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Title: Components of a Vector
Description:
In this lesson, one of a multipart unit from Illuminations, students manipulate a velocity vector to control the movement of an object in a gamelike setting. In the process, they develop an understanding that vectors are composed of both magnitude and direction.
Standard(s): [MA2013] AM1 (912) 1: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v,  v ,  v ), including the use of eigenvalues and eigenvectors. [NVM1] (Alabama) [MA2013] AM1 (912) 2: (+) Solve problems involving velocity and other quantities that can be represented by vectors, including navigation (e.g., airplane, aerospace, oceanic). [NVM3] (Alabama) [MA2013] AM1 (912) 3: (+) Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Find the dot product and the cross product of vectors. [NVM4a] (Alabama) [MA2013] AM1 (912) 4: (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. [NVM4b] (Alabama)
Subject: Mathematics Title: Components of a Vector
Description: In this lesson, one of a multipart unit from Illuminations, students manipulate a velocity vector to control the movement of an object in a gamelike setting. In the process, they develop an understanding that vectors are composed of both magnitude and direction. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Learning about Properties of Vectors and Vector Sums Using Dynamic Software
Description:
In this twolesson unit, from Illuminations, students manipulate a velocity vector to control the movement of an object in a gamelike setting. They develop an understanding that vectors are composed of both magnitude and direction, and extend their knowledge of number systems to the system of vectors.
Standard(s): [MA2013] PRE (912) 5: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, v, v, v). [NVM1] [MA2013] PRE (912) 7: (+) Solve problems involving velocity and other quantities that can be represented by vectors. [NVM3] [MA2013] PRE (912) 8: (+) Add and subtract vectors. [NVM4] [MA2013] PRE (912) 9: (+) Multiply a vector by a scalar. [NVM5] [MA2013] AM1 (912) 1: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v,  v ,  v ), including the use of eigenvalues and eigenvectors. [NVM1] (Alabama) [MA2013] AM1 (912) 2: (+) Solve problems involving velocity and other quantities that can be represented by vectors, including navigation (e.g., airplane, aerospace, oceanic). [NVM3] (Alabama) [MA2013] AM1 (912) 3: (+) Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Find the dot product and the cross product of vectors. [NVM4a] (Alabama) [MA2013] AM1 (912) 4: (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. [NVM4b] (Alabama) [MA2013] AM1 (912) 5: (+) Understand vector subtraction v  w as v + (w), where (w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise, including vectors in complex vector spaces. [NVM4c] (Alabama)
Subject: Mathematics Title: Learning about Properties of Vectors and Vector Sums Using Dynamic Software
Description: In this twolesson unit, from Illuminations, students manipulate a velocity vector to control the movement of an object in a gamelike setting. They develop an understanding that vectors are composed of both magnitude and direction, and extend their knowledge of number systems to the system of vectors. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Learning about Properties of Vectors and Vector Sums Using Dynamic Software: Components of a Vector
Description:
This eexample from Illuminations illustrates how using a dynamic geometrical representation can help students develop an understanding of vectors and their properties. Students manipulate a velocity vector to control the movement of an object in a gamelike setting. In this part, Components of a Vector, students will develop an understanding that vectors are composed of both magnitude and direction. In the second part, Sums of Vectors and Their Properties, students extend their knowledge of number systems to the system of vectors. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations.
Standard(s): [MA2013] PRE (912) 5: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, v, v, v). [NVM1] [MA2013] PRE (912) 8: (+) Add and subtract vectors. [NVM4] [MA2013] AM1 (912) 1: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v,  v ,  v ), including the use of eigenvalues and eigenvectors. [NVM1] (Alabama) [MA2013] AM1 (912) 3: (+) Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Find the dot product and the cross product of vectors. [NVM4a] (Alabama) [MA2013] AM1 (912) 4: (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. [NVM4b] (Alabama)
Subject: Mathematics,Science Title: Learning about Properties of Vectors and Vector Sums Using Dynamic Software: Components of a Vector
Description: This eexample from Illuminations illustrates how using a dynamic geometrical representation can help students develop an understanding of vectors and their properties. Students manipulate a velocity vector to control the movement of an object in a gamelike setting. In this part, Components of a Vector, students will develop an understanding that vectors are composed of both magnitude and direction. In the second part, Sums of Vectors and Their Properties, students extend their knowledge of number systems to the system of vectors. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Thinkfinity Learning Activities
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Title: Learning about Properties of Vectors and Vector Sums Using Dynamic Software: Sums of Vectors and Their Properties
Description:
This is part two of a twopart eexample from Illuminations that illustrates how using a dynamic geometrical representation can help students develop an understanding of vectors and their properties. In this part, Sums of Vectors and Their Properties, students extend their knowledge of number systems to the system of vectors. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath Investigations.
Standard(s): [MA2013] AM1 (912) 1: (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v,  v ,  v ), including the use of eigenvalues and eigenvectors. [NVM1] (Alabama) [MA2013] AM1 (912) 3: (+) Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Find the dot product and the cross product of vectors. [NVM4a] (Alabama) [MA2013] AM1 (912) 4: (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. [NVM4b] (Alabama) [MA2013] AM1 (912) 5: (+) Understand vector subtraction v  w as v + (w), where (w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise, including vectors in complex vector spaces. [NVM4c] (Alabama)
Subject: Mathematics Title: Learning about Properties of Vectors and Vector Sums Using Dynamic Software: Sums of Vectors and Their Properties
Description: This is part two of a twopart eexample from Illuminations that illustrates how using a dynamic geometrical representation can help students develop an understanding of vectors and their properties. In this part, Sums of Vectors and Their Properties, students extend their knowledge of number systems to the system of vectors. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath Investigations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

