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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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TEA AP Biology PowerPoint Slides

Instructor PowerPoint slides for TEA AP Biology open-source instructional materials.

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TEA AP Biology Textbook PDF

TEA AP Biology Textbook PDF

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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^{®} 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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Using Logical Reasoning to Prove Conjectures about Circles

Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

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Creating Nets for Three-Dimensional Figures

Given nets for three-dimensional figures, the student will apply the formulas for the total and lateral surface area of three-dimensional figures to solve problems using appropriate units of measure.

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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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Generalizing Geometric Properties of Ratios in Similar Figures

Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.

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Determining Area: Sectors of Circles

Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.

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Making Conjectures About Circles and Segments

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.