Lesson Plan
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Coin Codes

For Teachers 3rd - 7th
Students work on cracking coin codes in honor of the Navajo Code Talkers Medal. Students review the handout on Crack the Code. Students race to see who can crack the code the fastest.
Lesson Plan
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Estimating School Store Purchases

For Teachers 3rd - 5th
Students examine uses for estimating, and round purchase prices to estimate total purchases in a simulated school store setting. They discuss what it means for an item to be on sale, and observe the teacher work through the process of...
Lesson Plan
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Matrix Multiplication

For Teachers 11th - 12th
Students identify, analyze, and multiply matrices. They determine if various indicated operations are possible through classroom discussion and practice. Finally, students determine matrix product dimensions through problem-solving...
Lesson Plan
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What Are the Odds?

For Teachers 6th - 8th
Middle schoolers identify and interpret various ways of expressing probability as a decimal, fraction, percent, or ratio. They solve problems based on probability as they apply to real world applications.
Worksheet
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Linear Systems: Applications of Linear Algebra to Differential Equations

For Students 12th - Higher Ed
In this differential equations worksheet, students solve systems of simultaneous differential equations using linear algebra. This six-page worksheet contains approximately six problems, with explanations and examples.
Worksheet
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Linear Systems: Symmetric Matrices

For Students 12th - Higher Ed
In this symmetric matrices worksheet, students explore the characteristics of symmetric matrices. This two-page worksheet contains examples and explanations concerning symmetric matrices. Two problems are provided to solve.
Worksheet
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Linear Systems: The Column Space

For Students 11th - Higher Ed
In this column space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples of and explanations. One problem is provided for students to complete.
Worksheet
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Linear Systems: Definition of the Nullspace

For Students 11th - Higher Ed
In this nullspace learning exercise, students find the nullspace of matrices, write a rectangular matrix upper-triangular form, and convert augmented matrix to echelon form. This six-page learning exercise contains approximately 8...
Worksheet
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Linear Systems: Fundamental Theorem of Linear Algebra

For Students 11th - Higher Ed
In this linear algebra worksheet, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page worksheet contains examples, explanations, and approximately four problems to complete.
Worksheet
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Linear Systems: Vector Spaces

For Students 11th - Higher Ed
In this vector spaces worksheet, students explore the column and rowspace of a matrix. They find the basis of subspaces associated with a given matrix. Students observe the relationship between vectors and the nullspace. This...
Worksheet
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Linear Systems: Independence, Basis and Dimension

For Students 12th - Higher Ed
For this basis and dimension worksheet, learners explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.
Worksheet
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Linear Systems: General Solutions

For Students 11th - Higher Ed
For this linear system worksheet, students explore the characteristics of given matrices. They multiply matrices and determine pivots and multiply solutions. This four-page worksheet contains approximately seven problems.
Worksheet
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Linear Systems: Nullspace Matrix and Rank

For Students 11th - Higher Ed
In this nullspace matrix worksheet, students observe the rank and number of independent rows and columns a matrix has. They compute the product of matrices and describe the column space of each. This two-page worksheet contains...
Worksheet
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Linear Systems: Least Squares Approximations

For Students 11th - Higher Ed
In this least squares approximation worksheet, students use linear algebra to find the least square error and the equation of a line for given points. They find the equation of a parabola through provided points. This four-page...
Worksheet
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Linear Systems: Orthogonal Matrices

For Students 11th - Higher Ed
In this orthogonal matrices worksheet, students explore characteristics of an orthogonal matrix. They use Gram-Schmidt to convert linearly independent vectors to orthonormal vectors. This three-page worksheet contains approximately six...
Worksheet
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Linear Systems: Projections

For Students 11th - Higher Ed
In this projection worksheet, students determine the projections of a given matrix. This four-page worksheet contains explanations and examples and approximately ten problems to complete.
Worksheet
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Linear Systems: Review of Vectors

For Students 12th - Higher Ed
In this review of vectors worksheet, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page worksheet contains approximately ten problems.
Worksheet
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Linear Systems: Graphical Interpretation of Vectors

For Students 11th - Higher Ed
In this graphical interpretation of vectors worksheet, students execute operations of addition and multiplication by a scalar. They sketch results and determine the commutativity of vector addition. This three-page worksheet contains...
Worksheet
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Linear Systems: Least Squares Approximations

For Students Higher Ed
In this least squares approximation worksheet, students determine the number of solutions a given linear system has. They find the least square error and the equation of a line of best fit for a set of three points. Students find the...
Worksheet
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Linear Systems: Graphical Interpretation of Vectors and Linear Systems

For Students Higher Ed
In this interpretation of vectors and linear systems worksheet, students describe the geometric appearance of two vectors. They add the two vectors and sketch the sum as well as the vectors to determine the commutativity of vector...
Worksheet
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Linear Systems: Matrix Operations

For Students Higher Ed
In this matrix operations worksheet, students perform matrix addition and multiplication. This two-page worksheet contains six problems. Definitions, examples and explanations are also provided.
Worksheet
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Linear Systems: Using Matrix Operations

For Students 12th - Higher Ed
In this linear systems activity, students use matrix multiplication as an elimination technique to solve linear systems. They compare products and explore trends. This four-page activity contains explanations, examples and five problems.
Worksheet
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Linear Systems: LU Decomposition

For Students 12th - Higher Ed
In this LU decomposition worksheet, students multiply matrices, identify the elimination matrices, and the inverse of a matrix. This three-page worksheet contains approximately six problems.
Worksheet
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Linear Systems: Matrix Inverse

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