### Grades / Levels

### Standards

Code | Grade | Cluster | Standard | Object Count |
---|---|---|---|---|

N-VM.1 | High School - Number and Quantity | Represent and model with vector quantities. | (+) 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). | 0 |

N-VM.2 | High School - Number and Quantity | Represent and model with vector quantities. | (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | 0 |

N-VM.3 | High School - Number and Quantity | Represent and model with vector quantities. | (+) Solve problems involving velocity and other quantities that can be represented by vectors. | 0 |

N-VM.4 | High School - Number and Quantity | Perform operations on vectors. | (+) Add and subtract vectors. •Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. •Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. •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 component-wise. | 0 |

N-VM.5 | High School - Number and Quantity | Perform operations on vectors. | (+) Multiply a vector by a scalar. •Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v.x, v.y) = (cv.x, cv.y). •Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ? 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). | 0 |

N-VM.6 | High School - Number and Quantity | Perform operations on vectors. | (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | 0 |

N-VM.7 | High School - Number and Quantity | Perform operations on matrices and use matrices in applications. | (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | 0 |

N-VM.8 | High School - Number and Quantity | Perform operations on matrices and use matrices in applications. | (+) Add, subtract, and multiply matrices of appropriate dimensions. | 2 |

N-VM.9 | High School - Number and Quantity | Perform operations on matrices and use matrices in applications. | (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. | 0 |

N-VM.10 | High School - Number and Quantity | Perform operations on matrices and use matrices in applications. | (+) 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. | 0 |

N-VM.11 | High School - Number and Quantity | Perform operations on matrices and use matrices in applications. | (+) 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. | 0 |

N-VM.12 | High School - Number and Quantity | Perform operations on matrices and use matrices in applications. | (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. | 0 |