EngageNY
Linear Transformations Review
Time for matrices and complex numbers to come together. Individuals use matrices to add and multiply complex numbers by a scalar. The instructional activity makes a strong connection between the operations and graphical transformations.
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Linear Transformations Applied to Cubes
What do you get when you combine a matrix and a cube? Well that depends on the matrix! Pupils use online software to graph various transformations of a cube. Ultimately, they are able to describe the matrix that is responsible for a...
EngageNY
Composition of Linear Transformations 1
Learners discover that multiplying transformation matrices produces a composition of transformations. Using software, they map the transformations and relate their findings to the matrices.
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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 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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Getting a Handle on New Transformations 1
In the first of a two-day instructional activity on transformations with matrix notation the class transforms the unit square using general transformations, then calculates the area of the transformed image. They discover it is the same...
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Getting a Handle on New Transformations 2
Use 2x2 matrices to move along a line. The second day of a two-day lesson plan is the 28th installment in a 32-part unit. Pupils work together to create and solve systems of equations that will map a transformation to a given point. The...
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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 activity 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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When Can We Reverse a Transformation? 2
The second lesson on finding inverse matrices asks class members to look for a pattern in the inverse matrix and test it to see if it works for all matrices. The teacher leads a discussion to refine the process in finding inverses, then...
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Composition of Linear Transformations 2
Scholars take transformations from the second to the third dimension as they extend their thinking of transformations to include three-dimensional figures. They explore how to use matrices to represent compositions of transformations.
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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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Counting Rules—The Fundamental Counting Principle and Permutations
Count the benefits of using the resource. The second installment of a 21-part module focuses on the fundamental counting principle to determine the number of outcomes in a sample space. It formalizes concepts of permutations and...
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Using Permutations and Combinations to Compute Probabilities
Now that we know about permutations and combinations, we can finally solve probability problems. The fourth installment of a 21-part module has future mathematicians analyzing word problems to determine whether permutations or...
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Why Are Vectors Useful? 2
Investigate the application of vector transformations applied to linear systems. Individuals use vectors to transform a linear system translating the solution to the origin. They apply their understanding of vectors, matrices,...
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Projecting a 3-D Object onto a 2-D Plane
Teach how graphic designers can use mathematics to represent three-dimensional movement on a two-dimensional television surface. Pupils use matrices, vectors, and transformations to model rotational movement. Their exploration involves...
EngageNY
First-Person Computer Games
How do graphic designers project three-dimensional images onto two-dimensional spaces? Scholars connect their learning of matrix transformations to graphic design. They understand how to apply matrix transformations to make...
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Linear Transformations of Lines
Discover the extension of parametric equations to model linear transformations. Scholars first write parametric equations to model lines through two points. They then find the parametric equations that represent a linear transformation.
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Why Are Vectors Useful? 1
How do vectors help make problem solving more efficient? Math scholars use vectors to represent different phenomenon and calculate resultant vectors to answer questions. Problems vary from modeling airplane motion to the path of a robot.
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Vectors and Translation Maps
Discover the connection between vectors and translations. Through the activity, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...
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Vectors and Stone Bridges
What does it take to build a stable arch? Pupils apply vectors and physics as they examine arched bridges and their structural integrity. They use vectors to represent the forces acting on the stone sections and make conclusions based on...
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Solving Equations Involving Linear Transformations of the Coordinate Plane
How can matrices help us solve linear systems? Learners explore this question as they apply their understanding of transformation matrices to linear systems. They discover the inverse matrix and use it to solve the matrix equation...
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Solving Equations Involving Linear Transformations of the Coordinate Space
Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application questions...
EngageNY
Using Matrix Operations for Encryption
Data encryption is an important security measure for sensitive data stored on computers. Pupils learn how to utilize matrices for creating code. They also get a great review of matrix multiplication, inverse matrices, and the identity...
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Matrix Addition Is Commutative
Explore properties of addition as they relate to matrices. Using graphical representations of vector matrices, scholars test the commutative and associative properties of addition. They determine if the properties are consistent for...
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