Los Angeles County Office of Education
California State Standards: Algebra I
Starting a year of Algebra I? This mighty packet practices all of the major topics with different ranges of difficulty. Standards include everything from linear to quadratic to rational expressions. Use it in a variety of ways to...
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Mid-Module Assessment Task - Precalculus (module 1)
Individuals show what they know about the geometric representations of complex numbers and linearity. Seventeen questions challenge them to demonstrate their knowledge of moduli and operations with complex numbers. The assessment is the...
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Modeling Video Game Motion with Matrices 2
The second day of a two-part lesson plan 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...
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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 activity 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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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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End-of-Module Assessment Task — Precalculus (Module 1)
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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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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The Hunt for Better Notation
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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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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Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first instructional activity in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear...
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Modeling Video Game Motion with Matrices 1
Video game characters move straight with matrices. The first day of a two-day lesson introduces the class to linear transformations that produce straight line motion. The 23rd part in a 32-part series has pupils determine the...
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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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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,...
Curated OER
MA 371 - Vector Norm: Dot Product
In this dot product worksheet, students solve 6 short answer problems. Students find unit vectors in the same direction as a given vector. Students express vectors as a linear combination of the standard basis vectors. Students find a...
Curated OER
Continuous Probability Distributions
In this continuous probability distribution worksheet, students identify discrete and continuous distributions. They calculate the linear combination of the independent normal random variable and determine probabilities using exponential...
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MT-A314 Introduction to Linear Algebra Worksheet 1.4(b)
A linear algebra worksheet where pupils explore three linear equations and use Gaussain elimination to solve the system of equations. They identify values that have no solution, one solution, and many solutions. There is one open-ended,...
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Numerical Analysis: Polynomial Interpolation
In this polynomial worksheet, students find interpolating functions that can be expressed as a linear combination of basis functions. This four-page worksheet contains five multi-step problems.
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Multivariable Calculus: Review of Linear Systems
In this linear system worksheet, students determine the point of intersection between two lines, they complete linear combination problems. This two-page worksheet contains four multi-step problems.
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Linear Systems: Applications of Linear Algebra to Differential Equations
In this differential equations worksheet, learners solve systems of simultaneous differential equations using linear algebra. This six-page worksheet contains approximately six problems, with explanations and examples.
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Linear Systems: Fundamental Theorem of Linear Algebra
In this linear algebra instructional activity, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page instructional activity contains examples, explanations, and approximately...
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Linear Systems: Differential Equations
In this differential equations worksheet, students determine the stability of matrices and evaluate a matrix with an exponent. This two-page worksheet contains examples, explanations, and two problems to solve.
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Using Linear Algebra to Solve Systems of ODE's
In this math worksheet, students examine the coupled differential equations. Then they find the eigenvalues and eigenvectors for the 2x2 matrix.
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MT-A315I introduction to Linear Algebra
In this linear algebra worksheet, students apply the basics of algebraic reasoning to evaluate different expressions looking for the pattern of finding the unknowns.
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MT-A315 Introduction to Linear Algebra
In this algebra learning exercise, students practice using number sets and principles of algebra to solve each complex problem using number sense.