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...
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Linear Systems: Orthogonality of Vector Spaces of a Matrix
In this vector spaces of a matrix worksheet, students decompose any vector into two orthogonal pieces. They identify the nullspace, row space, and find a reduced echelon. This two-page worksheet contains examples and two problems.
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Worksheet 31
In this math learning exercise, students investigate vectors and polar coordinates. They convert the paths of polar coordinates to Euclidian points.
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The Haar Wavelet Filter Bank
In this Haar Wavelet learning exercise, students solve and complete 4 different problems related to the Haar Wavelet filter bank. First, they define the properties of Haar basis. Then, students compute the matrices for the first, second...
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Linear Systems: Independence, Basis and Dimension
In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.
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Linear Systems: Vector Spaces
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...
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MA 371 - Matrices: Solving Systems and Determinants
In this solving systems and determinants worksheet, students solve 4 multi-part short answer problems. Students solving systems of equations using matrices. Students find a basis for row spaces and column spaces. Students find the...
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Linear Independence, Bases and Coordinate Systems
Students define vocabulary related to vectors and investigate vector problems. In this math lesson, students define basis and explore plotting vectors in correlation to their basis. Plotting polynomials facilitates student understanding.
National Center for Case Study Teaching in Science
Applying Newton’s Third Law of Motion in the Gravitron Ride
Here is a collection of readings to be discussed in the science classroom. This one is in the form of a dialog between two boys in an amusement park, talking about the forces involved in a Graviton ride. Questions are listed at the...
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Dimension and Rank
Students determine the dimension of a subspace. In this dimension and rank lesson, students explore the dimension of a vector space. They compare and explore the relationship in a matrix.
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MT-A315 Introduction to Linear Algebra
In this algebra worksheet, students figure out the equation of the general vector, they find the orthogonal basis and apply the formula to solve the problems.
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Bioterrorism: Development of a "Superbug"
High schoolers compare bacteria and viruses and their roles in biotechnology and bioterrorism. They outline fundamental steps of bacterial transformation and the possible selection processes to identify transformants. They discuss...
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Crash Test Dummies
Fifth graders are introduced to Newton's First Law of Motion. In groups, they describe the differences between balanced and unbalanced forces. They participate in experiments that demonstrate how equal and opposite forces act upon...
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Illuminating Climate Change: Connecting Lighting and Global Warming
Learners analyze energy usage and connect energy usage to fossil fuel consumption. In this global warming and pollution lesson, students what fuels are used to generate electricity and how much CO2 each fuel produces, then graph the...
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Linear Systems
For this linear systems worksheet, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to the column...