(+) 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).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Vector quantities
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1 - Recognize (magnitude of vector quantities)
1 - Recognize (direction of vector quantities)
2 - Represent (vector quantities by directed line segments)
3 - Use (appropriate symbols for vectors and magnitudes)
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1 - I can recognize magnitude of vector quantities.
1 - I can recognize direction of vector quantities.
2 - I can represent vector quantities by directed line segments.
3 - I can use appropriate symbols for vectors and magnitudes.
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A. Vectors have magnitude and direction.
B. There are symbols that represent quantities of vectors.
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A.1. How do I know how long a vector is?
A.2. How do I know which direction a vector goes?
B.1 What do the symbols mean?
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(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Vectors
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2 - Find (Components of a vector by subtracting coordinates of initial from terminal points)
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2 - I can find Components of a vector by subtracting coordinates of initial from terminal points.
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A. One finds the components of a vector by subtracting the coordinates at the beginning and end of the vector.
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A.1 How do I find the components of a vector?
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(+) Solve problems involving velocity and other quantities that can be represented by vectors.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Problem solving
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2 - Solve (problems involving velocity represented by vectors)
2 - Solve (problems involving quantities represented by vectors)
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2 - I can solve problems involving velocity represented by vectors.
2 - I can solve problems involving quantities represented by vectors.
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A. Vectors can be used to represent quantities in problem solving.
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A.1 How can vectors be used?
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(+) Add and subtract vectors.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Vectors [a]
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2 - Add (vectors end-to-end [a])
2 - Add (vectors by components [a])
2 - Add (vectors by parallelogram rule [a])
2 - Understand (Magnitude of a sum is not the sum of the magnitudes [a])
2 - Determine (magnitude of sum of 2 vectors in magnitude/direction form [b])
2 - Determine (direction of sum of 2 vectors in magnitude/direction form [b])
2 - Understand (vector subtraction as additive inverse [c])
2 - Understand (-w is same magnitude as w but in opposite direction [c])
2 - Represent (vector subtraction graphically by connecting tips in order [c])
2 - Perform (vector subtraction by components [c])
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2 - I can add vectors end-to-end [a].
2 - I can add vectors by components [a].
2 - I can add vectors by parallelogram rule [a].
2 - I can understand magnitude of a sum is not the sum of the magnitudes [a].
2 - I can determine magnitude of sum of 2 vectors in magnitude/direction form [b].
2 - I can determine direction of sum of 2 vectors in magnitude/direction form [b].
2 - I can understand vector subtraction as additive inverse [c].
2 - I can understand -w is same magnitude as w but in opposite direction [c]
2 - I can represent vector subtraction graphically by connecting tips in order [c].
2 - I can perform vector subtraction by components [c].
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A. Vectors can be added using several different methods.
B. Vector sums have magnitude and direction.
C. Vectors can be subtracted using several methods.
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A.1 How do I add vectors?
B.1 What are the characteristics of the sum of 2 vectors?
C.1 How do I subtract vectors?
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(+) Multiply a vector by a scalar.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Represent (scalar multiplication graphically by scaling vectors [a])
2 - Represent (scalar multiplication graphically by reversing vector's direction a])
2 - Perform (scalar multiplication by components [a])
2 - Compute (magnitude of scalar multiple [b])
3 - Use (||cv||=|c|v [b])
2 - Compute (direction of scalar multiple [b])
1 - Know (direction is along v for c>0 or against v for c<0 [b])
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2 - I can represent scalar multiplication graphically by scaling vectors [a].
2 - I can represent scalar multiplication graphically by reversing vector's direction [a].
2 - I can perform scalar multiplication by components [a].
2 - I can compute magnitude of scalar multiple [b].
3 - I can use ||cv||=|c|v [b].
2 - I can compute direction of scalar multiple [b].
1 - I know that direction is along v for c>0 or against v for c<0 [b].
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A. Vectors can be multiplied.
B. One can multiply a vector by a constant value.
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A.1. How do I multiply vectors?
A.2. How do I find the magnitude and direction of a vector product?
B.1 Why would I need to multiply a vector by a number?
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Perform operations on matrices and use matrices in applications.
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Matrices
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3 - Use (matrices to represent data)
3 - Use (matrices to manipulate data)
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3 - I can use matrices to represent data.
3 - I can use matrices to manipulate data.
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A. Matrices can be used to organize data.
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A.1 How do I set up a matrix?
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(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Matrices
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2 - Multiply (matrices by scalars)
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2 - I can multiply matrices by scalars.
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A. One can multiply matrices by a number.
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A.1 What is scalar multiplication?
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(+) Add, subtract, and multiply matrices of appropriate dimensions.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Add (matrices of appropriate dimensions)
2 - Subtract (matrices of appropriate dimensions)
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2 - I can add matrices of appropriate dimensions.
2 - I can subtract matrices of appropriate dimensions.
1 - I can multiply matrices of appropriate dimensions.
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A. Matrices can be added, subtracted, and multiplied.
B. One must have appropriate dimensions in order to perform operations on matrices.
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A.1 Can I perform operations on just any matrices?
B.1 How do I find the dimensions of a matrix?
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(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Understand (matrix multiplication for square matrices is not commutative)
2 - Understand (matrix multiplication for square matrices is associative)
2 - Understand (matrix multiplication for square matrices is distributive)
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2 - I can understand matrix multiplication for square matrices is not commutative.
2 - I can understand matrix multiplication for square matrices is associative.
2 - I can understand matrix multiplication for square matrices is distributive.
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A. The associative and distributive properties apply to multiplication of square matrices.
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A.1 Do operational properties apply to matrices?
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(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Understand (role of zero matrix in matrix addition)
2 - Understand (role of identity matrix in matrix multiplication)
2 - Understand (determinants of square matrices are nonzero if multiplicative inverses exist)
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2 - I can understand role of zero matrix in matrix addition.
2 - I can understand role of identity matrix in matrix multiplication.
2 - I can understand determinants of square matrices are nonzero if multiplicative inverses exist.
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A. The zero matrix functions in matrix addition just as 0 functions in real number addition.
B. The identity matrix functions in matrix multiplication just as 1 functions in real number multiplication.
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A.1 Why do we need the zero matrix?
B.1 Why do we need an identity matrix?
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(+) 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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Multiply (a vector [a one-column matrix] by a matrix of suitable dimensions)
3 - Work with (matrices as transformations of vectors)
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2 - I can multiply a vector [a one-column matrix] by a matrix of suitable dimensions.
3 - I can work with matrices as transformations of vectors.
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A. One can multiply a vector by a matrix to create another vector.
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A.1 How do I multiply a vector by a matrix?
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(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Work with (2x2 matrices as transformations of the plane)
2 - Interpret (absolute value of determinant as area)
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2 - I can work with 2x2 matrices as transformations of the plane.
2 - I can interpret absolute value of determinant as area.
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A. The absolute value of a determinant can represent area.
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A.1 How is the absolute value of a determinant used?
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