In this lesson, students will use an investigation to explore rational functions. Students will formalize their understanding of a rational function and continue to investigate the relationship between the equation of a simple rational function and its graph. Read more »
Investigating Graphs of Rational Functions
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In this lesson, students will learn about the concepts of growth mindset and neuroplasticity, how to identify their own mindsets, and methods to change them. Students will play through Advance U: The TALENT Machine, a digital game-based learning (DGBL) module, to explore these concepts in an interactive... Read more »
Mindset and Neuroplasticity
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In collaborative groups, students will work to understand and create point-of-view statements, such as tweets for a mock Twitter debate, for both Federalists' and Anti-Federalists' viewpoints on ratifying the U.S. Constitution. Then, students will identify important issues currently being debated on... Read more »
Ratification of the Constitution Debate
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In this lesson, students will learn the relationship between position, velocity, speed, and acceleration to solve real-world problems involving motion along a line. Students are expected to know the chain rule and how to find higher-order derivatives for both power and trigonometric functions before... Read more »
Connecting Position, Velocity, and Acceleration
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In this lesson about the Emancipation Proclamation and expanding the goals of the Civil War, students will analyze the Emancipation Proclamation in comparison to an excerpt from President Lincoln's first inaugural address. Students will work in groups using a Card Sort strategy and Paired Text Analysis... Read more »
Expanding the Goals of the Civil War
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This lesson focuses on the properties of real numbers, properties of equality, and inverse operations to help students solve linear equations. The goal is for students to understand the fundamentals of isolating a variable. Students will then be able to solve two-step equations by applying properties... Read more »
Solving Two-Step Equations
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In this lesson, students will build on their prior knowledge of solving equations to learn how to solve absolute value equations. Students will then compare and contrast the four types of equations: two-step, multi-step, literal, and absolute value equations. This is the fourth lesson of four in the... Read more »
Absolute Value Equations
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This lesson focuses on the properties of real numbers, properties of equality, and inverse operations to help students solve linear equations on a deeper level. The goal is for students to understand the fundamentals of isolating a variable and to apply that knowledge to more complex problems. Students... Read more »
Solving Multi-Step Equations
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In this lesson, students will explore different research methods used by sociologists. Students will work in groups to analyze different readings and summarize what they have read. To extend their learning, students will create visual representations of the different research methods to display across... Read more »
The Foundations of Sociology
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In this geometry lesson, students will recall vocabulary about a circle, use their knowledge of midpoint and distance formulas to write the equation of a circle, and explore the connection between the equation of a circle and the Pythagorean Theorem. This is a multimodality lesson, which means it includes... Read more »
Writing the Equation of a Circle
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This lesson focuses on how to analyze and solve systems of linear equations by using the graphing method. The goal is for students to use prior knowledge to expand their understanding of equations and how they connect to real-world scenarios. Students will be able to identify, solve, and write equations... Read more »
Systems of Linear Equations: Graphing
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In this lesson, students will be introduced to imaginary numbers and their history. Students will learn how to simplify the square root of a negative number and how to simplify i to a power. Before beginning this lesson, students need to (1) know how to simplify the square root of a whole number and... Read more »
Understanding and Simplifying Imaginary Numbers
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Systems of Linear Equations: Substitution and Elimination
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This lesson focuses on how to analyze and solve systems of linear equations by using the substitution and elimination methods. Students will use their prior knowledge of the components of a system to solve problems algebraically. Students will identify, solve, and write equations using substitution... Read more »
Systems of Linear Equations: Substitution and Elimination
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To complete this lesson, students need to know how to simplify the square root of a negative number and how to simplify i to a power.* This lesson is contained within an escape room. Students will navigate through a spaceship and, along the way, will perform operations on complex numbers so they can... Read more »
Operations With Complex Numbers
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In this lesson, students will engage in several activities to understand Machiavelli's political writing, "The Prince." Students analyze excerpts from "The Prince," view a video about Machiavelli, participate in an activity to examine Machiavellian characteristics, and have a class debate about the... Read more »
The Political Thought of Machiavelli
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In this lesson, students will recall properties of exponents and how to simplify square roots and cube roots. Then, students will learn how to write radical expressions as expressions with rational exponents and vice versa. Students will use this knowledge to simplify expressions using either approach.... Read more »
Rewriting Rational Exponents and Radicals
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In this lesson, students will recall solving quadratic equations and rewriting radical expressions as expressions with rational exponents and vice versa. Students will learn how to solve equations with rational exponents and radicals. Then, students will apply this new knowledge to both mathematical... Read more »
Solving With Rational Exponents and Radicals
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In this lesson, students will recall solving equations with rational exponents and radicals. Using graphs, students will recall evaluating and solving equations with function notation. Students then will learn how to address extraneous solutions and why they exist. Students will apply this new knowledge... Read more »
Extraneous Solutions
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In this lesson, students will use their knowledge of domain and range to match pictures of graphs of rational functions with their corresponding domains and ranges. Students will learn about asymptotes, including what they are and how to find vertical and horizontal asymptotes of rational functions.... Read more »
Graphing Rational Functions
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In this lesson, students will work with rational functions that have 0, 1, or 2 vertical asymptotes and 0 or 1 horizontal asymptotes. Students will explore the relationship between the equation and graph of a rational function, learn what causes different types of asymptotes, and apply their knowledge... Read more »
Graphing Rational Functions
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In this lesson, students will discover how to evaluate logarithms and use that knowledge to write equations in logarithmic and exponential forms. Students will learn how to solve exponential equations with and without using logarithms and then apply their knowledge to solve real-world problems involving... Read more »
Solving Exponential Equations
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In this lesson, students will discover properties of logarithms. Students will use the properties to work through a proof of the change of base formula, to solve logarithmic equations, and to evaluate logarithmic expressions. Prerequisites for this lesson include solving exponential equations using... Read more »
Solving Logarithmic Equations
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In this lesson, students will learn how to graph and analyze piecewise functions. The piecewise functions in this lesson will have a maximum of three branches, which could contain any combination of linear, quadratic, and exponential branches. (Note: This lesson is written so that it could be taught... Read more »
Graphing and Analyzing Piecewise Functions
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In this lesson, students will use their knowledge of functions and function notation to perform basic operations on functions. Students will learn how to find domain restrictions caused by function operations. This lesson should be taught after students learn about radical functions, as using notation... Read more »
Basic Operations and Domain Restrictions
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In this lesson, students are introduced to function composition through a real-world scenario and pattern recognition. Students will learn composition notation and review domain restrictions caused by function operations. Students will use function composition to determine if functions are inverses.... Read more »
Function Composition
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In this lesson, students will recall expanding polynomials and factoring quadratics. Students will learn how to factor polynomials with two, three, or four terms: difference of two squares, sum or difference of two cubes, trinomials of the quadratic form that are not quadratics, and grouping. Students... Read more »
Factoring Polynomials
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In this lesson, students discover the attributes of three systems of government by discussing advantages and disadvantages of each type, sorting characteristics of each type, reflect on potential issues faced by citizens living under each type of system, and summarize their learning by giving each system... Read more »
Unitary, Federal, and Confederal Systems
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