Thinkfinity Lesson Plans
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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: Sums of Vectors and Their Properties
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 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] 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)
Subject: Mathematics Title: Sums of Vectors and Their Properties
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 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
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
Web Resources
Podcasts
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Title: Math in Basketball
Description:
Basketball player Elton Brand describes how he became an NBA star, then presents a challenge about the math behind the perfect free throw shot.
Standard(s): [S1] PHS (912) 7: Relate velocity, acceleration, and kinetic energy to mass, distance, force, and time. [S1] PHS (912) 12: Identify metric units for mass, distance, time, temperature, velocity, acceleration, density, force, energy, and power. [S1] PHY (912) 1: Explain linear, uniform circular, and projectile motions using one and twodimensional vectors. [S1] PHY (912) 4: Describe quantitative relationships for velocity, acceleration, force, work, power, potential energy, and kinetic energy. [MA2013] PRE (912) 7: (+) Solve problems involving velocity and other quantities that can be represented by vectors. [NVM3] [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)
Math in Basketball
http://www.thirteen....
Basketball player Elton Brand describes how he became an NBA star, then presents a challenge about the math behind the perfect free throw shot.
Interactives/Games
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Title: The Moving Man
Description:
Learn about position, velocity, and acceleration graphs. Move the little man back and forth with the mouse and plot his motion. Set the position, velocity, or acceleration and let the simulation move the man for you.
Standard(s): [S1] PHS (912) 7: Relate velocity, acceleration, and kinetic energy to mass, distance, force, and time. [S1] PHY (912) 4: Describe quantitative relationships for velocity, acceleration, force, work, power, potential energy, and kinetic energy. [MA2013] PRE (912) 7: (+) Solve problems involving velocity and other quantities that can be represented by vectors. [NVM3] [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)
The Moving Man
http://phet.colorado...
Learn about position, velocity, and acceleration graphs. Move the little man back and forth with the mouse and plot his motion. Set the position, velocity, or acceleration and let the simulation move the man for you.
Thinkfinity Learning Activities
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Title: Vector Investigation: Boat to the Island
Description:
In this student interactive, from Illuminations, students '' drive'' a boat by adjusting the magnitude and direction of a velocity vector. The goal is to land the boat on the island without hitting the walls.
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] 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)
Subject: Mathematics Title: Vector Investigation: Boat to the Island
Description: In this student interactive, from Illuminations, students '' drive'' a boat by adjusting the magnitude and direction of a velocity vector. The goal is to land the boat on the island without hitting the walls. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12

