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When Can We Reverse a Transformation? 1
Wait, let's start over — teach your class how to return to the beginning. The first lesson looking at inverse matrices introduces the concept of being able to undo a matrix transformation. Learners work with matrices with a determinant...
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Representing, Naming, and Evaluating Functions (Part 1)
Begin the discussion of domain and range using something familiar. Before introducing numbers, the lesson uses words to explore the idea of input and outputs and addresses the concept of a function along with domain and range.
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Determining Discrete Probability Distributions 2
Investigate how long-run outcomes approach the calculated probability distribution. The 10th installment of a 21-part module continues work on probability distributions from the previous lesson. They pool class data to see how conducting...
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End-of-Module Assessment Task - Precalculus (Module 5)
Give your young scholars a chance to show what they've learned from the module. The last installment of a 21-part series is an end-of-module assessment task. It covers basic and conditional probabilities, expected value, and analyzing...
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Modeling Video Game Motion with Matrices 2
The second day of a two-part lesson on motion introduces the class to circular motion. Pupils learn how to incorporate a time parameter into the rotational matrix transformations they already know. The 24th installment in the 32-part...
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When Can We Reverse a Transformation? 3
When working with matrix multiplication, it all comes back around. The 31st portion of the unit is the third lesson on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous two lessons....
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Matrix Multiplication Is Not Commutative
Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...
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Matrix Multiplication Is Distributive and Associative
Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous lesson in the series, pupils now test the associative and distributive properties. The...
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Copy and Bisect an Angle
More constructions! For this third installment of a 36-part series, learners watch a YouTube video on creating door trim to see how to bisect an angle. They then investigate how to copy an angle by ordering a given list of steps.
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Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
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Wishful Thinking—Does Linearity Hold? (Part 2)
Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...
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Which Real Number Functions Define a Linear Transformation?
Not all linear functions are linear transformations, only those that go through the origin. The third lesson in the 32-part unit proves that linear transformations are of the form f(x) = ax. The lesson plan takes another look at examples...
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An Appearance of Complex Numbers 1
Complex solutions are not always simple to find. In the fourth instructional activity of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the...
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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 the...
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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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The Geometric Effect of Some Complex Arithmetic 2
The 10th lesson in a series of 32, continues with the geometry of arithmetic of complex numbers focusing on multiplication. Class members find the effects of multiplying a complex number by a real number, an imaginary number, and another...
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Distance and Complex Numbers 1
To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...
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Distance and Complex Numbers 2
Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th lesson in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a formula to find...
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Trigonometry and Complex Numbers
Complex numbers were first represented on the complex plane, now they are being represented using sine and cosine. Introduce the class to the polar form of a complex number with the 13th part of a 32-part series that defines the argument...
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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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Representing Reflections with Transformations
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
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The Geometric Effect of Multiplying by a Reciprocal
Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...
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Matrix Notation Encompasses New Transformations!
Class members make a real connection to matrices in the 25th part of a series of 32 by looking at the identity matrix and making the connection to the multiplicative identity in the real numbers. Pupils explore different matrices and...
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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 activity focuses on the effect of performing one transformation after another one. The pupils develop the procedure in order to multiply two 2 X 2...