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Lesson Plan
EngageNY

Getting a Handle on New Transformations 1

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Getting a Handle on New Transformations 2

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

When Can We Reverse a Transformation? 1

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

When Can We Reverse a Transformation? 2

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Composition of Linear Transformations 2

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Exploiting the Connection to Cartesian Coordinates

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Counting Rules—The Fundamental Counting Principle and Permutations

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Using Permutations and Combinations to Compute Probabilities

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Why Are Vectors Useful? 2

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Projecting a 3-D Object onto a 2-D Plane

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

First-Person Computer Games

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Linear Transformations of Lines

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Why Are Vectors Useful? 1

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Vectors and Translation Maps

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Vectors and Stone Bridges

For Teachers 11th - 12th Standards
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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Lesson Plan
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EngageNY

Solving Equations Involving Linear Transformations of the Coordinate Plane

For Teachers 11th - 12th Standards
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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Lesson Plan
1
1
EngageNY

Solving Equations Involving Linear Transformations of the Coordinate Space

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Using Matrix Operations for Encryption

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Matrix Addition Is Commutative

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

The Hunt for Better Notation

For Teachers 11th - 12th Standards
The matrix — it's not just a movie. The lesson introduces the concept of 2 x 2 matrix multiplication as a way to represent linear transformations. Class members determine when a linear transformation represented as matrix multiplication...
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Lesson Plan
EngageNY

The General Multiplication Rule

For Teachers 11th - 12th Standards
In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.
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Lesson Plan
EngageNY

Discrete Random Variables

For Teachers 11th - 12th Standards
You don't need to be discreet about using the resource on discrete variables. In the fifth installment of a 21-part module, scholars explore random variables and learn to distinguish between discrete and continuous random variables. They...
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Lesson Plan
EngageNY

Probability Distribution of a Discrete Random Variable

For Teachers 11th - 12th Standards
Learn how to analyze probability distributions. The sixth installment of a 21-part module teaches pupils to use probability distributions to determine the long-run behavior of a discrete random variable. They create graphs of probability...
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Lesson Plan
EngageNY

Expected Value of a Discrete Random Variable

For Teachers 11th - 12th Standards
Discover how to calculate the expected value of a random variable. In the seventh installment of a 21-part module, young mathematicians develop the formula for expected value. They connect this concept the dot product of vectors.