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Lesson Plan
IMSA

Geometric Transformations with Matrices

For Teachers 10th - 12th Standards
In this math worksheet, learners find the values associated with the geometric transformations. They read the instruction sheet for completing matrices with translations, rotations, reflections, and scaling by adding and multiplying...
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Instructional Video12:51
1
1
3Blue1Brown

Change of Basis | Essence of Linear Algebra, Chapter 9

For Students 11th - Higher Ed Standards
It is all about perspective. A video introduces the idea that the view of a vector all depends upon the perspective of the basis vectors. Knowing how to go from one coordinate system's basis vectors to another system's basis vectors...
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Worksheet
Curated OER

Linear Algebra

For Students 12th - Higher Ed
In this linear algebra worksheet, students solve 3 different sets of problems that include rank, dimension, nullspace and range of linear algebra. They determine the relation between the rank of a matrix and the dimension of its range....
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Worksheet
Curated OER

Linear Systems: Matrix Inverse

For Students 11th - Higher Ed
In this linear systems worksheet students multiply matrices and find the coefficient matrix in the upper-triangular form. This four-page worksheet contains approximately four problems, with examples and explanations.
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Lesson Plan
Curated OER

Transformers

For Teachers 9th - 11th
Young scholars use transformation to move the graph around. In this geometry lesson plan, students observe transformation of symmetry groups. They use the TI to move the sides of the polygons around and make predictions.
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Assessment
EngageNY

End-of-Module Assessment Task — Precalculus (Module 1)

For Teachers 11th - 12th Standards
A transformational assessment determines how far pupils are advancing toward mastering complex and matrix standards. The assessment checks the learners' understanding of linear transformations, complex numbers and the complex plane,...
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Instructional Video14:12
1
1
3Blue1Brown

Dot Products and Duality | Essence of Linear Algebra, Chapter 7

For Students 11th - Higher Ed Standards
The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical...
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Instructional Video10:03
1
1
3Blue1Brown

The Determinant | Essence of Linear Algebra, Chapter 5

For Students 11th - Higher Ed Standards
Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...
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Lesson Plan
EngageNY

Designing Your Own Game

For Teachers 11th - 12th Standards
Your classes become video game designers for a day! They utilize their matrices, vectors, and transformation skills to create and design their own game images. The complex task requires learners to apply multiple concepts to create their...
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Lesson Plan
1
1
EngageNY

Solving General Systems of Linear Equations

For Teachers 11th - 12th Standards
Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and apply...
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Assessment
EngageNY

End-of-Module Assessment Task: Pre-Calculus Module 2

For Students 11th - 12th Standards
Assess pupil understanding of the relationship between matrices, vectors, linear transformations, and parametric equations. Questions range from recall to more complex levels of thinking. Problems represent topics learned throughout the...
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Lesson Plan
EngageNY

Introduction to Networks

For Teachers 11th - 12th Standards
Watch as matrices break networks down into rows and columns! Individuals learn how a network can be represented as a matrix. They also identify the notation of matrices.
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Worksheet
Curated OER

Linear Systems: The Matrix Inverse

For Students Higher Ed
In this matrix inverse instructional activity, students identify a matrix which when multiplied by a coefficient matrix, it transforms into an identify matrix. They use the Gauss-Jordan elimination process to find an inverse matrix. ...
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Lesson Plan
EngageNY

The Geometric Effect of Multiplying by a Reciprocal

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Coordinates of Points in Space

For Teachers 11th - 12th Standards
Combine vectors and matrices to describe transformations in space. Class members create visual representations of the addition of ordered pairs to discover the resulting parallelogram. They also examine the graphical representation...
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Instructional Video8:17
Corbett Maths

Column Vectors

For Students 10th - 12th Standards
Column right! Using visual representations, a short video introduces the concept of column vectors. Next, the resource shows how adding two vectors end-to-end is simplified by adding the components in the column vector. The presentation...
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Instructional Video17:16
1
1
3Blue1Brown

Eigenvectors and Eigenvalues | Essence of Linear Algebra, Chapter 10

For Students 11th - Higher Ed Standards
Find vectors that stay on their spans after a linear transformation. The 14th video in the series of 15 introduces the concept of eigenvectors, vectors that are only scaled during a linear transformation. The presentation illustrates the...
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Lesson Plan
Curated OER

Worksheet 36-Spring 1996

For Teachers Higher Ed
In this math worksheet, students sketch the regions that give rise to three integrals. They find the volume of a solid in the first octant bounded by a defined cylinder and a parabaloid. Students change a function to polar coordinates....
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Lesson Plan
Curated OER

Similarity and Dilations - Discover Properties of Similar Figures

For Teachers 9th - 12th Standards
Learners investigate properties of similar figures. In this properties of similar figures lesson, pupils construct similar figures using Cabri Jr. They dilate their figure to create a similar one, and discuss the relationships between...
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Worksheet
Curated OER

MA 439-Math of Image Processing

For Students Higher Ed
In this image processing worksheet, students use a matrix to solve ten problems. For the first six problems, students are guided to the answer by carefully sequenced questions. The final four problems require students to make a series of...
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Instructional Video5:09
1
1
3Blue1Brown

Essence of Linear Algebra Preview

For Students 11th - Higher Ed Standards
Make connections with linear algebra. The video introduces the concept of linear algebra and its geometric underpinnings. The resource makes the case that a complete understanding of linear algebra topics should include geometric...
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Lesson Plan
Curated OER

Solving Systems with Row Operations 1

For Teachers 9th - 12th Standards
Students solve systems of equations. In this algebra lesson, students use matrices to solve linear equations. They use reduced row echelon-form and scalar multiplier to simplify the matrices completely.
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Lesson Plan
Agriculture in the Classroom

Design 'Y'er Genes

For Teachers 9th - 12th Standards
How do changes in DNA affect an organism? Scholars explore chromosomes, genes, DNA, and mutations by modeling the DNA of a strawberry. They build a DNA model, then manipulate it to show how changing the genes transforms the strawberry...
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Worksheet
Curated OER

Linear Systems: Identifying Pivots and Multipliers

For Students Higher Ed
In this pivot worksheet, students explore the elimination process, and write a matrix in upper triangular form. They identify equivalent systems. This four-page worksheet contains examples, explanations, and approximately ten problems.

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