N-VM - Domain

Vector & Matrix Quantities

High School Number & Quantity · Common Core State Standards · Common Core 2010

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Vocabulary
vector quantitiesmagnitudedirectioncomponentsinitial pointterminal pointvelocityscalardirected line segmentsmagnitude and direction formadditive inversescalar multiplicationmatrixmatricestransformationsplanedeterminant
Skills
  • Recognize (vector quantities as having both magnitude and direction) #dok1
  • Represent (vector quantities by directed line segments) #dok1
  • Use (appropriate symbols for vectors and their magnitudes) #dok1
  • Find (components of a vector by subtracting coordinates of an initial point from a terminal point) #dok2
  • Solve (problems involving velocity and other quantities with vectors) #dok2
  • Add and subtract (vectors) #dok2
  • Multiply (a vector by a scalar) #dok3
  • Use (matrices to represent and manipulate data) #dok3
  • Perform (operations on matrices and use matrices in applications) #dok4
Learning Targets
  • I can recognize vector quantities as having both magnitude and direction. #dok1
  • I can represent vector quantities by directed line segments. #dok1
  • I can use appropriate symbols for vectors and their magnitudes. #dok1
  • I can find the components of a vector by subtracting coordinates of an initial point from a terminal point. #dok2
  • I can solve problems involving velocity and other quantities that can be represented by vectors. #dok2
  • I can add and subtract vectors. #dok2
  • I can multiply a vector by a scalar. #dok3
  • I can use matrices to represent and manipulate data. #dok3
  • I can perform operations on vectors and matrices within various applications. #dok4
Big Ideas
  • Vectors are quantities that have both magnitude and direction and can be visually represented.
  • Operations such as addition, subtraction, and scalar multiplication can be applied to vectors and matrices to solve real-world problems.
Essential Questions
  • What are vector quantities, and how do they differ from scalar quantities?
  • How can vector operations like addition and subtraction be represented graphically?
  • In what ways can scalar multiplication affect the magnitude and direction of a vector?
  • How can matrices represent and manipulate data in mathematical and real-world contexts?
  • How do matrix operations relate to geometric transformations on the plane?