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Instructional Video2:20
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\n\"Finding\n\n
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\nCurated OER\n
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\nFinding the Dot Product\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nAre you just starting a unit of vectors or matrices? Help your class learn how to find the dot product with this simplistic video tutorial. The procedure is shown as the tutor determines the dot product of A and B by transposing numbers...\n
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Instructional Video14:12
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\n\"Dot\n\n
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\n3Blue1Brown\n
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\nDot Products and Duality | Essence of Linear Algebra, Chapter 7\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nThe 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...\n
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\n\"MA\n\n
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\nCurated OER\n
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\nMA 371 - Vector Norm: Dot Product\n

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\n\nFor Teachers\n\n12th - Higher Ed\n
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\nIn 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...\n
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\n\"Applications\n\n
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\nCurated OER\n
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\nApplications of the Cross Product and Dot Product\n

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\n\nFor Students\n\n9th - 12th\n
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\nIn this cross product and dot product learning exercise, learners solve 2 problems including finding the magnetic field between 2 poles of a magnet and determining angles between vectors in a word problem about television watching given...\n
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Worksheet
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\n\"Math\n\n
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\nCurated OER\n
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\nMath 212: Dot Product and Cross Product\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this dot product worksheet, students consider vectors, find the value of an angle, and confirm the area of a given parallelogram. This two-page worksheet contains three problems.\n
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\n\"Math\n\n
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\nCurated OER\n
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\nMath 224 Spring 2004: Dot Product\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this dot product worksheet, students consider two vectors and compute the dot product and cross product of the given vectors. This two-page worksheet contains four problems.\n
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\n\"Multivariable\n\n
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\nCurated OER\n
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\nMultivariable Calculus: Dot Product\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this dot product instructional activity, students identify the properties of the dot product. They sketch vectors and obtain expressions for diagonals. This two-page instructional activity contains examples and explanations with two...\n
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\n\"Linear\n\n
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\nCurated OER\n
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\nLinear Systems: Lengths and Dot Products\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this dot product worksheet, students explore the multiplication of vectors. This two-page worksheet contains explanations, examples, and approximately ten problems.\n
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\nWorksheet 8 - Vectors\n

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\nIn this vector worksheet, students find the area of a parallelogram spanned by vectors, they give the geometric and algebraic definitions of the dot product and describe a sequence of vectors. This one-page worksheet contains six...\n
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\n\"Expected\n\n
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\nEngageNY\n
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\nExpected Value of a Discrete Random Variable\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nDiscover how to calculate the expected value of a random variable. In the seventh installment of a 21-part module, young mathematicians develop the formula for expected value. They connect this concept the dot product of vectors.\n
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\n\"Linear\n\n
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\nLinear Systems\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this multiplication of vectors instructional activity, students prove that the dot product operation is commutative. They normalize a vector so it has the same direction with a magnitude of one. Students use the angle formula to...\n
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\nWorksheet 4 - Geometric Mean\n

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\n\nFor Teachers\n\nHigher Ed\n
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\nIn this geometric worksheet, students examine the geometric and algebraic definition of the dot product. They find angles between two curves, determine if two vectors are parallel, and explain conditions on vectors. This one-page...\n
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\n\"Linear\n\n
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\nLinear Systems: Matrix Operations\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this matrix operations worksheet, students find the dot product of matrices. They use the elimination method to solve linear equations. This two-page worksheet contains explanations, examples and three problems.\n
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Instructional Video9:59
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\n\"Linear\n\n
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\nLinear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nWhat does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...\n
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\n\"On\n\n
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\nCurated OER\n
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\nOn the Dots\n

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\n\nFor Students\n\n8th - 10th\n
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\nIf you want your class to practice reading informational texts and answering related questions, this short exercise from The New York Times' \"Learning Network\" might be helpful. It includes an article on Dippin' Dots and uses...\n
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PPT
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\n\"Work,\n\n
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\nBowels Physics\n
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\nWork, Energy, and Power\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nWork, energy, and their relationship to power: what is the common thread? Explore this with your class as they learn the concepts of work and energy, both kinetic and potential, before completing multiple practice problems to...\n
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Instructional Video10:04
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\n\"Matrix\n\n
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\nMatrix Multiplication as Composition | Essence of Linear Algebra, Chapter 4\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nTake a different view at matrix multiplication. Based on vector transformations, the video presents matrix multiplication as the result of the composition of multiple linear transformations. The presentation explains the numerical...\n
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Instructional Video12:09
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\n\"Inverse\n\n
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\nInverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nDetermine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse...\n
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Instructional Video10:03
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\n\"The\n\n
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\nThe Determinant | Essence of Linear Algebra, Chapter 5\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nDetermine 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...\n
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Instructional Video10:59
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\n\"Linear\n\n
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\nLinear Transformations and Matrices | Essence of Linear Algebra, Chapter 3\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nAre all transformations of the plane linear transformations? The video provides examples of transformations of the plane and provides the definition of linear transformations. The resource begins the discussion of using matrix...\n
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\nWorksheet 22 - Functions\n

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\n\nFor Teachers\n\nHigher Ed\n
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\nIn this function worksheet, students use functions to identify an electron traveling along a path. They examine the velocity vector and compute the directional derivative. This two-page worksheet contains six multi-step problems.\n
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Interactive
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\n\"Energy,\n\n
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\nEnergy, Work and Power\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this energy, work and power worksheet, students solve 12 problems about circuits, electric motors, Ohm's Law and electric currents.\n
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Worksheet
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\n\"Linear\n\n
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\nCurated OER\n
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\nLinear Systems: Orthogonal Matrices\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn 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...\n
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\n\"Phone\n\n
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\nCurated OER\n
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\nPhone Button Boggle\n

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\n\nFor Students\n\n7th - 9th\n
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\nIn this phone button boggle worksheet, learners identify the number of math words they can find on a phone keypad according to given directions.  This one-page worksheet contains one problem.  Answers are provided.\n
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