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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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8 Chapter 5: Introduction to Trigonometry and Graphs

In this chapter, we will explore angle measures and the trigonometric ratios, including graphing and inverses.

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5 Chapter 7: Sequences and Series

In this chapter, we introduce sequences and series, some of their applications, and the Binomial Theorem.

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3 Chapter 4: Systems of Equations

In this chapter, we will explore the methods used to solve systems of equations, and real-world situations involving systems of equations.

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6 Chapter 2: Polynomial and Rational Functions

In this chapter, we will explore beyond linear functions and learn about polynomial and rational functions.

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8 Chapter 6: Trigonometric Identities and Applications

In this chapter, students will learn a robust list of trigonometric identities along with their applications. Students will also be introduced to vectors.

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7 Chapter 8: Conic Sections, Parametric Equations, and Polar Coordinates

In this chapter, we introduce conic sections, parametric equations, and polar coordinates.

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5 Chapter 1: Introduction to Functions and Graphs

In this chapter, students are introduced to lines, functions, and graphs of functions.

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8 Chapter 3: Exponential and Logarithmic Functions

In this chapter, students are introduced to exponential and logarithmic functions. Students will learn about the functions' graphs, how to solve equations involving those functions, and their real-world applications.

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Using Logical Reasoning to Prove Conjectures About Quadrilaterals

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

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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.

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Determining Area: Regular Polygons and Circles

The student will apply the formula for the area of regular polygons to solve problems.

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Making Conjectures About Circles and Angles

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 of and relationships among the resulting angles.

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Solving Problems With Similar Figures

Given problem situations involving similar figures, the student will use ratios to solve the problems.