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Pilots, Airplanes, and the Tangent of Three Degrees
Students explore how to use trigonometry in the aviation field. In this aviation instructional activity students complete trigonometry equations that show what planes should do to land their airplanes.
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Awareness of Pre-algebra Concepts
Students demonstrate different algebraic equations using Borenson's Hands-On Equation materials. They work in a cooperative group to solve algebraic equations.
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Today's Number
Using the number of days they have been in school, learners practice fining sums by adding ten, subtracting ten, and determining even and odd numbers. They write equations and build numbers with the fewest number of base ten blocks.
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Gauss' Law
Learners derive the equation of Gauss's law. In this physics lesson, students investigate the factors affecting the strength of the electric field. They perform simulation on Gauss's law.
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Solving Right Triangles
Students investigate the basic trigonometric functions. In this geometry/trigonometry lesson, students explore strategies to solve right triangles using basic trigonometric functions. The lesson includes an application...
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Linear Systems: Fundamental Theorem
For this fundamental theorem worksheet, student explore the nullspace and column space of given matrices. They explore the vectors needed to make it linearly independent and construct free variable columns. This two-page worksheet...
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Linear Systems: Vector Spaces of a Matrix
In this vector space matrix instructional activity, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page instructional activity contains examples and...
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Linear Systems: Projections
In this projection worksheet, students determine the projections if a given matrix. They take a vector and project it onto a line and subspace. This four-page worksheet contains examples and approximately seven problems.
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Linear Systems: Applications of Eigenvalues and Eigenvectors
In this Eigenvalue worksheet, students examine the applications of matrix exponentiation. This four-page worksheet contains examples, explanations and approximately three problems to complete.
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Linear Systems: Geometric Interpretation of Eigenvalues and Eigenvectors
In this interpretation of eigenvalues and eigenvectors worksheet, students probe the given results of exponentiation of a matrix. They tell the implications of this result. Students prove that the eigenvectors of a symmetric matrix are...
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Linear Systems: Introduction to Vector Space
In this vector space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples, theorems, explanations, and approximately three problems.
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Linear Systems: Symmetric Matrices
In this symmetric matrices worksheet, students find the eigenvalues of a matrix and discover that symmetric matrices are diagonalizable. This two-page worksheet contains examples, explanations and two problems.
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Linear Systems: Vector Spaces and Subspaces
In this vector spaces and subspaces worksheet, students review column spaces of matrices. They determine if the set of all 2 by 2 matrices is a vector space. Students determine if the set of all invertible 2 by 2 matrices is a vector...
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Linear Systems: Vector Spaces
In this vector space worksheet, students explore linearly independent vectors. They identify the row space, null space and subspaces of a given matrix. This four-page worksheet contains approximately eight problems.
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Linear Systems: Column Space and Nullspace of a Matrix
In this column space and nullspace of a matrix worksheet, students are give a three by three matrix. They describe the kind of subspace it is. Students find the nullspace of the matrix.
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Linear Systems: Properties of the Four Matrix Subspaces
In this four matrix subspaces instructional activity, students identify statements which are always true for given matrices. Students are given five matrices and a list of ten statements.
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Linear Systems: Lengths and Dot Products
In this dot product instructional activity, students explore the multiplication of vectors. This two-page instructional activity contains explanations, examples, and approximately ten problems.
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Linear Systems: Matrix Operations
This matrix operations activity covers topics such as matrix addition, multiplication and properties such as associative, commutative and distributive. Students give examples and counter examples of matrix addition and multiplication. ...
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Linear Systems: Applications of Determinants
In this determinant learning exercise, students use determinants to find area and volume. This two-page learning exercise contains examples, explanations and four problems.
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Linear Systems: Permutations and Transposes
In this permutation worksheet, students multiply matrices, explore symmetric matrices, permutation matrices, and properties of the transpose. This three-page worksheet contains explanations, examples and four problems.
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Linear Systems: The Determinant
In this determinant worksheet, students explore the determinant of a matrix. After examining the given examples and explanations, they find the determinants of given matrices. This two-page worksheet contains nine problems.
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Linear Systems: The Matrix Inverse
In this matrix inverse worksheet, 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. This four-page...
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Linear Systems: The Reduced Row Echelon Matrix
In this echelon matrix, students identify the nullspace of a matrix by finding the reduced row echelon matrix. This two-page worksheet contains explanations, examples and six problems.
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Linear Systems: The Nullspace Matrix and Rank
In this nullspace worksheet, students identify the rank and nullspace in a matrix. They compare the nullspace and column space of given matrices. This two-page worksheet contains examples, explanations and five problems.
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