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45-45-90 Triangles

To learn the pattern of the side lengths of a 45-45-90 triangle, students complete a gallery walk, a card sort activity starting with using the Pythagorean theorem, and activity to locate if there is an error in a presented problem and if so to identify what the error is.

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6.08 Bonus Video: Law of Sines—The Ambiguous Case

The Law of Sines can be used to solve for sides and angles of oblique triangles. However, in some cases more than one triangle may satisfy the given conditions. We refer to this as an ambiguous case.

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Study Edge Precalculus

Precalculus is the preparation for calculus. The course approaches is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations. Precalculus can deepen students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students will investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems (TAC §111.42(b)(3)).

This video book is brought to you by TEA and Study Edge. It may be used to teach an entire Precalculus course or to supplement traditional Precalculus textbooks.

This open-education-resource instructional material by TEA is licensed under a Creative Commons Attribution 4.0 International Public License in accordance with Chapter 31 of the Texas Education Code.

Please provide feedback on Study Edge's open-education resource instructional materials.

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TEA AP^{®} Physics 1: Algebra-Based

^{®}Physics 1: Algebra-Based

*AP ^{®} Physics* is the result of an effort to better serve teachers and students. The textbook focuses on the College Board’s AP

^{®}framework concepts and practices.

The AP^{®} Physics curriculum framework outlines the two full-year physics courses AP^{®} Physics 1: Algebra-Based and AP^{®} Physics 2: Algebra-Based. These two courses focus on the big ideas typically included in the first and second semesters of an algebra-based, introductory college-level physics course. They provide students with the essential knowledge and skills required to support future advanced coursework in physics. The AP^{®} Physics 1 curriculum includes mechanics, mechanical waves, sound, and electrostatics. The AP^{®} Physics 2 curriculum focuses on thermodynamics, fluid statics, dynamics, electromagnetism, geometric and physical optics, quantum physics, atomic physics, and nuclear physics. AP^{®} Science Practices emphasize inquiry-based learning and development of critical thinking and reasoning skills. Inquiry-based learning involves exploratory learning as a way to gain new knowledge. Students begin by making an observation regarding a given physics topic. Students then explore that topic using scientific methodology, as opposed to simply being told about it in lecture. In this way, students learn the content through self-discovery rather than memorization.

The AP^{®} framework has identified seven major science practices, which are described using short phrases that include using representations and models to communicate information and solve problems, using mathematics appropriately, engaging in questioning, planning and implementing data collection strategies, analyzing and evaluating data, justifying scientific explanations, and connecting concepts. The AP^{®} framework’s Learning Objectives merge content with one or more of the seven science practices that students should develop as they prepare for the AP^{®} Physics exam. Each chapter of AP^{®} Physics begins with a “Connection for AP^{®} Courses” that explains how the content in the chapter sections align to the Big Ideas, Enduring Understandings, Essential Knowledge, and Learning Objectives of the AP^{®} framework. These sections help students quickly and easily locate where components of the AP^{®} framework are covered in the book, as well as clearly indicate material that, although interesting, exceeds the scope of the AP^{®} framework. Content requirements for AP^{®} Physics are prescribed in the College Board Publication Advanced Placement Course Description: Physics, published by The College Board (http://ritter.tea.state.tx.us/rules/tac/chapter112/ch112d.html#112.64) and (http://ritter.tea.state.tx.us/rules/tac/chapter112/ch112d.html#112.65).

This open-education-resource instructional material by TEA is licensed under a Creative Commons Attribution 4.0 International Public License in accordance with Chapter 31 of the Texas Education Code.

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TEA AP^{®} Biology

^{®}Biology

*AP ^{®} Biology* covers the scope and sequence requirements of a typical two-semester biology course for AP

^{®}students. The text provides comprehensive coverage of foundational research and core biology concepts through an evolutionary lens. AP

^{®}Biology was designed to meet and exceed the requirements of the College Board’s AP

^{®}Biology Framework, while allowing significant flexibility for instructors. Each section of the book includes an introduction based on the AP

^{®}curriculum as well as rich features that engage students in scientific practice and AP

^{®}test preparation. It also highlights careers and research opportunities in the biological sciences. Content requirements for AP

^{®}Biology are prescribed in the College Board Publication Advanced Placement Course Description: Biology, published by The College Board (http://ritter.tea.state.tx.us/rules/tac/chapter112/ch112d.html#112.62).

This open-education-resource instructional material by TEA is licensed under a Creative Commons Attribution 4.0 International Public License in accordance with Chapter 31 of the Texas Education Code.

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5.01 Radians and Degree Measurements

In this video, students will learn the basics of angle measurements, definitions of various types of angles, radians and degrees, along with arc length and area of a sector.

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5.02 Linear and Angular Velocity

In this video, students will learn about angular and linear velocity and how each relates to unit conversions.

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5.03 Trigonometric Ratios

In this video, we will define the trigonometric ratios in terms of the sides of a right triangle.

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5.04 Trigonometric Angles and the Unit Circle

In this video, students will learn special angles and the unit circle, and learn how to apply them.

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5.05 Graphs of Sine and Cosine

In this video, students will learn how to graph sine and cosine and how to interpret graphs of sine and cosine.

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5.06 Graphs of Secant and Cosecant

In this video, students will learn how to graph and interpret graphs of secant and cosecant, and how secant and cosecant relate to sine and cosine.

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5.07 Graphs of Tangent and Cotangent

In this video, students will learn how to graph and how to interpret graphs of tangent and cotangent.

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5.08 Inverse Trigonometric Functions and Graphs

In this video, students will explore the relationship between trigonometric functions and their inverses.

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Drawing Conclusions about Three-Dimensional Figures from Nets

Given a net for a three-dimensional figure, the student will make conjectures and draw conclusions about the three-dimensional figure formed by the given net.

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8.01 Conic Sections

In this video, students will learn the definition of a double-napped cone, and how conic sections are formed at the intersection of a plane and a double-napped cone.

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8.02 Ellipses

In this video, students will learn the analytic definition of an ellipse, the standard form of the equation of an ellipse, and how to graph ellipses.

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8.03 Hyperbolas

In this video, students will learn the analytic definition of a hyperbola, the standard form of the equation of a hyperbola, and how to graph hyperbolas.

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8.05 Polar Coordinates and Equations

In this video, students will learn about the polar coordinate system and how to convert to and from the rectangular coordinate system.

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8.06 Polar Graphs

In this video, students will learn how to graph polar curves.

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8.07 Special Polar Graphs

In this video, students will learn the equations and graphs of special polar curves.