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Extending the Domain of Sine and Cosine to All Real Numbers
Round and round we go! Pupils use reference angles to evaluate common sine and cosine values of angles greater than 360 degrees. Once they have mastered the reference angle, learners repeat the process with negative angles.
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Proving Trigonometric Identities
Young mathematicians first learn the basics of proving trigonometric identities. They then practice this skill on several examples.
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From Circle-ometry to Trigonometry
Can you use triangles to create a circle? Learners develop the unit circle using right triangle trigonometry. They then use the unit circle to evaluate common sine and cosine values.
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Graphs Can Solve Equations Too
There are many equations Algebra I students are not ready to solve. Graphing to solve gives them a strategy to use when they are unsure of an algebraic approach to solve the problem. The lesson exposes learners to a wide variety of...
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Solving Exponential Equations
Use the resource to teach methods for solving exponential equations. Scholars solve exponential equations using logarithms in the twenty-fifth installment of a 35-part module. Equations of the form ab^(ct) = d and f(x) = g(x) are...
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The Special Role of Zero in Factoring
Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...
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What Is a Trigonometric Identity?
Protect yourself from identity theft! Establishing a strong understanding of the Pythagorean identity allows learners to prove that sine^2x + cos^2x = 1. They then use the identity to find sine or cosine ratios given the other.
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Rational and Irrational Numbers
Back to the basics: learning how to add numbers. The 17th installment of a 35-part module first reviews addition techniques for rational numbers, such as graphical methods (number line) and numerical methods (standard algorithm). It goes...
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The Computation of the Slope of a Non-Vertical Line
Determine the slope when the unit rate is difficult to see. The 17th part of a 33-part series presents a situation that calls for a method to calculate the slope for any two points. It provides examples when the slope is hard to...
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The Slope of a Non-Vertical Line
This lesson introduces the idea of slope and defines it as a numerical measurement of the steepness of a line. Pupils then use the definition to compare lines, find positive and negative slopes, and notice their definition holds for...
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From Ratio Tables, Equations and Double Number Line Diagrams to Plots on the Coordinate Plane
Represent ratios using a variety of methods. Classmates combine the representations of ratios previously learned with the coordinate plane. Using ratio tables, equations, double number lines, and ordered pairs to represent...
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Linear Systems in Three Variables
Put all that algebra learning to use! Using algebraic strategies, learners solve three-variable systems. They then use the three-variable systems to write a quadratic equation given three points on the parabola.
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Trigonometry and the Pythagorean Theorem
Ancient Egyptians sure knew their trigonometry! Pupils learn how the pyramid architects applied right triangle trigonometry. When comparing the Pythagorean theorem to the trigonometric ratios, they learn an important connection that...
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Exploiting the Connection to Cartesian Coordinates
Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...
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Vectors and the Equation of a Line
Represent linear equations in both two and three dimensions using parametric equations. Learners write parametric equations for linear equations in both two and three variables. They graph and convert the parametric equations to...
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Modeling Relationships with a Line
What linear equation will fit this data, and how close is it? Through discussion and partner work, young mathematicians learn the procedure to determine a regression line in order to make predictions from the data.
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Algebraic Expressions—The Distributive Property
Do your classes truly understand the distributive property? Use a demonstrative lesson to represent the distributive property in various ways. Learners solidify understanding by creating a geometric pattern for distributive...
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Equivalent Rational Expressions
Rational expressions are just fancy fractions! Pupils apply fractions concepts to rational expressions. They find equivalent expressions by simplifying rational expressions using factoring. They include limits to the domain of the...
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Solving Rational Equations
What do fractions and rational expressions have in common? Everything! Learners use common denominators to solve rational equations. Problems advance from simple to more complex, allowing pupils to fully understand the material before...
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Multiplying and Factoring Polynomial Expressions (part 2)
If you can multiply binomials, you can factor trinomials! This is the premise for a lesson on factoring. Pupils look for patterns in the binomials they multiply and apply them in reverse. Examples include leading coefficients of one...
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Using the Quadratic Formula
What is the connection between the quadratic formula and the types of solutions of a quadratic equation? Guide young mathematicians through this discovery as they use the discriminant to determine the number and types of solutions,...
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The Most Important Property of Logarithms
Won't the other properties be sad to learn that they're not the most important? The 11th installment of a 35-part module is essentially a continuation of the previous lesson, using logarithm tables to develop properties. Scholars...
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Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
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Fundamental Theorem of Similarity (FTS)
How do dilated line segments relate? Lead the class in an activity to determine the relationship between line segments and their dilated images. In the fourth section in a unit of 16, pupils discover the dilated line...