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Perimeter and Area of Polygonal Regions in the Cartesian Plane
How many sides does that polygon have? Building directly from instructional activity number eight in this series, learners now find the area and perimeter of any polygon on the coordinate plane. They decompose the polygons into triangles...
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Radicals and Conjugates
Make the irrational rational again! Continuing the theme from previous lessons in the series, the lesson relates the polynomial identity difference of squares to conjugates. Learners develop the idea of a conjugate through analysis and...
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The Power of Algebra—Finding Pythagorean Triples
The Pythagorean Theorem makes an appearance yet again in this instructional activity on polynomial identities. Learners prove a method for finding Pythagorean triples by applying the difference of squares identity.
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Probability Rules (part 2)
Ensure your pupils are rule followers! Learners add the addition rule to the set of probability rules examined in the previous lesson. Problems require both the multiplication and addition rule.
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Normal Distributions (part 2)
From z-scores to probability. Learners put together the concepts from the previous lessons to determine the probability of a given range of outcomes. They make predictions and interpret them in the context of the problem.
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Margin of Error When Estimating a Population Proportion (part 2)
Error does not mean something went wrong! Learners complete a problem from beginning to end using concepts developed throughout the last five lessons. They begin with a set of data, determine a population proportion, analyze their result...
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Ruling Out Chance (part 2)
Help your classes find the significance in this instructional activity! Learners analyze the probability of Diff values. They then determine if the difference is significant based on their probability of occurrence.
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Rational Exponents—What are 2^1/2 and 2^1/3?
Are you rooting for your high schoolers to learn about rational exponents? In the third installment of a 35-part module, pupils first learn the meaning of 2^(1/n) by estimating values on the graph of y = 2^x and by using algebraic...
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Four Interesting Transformations of Functions (Part 2)
What happens to a function whose graph is translated horizontally? Groups find out as they investigate the effects of addition and subtraction within a function. This nineteenth lesson in a 26-part series focuses on horizontal...
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Four Interesting Transformations of Functions (Part 4)
What do you get when you cross piecewise functions with transformations? An engaging lesson! The conclusion of a four-part series on the transformations of functions asks class members to apply transformations to piecewise...
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Graphing Quadratic Equations from the Vertex Form
Graphing doesn't need to be tedious! When pupils understand key features and transformations, graphing becomes efficient. This activity connects transformations to the vertex form of a quadratic equation.
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Recursive Formulas for Sequences
Provide Algebra I learners with a logical approach to making connections between the types of sequences and formulas with a lesson that uses what class members know about explicit formulas to develop an understanding of...
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Base 10 and Scientific Notation
Use a resource on which you can base your lesson on base 10 and scientific notation. The second installment of a 35-part module presents scholars with a review of scientific notation. After getting comfortable with scientific...
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An Appearance of Complex Numbers 2
Help the class visualize operations with complex numbers with a lesson that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series reviews...
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The Geometric Effect of Some Complex Arithmetic 1
Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads pupils into what it...
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Justifying the Geometric Effect of Complex Multiplication
The 14th lesson in the unit has the class prove the nine general cases of the geometric representation of complex number multiplication. Class members determine the modulus of the product and hypothesize the relationship for the...
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Matrix Multiplication and Addition
To commute or not to commute, that is the question. The 26th segment in a 32-segment lesson focuses on the effect of performing one transformation after another one. The pupils develop the procedure in order to multiply two 2 X 2...
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Graphing Quadratic Functions from Factored Form
How do you graph a quadratic function efficiently? Explore graphing quadratic functions by writing in intercept form with a lesson that makes a strong connection to the symmetry of the graph and its key features before individuals write...
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Applications of Systems of Equations and Inequalities
Is the application of systems of equations giving your class headaches? Use this resource to build on your pupils' logic to lead them to building equations and using algebraic methods. The lesson begins with an exploration of...
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Representing, Naming, and Evaluating Functions (Part 2)
Notation in mathematics can be intimidating. Use this lesson to expose pupils to the various ways of representing a function and the accompanying notation. The material also addresses the importance of including a domain if necessary....
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Informal Proofs of Properties of Dilations
Challenge the class to prove that the dilation properties always hold. The lesson develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...
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Inverse Trigonometric Functions
Build on the understanding of finding angles using trigonometric ratios. Pupils develop the definitions of inverse trigonometric functions by restricting their domains in the 13th lesson of a 16-part series. They use inverse functional...
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The Converse of the Pythagorean Theorem
Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
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Numbers in Exponential Form Raised to a Power
Develop an understanding of the properties of exponents through this series of activities. This third lesson of 15 explores the patterns associated with the power property. Scholars expand the powers before applying the property.