Mathematical Analysis (Honors)
Unit 3: Vectors and Parametrics
In this unit, students are introduced to algebraic vectors and parametric equations. Students interpret algebraic vectors as an ordered pair of real numbers in the coordinate plane and use operations to identify the components of a vector. Students recognize vector quantities as having both magnitude and direction, and calculate for a vector and resultant vector. Students perform operations on vectors to model and solve work applications, as well as find the dot product, unit vector, and angle between vectors. They represent vectors as a one column matrix and perform scalar and matrix multiplication as transformations of vectors on the coordinate plane.
For parametric equations, students define a curve using functions with respect to a common variable. Students then model a path of an object using parametric equations and define the curve by eliminating the parameter.
For parametric equations, students define a curve using functions with respect to a common variable. Students then model a path of an object using parametric equations and define the curve by eliminating the parameter.
Students will:
Perform operations on algebraic vectors.
MA.VP.A.1
Define algebraic vectors, magnitude and direction, and calculate their values.
MA.VP.A.2
Define a unit vector.
N.VM.A.2
Find the components of an algebraic vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
Perform operations with algebraic vectors.
PC.VP.A.1
Perform operations with algebraic vectors, including scalar multiplication, addition, subtraction, and finding the dot product.
PC.VP.A.2
Use vector operations to determine of vectors are parallel or orthogonal (perpendicular). Find the angle between vectors.
Perform operations on matrices and use matrices in applications.
N.VM.C.11
Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
Work with parametric equations.
PC.VP.B.3
Find a parametrization of a given equation.
PC.VP.B.4
Graph parametric equations and make comparisons to the equivalent Cartesian equations.
PC.VP.B.5
Use parametric equations to solve motion problems.
Perform operations on algebraic vectors.
MA.VP.A.1
Define algebraic vectors, magnitude and direction, and calculate their values.
 Check for Understanding: Recognizing Vectors  Equivalent Vectors
 Review/Rewind: Vector Introduction  Equivalent Vectors  Magnitude of Vector from Components
MA.VP.A.2
Define a unit vector.
 Check for Understanding: Unit Vectors
 Review/Rewind: Unit Vector Notation
N.VM.A.2
Find the components of an algebraic vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
 Check for Understanding: Components of Vectors  Magnitude of Vectors
 Review/Rewind: Components of Vectors  Components of Vectors Part 2  Magnitude from Components  Magnitude from Points
Perform operations with algebraic vectors.
PC.VP.A.1
Perform operations with algebraic vectors, including scalar multiplication, addition, subtraction, and finding the dot product.
 Check for Understanding: Scalar Multiplication  Analyzing Scalar Multiplication  Add and Subtract Vectors
 Review/Rewind: Scalar Multiplication  Adding and Subtracting Vectors  Adding and Subtracting Vectors in Matrix Notation
PC.VP.A.2
Use vector operations to determine of vectors are parallel or orthogonal (perpendicular). Find the angle between vectors.
 Check for Understanding: Direction of Vectors
 Review/Rewind: Vector Dot Product  Vector Cross Product  Dot Product vs Cross Product Comparison  Direction of Vector from Component Form
Perform operations on matrices and use matrices in applications.
N.VM.C.11
Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
 Check for Understanding: Transform Vectors Using Matrices  Matrices as Transformation
 Review/Rewind: Matrix Vector Products  Transform Vectors Using Matrices  Matrices as Transformation
Work with parametric equations.
PC.VP.B.3
Find a parametrization of a given equation.
PC.VP.B.4
Graph parametric equations and make comparisons to the equivalent Cartesian equations.
 Review/Rewind: Sketch Parametric Equations
PC.VP.B.5
Use parametric equations to solve motion problems.
What are some signs of student mastery?

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