AP Calculus AB

This course uses a problem-based, student centered approach to learning single variable calculus. The curriculum covered is equivalent to that of a first semester college calculus course. Students will work within contexts to explore concepts, make connections, and use multiple representations to solve problems centered around limits and continuity, derivatives, and integrals with a focus on their applications. Each class, students will collaborate to present their discoveries, reasoning, and proposed solutions and the subsequent discussions will develop both the theory and mathematical tools. Throughout the year, students will write about the calculus ideas they encounter.

### GRADE 11/12 Elective: AP Calculus BC

This course uses a problem-based, student centered approach to extend knowledge of single variable calculus. The curriculum covered is equivalent to that of two semesters of college calculus. Students will work within contexts to explore concepts, make connections, and use multiple representations to apply the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions, develop additional integration techniques and applications, and study infinite sequences and series. Each class, students will collaborate to present their discoveries, reasoning, and proposed solutions and the subsequent discussions will develop both the theory and mathematical tools. Throughout the year, students will write about the calculus ideas they encounter.

*Prerequisite: Successful completion of AP Calculus AB

### GRADE 12 Elective: Independent Study in Multivariable Calculus and Differential Equations

This course extends single variable differential and integral calculus to functions of several variables and a variety of applications. Students will use their prior knowledge of calculus to investigate vectors, cylindrical and spherical coordinates, partial derivatives, level curves, gradients, optimization, multiple integration, Lagrange multipliers, and methods of solving differential equations as well as generalize the Fundamental Theorem of Calculus through Green’s theorem, Stokes’ Theorem, and Gauss’s theorem. Much work will be independently explored by the students in the course.

*Prerequisite: Successful completion of AP Calculus BC

### GRADE 11/12 Elective: AP Statistics

*From the College Board:* The AP Statistics course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes evident in the content, skills, and assessment in the AP Statistics course: exploring data, sampling and experimentation, probability and simulation, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics.