ALCA PLC Members 7 Steps Data Standards Map Plan Curriculum Assessment Strategies
Comments
Favorite
Send

N - Complex Number System

This text resource illustrates the Standards Map for the Number and Quantity Overview Complex Number System domain in the Common Core State Standards.

Standards

  3. Common Core Mathematics: Number and Quantity > CN > C.1

    Perform arithmetic operations with complex numbers.

  4. Common Core Mathematics: Number and Quantity > CN > C.1 > S.1

    Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

    Content Skills Learning Targets Big Ideas Essential Questions
    Complex numbers
    1 - Know (i denotes a complex number)
    1 - Know (i^2 = -1)
    1 - Know (complex numbers are of the form a + bi, with a and b real)
    1 - I can know that i denotes a complex number.
    1 - I can know that i^2 = -1.
    1 - I can know that complex numbers are of the form a + bi, with a and b real.
    A. There is a set of complex numbers in which i represents an imaginary number.
    A. Why do we need imaginary numbers?
  5. Common Core Mathematics: Number and Quantity > CN > C.1 > S.2

    Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

    Content Skills Learning Targets Big Ideas Essential Questions
    3 - Use (i^2 = -1 and the commutative property to add, subtract, and multiply complex numbers)
    3 - Use (i^2 = -1 and the associative property to add, subtract, and multiply complex numbers)
    3 - Use (i^2 = -1 and the distributive property to add, subtract, and multiply complex numbers)
    3 - I can use i^2 = -1 and the commutative property to add, subtract, and multiply complex numbers.
    3 - I can use i^2 = -1 and the associative property to add, subtract, and multiply complex numbers.
    3 - I can use i^2 = -1 and the distributive property to add, subtract, and multiply complex numbers.
    A. The properties of real numbers apply also to complex numbers.
    A.1 Do complex numbers relate to real numbers?
  6. Common Core Mathematics: Number and Quantity > CN > C.1 > S.3

    (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

    Content Skills Learning Targets Big Ideas Essential Questions
    Complex numbers
    2 - Find (conjugate of a complex number)
    3 - Use (conjugates to find moduli of complex numbers)
    3 - Use (conjugates to find quotients of complex numbers)
    2 - I can find the conjugate of a complex number.
    3 - I can use conjugates to find moduli of complex numbers.
    3 - I can use conjugates to find quotients of complex numbers.
    A. Conjugates of complex numbers are used in several ways when working with complex numbers.
    A.1. What is a conjugate of a complex number?
    A.2. How do I use the conjugate of a complex number?
  7. Common Core Mathematics: Number and Quantity > CN > C.2

    Represent complex numbers and their operations on the complex plane.

  8. Common Core Mathematics: Number and Quantity > CN > C.2 > S.4

    (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Represent (complex numbers in rectangular form on the complex plane)
    2 - Represent (complex numbers in polar form on the complex plane)
    2 - Explain (why rectangular and polar forms represent the same number)
    2 - I can represent complex numbers in rectangular form on the complex plane.
    2 - I can represent complex numbers in polar form on the complex plane.
    2 - I can explain why rectangular and polar forms represent the same number.
    A. Complex numbers can be written in polar form and rectangular form.
    A. Why do I need to know how to write complex numbers in different forms?
  9. Common Core Mathematics: Number and Quantity > CN > C.2 > S.5

    (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (1 – √3i)3 = 8 because (1 – √3i) has modulus 2 and argument 120°.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Represent (addition of complex numbers geometrically on complex plane)
    2 - Represent (subtraction of complex numbers geometrically on complex plane)
    2 - Represent (multiplication of complex numbers geometrically on complex plane)
    3 - Use (properties for computation)
    2 - I can represent addition of complex numbers geometrically on complex plane.
    2 - I can represent subtraction of complex numbers geometrically on complex plane.
    2 - I can represent multiplication of complex numbers geometrically on complex plane.
    1 - I can represent conjugation of complex numbers geometrically on complex plane.
    3 - I can use properties for computation.
    A. One can represent the operations of addition, subtraction, and multiplication geometrically on the complex number plane.
    A.1 How can graphing complex numbers on the complex number plane be useful?
  10. Common Core Mathematics: Number and Quantity > CN > C.2 > S.6

    (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Calculate (distance between numbers as modulus of difference)
    2 - Calculate (midpoint of a segment is the average of the coordinates of the endpoints)
    2 - I can calculate the distance between numbers in the complex plane as modulus of difference.
    2 - I can calculate the midpoint of a segment is the average of the coordinates of the endpoints.
    A. One can find the distance and the midpoint of segments graphed on the complex plane.
    A.1 Are there any similarities between points on the coordinate plane and points on the complex plane?
  11. Common Core Mathematics: Number and Quantity > CN > C.3

    Use complex numbers in polynomial identities and equations.

  12. Common Core Mathematics: Number and Quantity > CN > C.3 > S.7

    Solve quadratic equations with real coefficients that have complex solutions.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Solve (quadratic equations with real coefficients having complex solutions)
    2 - I can solve quadratic equations with real coefficients having complex solutions.
    A. Solutions to quadratic equations can be real or complex numbers.
    A. Do complex roots tell me anything about the function they came from?
  13. Common Core Mathematics: Number and Quantity > CN > C.3 > S.8

    (+) Extend polynomial identities to the complex numbers.

    For example, rewrite x2 + 4 as (x + 2i)(x - 2i).

    Content Skills Learning Targets Big Ideas Essential Questions
    Complex numbers
    2 - Extend (polynomial identities to complex numbers)
    2 - I can extend polynomial identities to complex numbers.
    A. Polynomial identities extend to complex numbers.
    A. How do complex numbers connect to polynomials?
  14. Common Core Mathematics: Number and Quantity > CN > C.3 > S.9

    (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

    Content Skills Learning Targets Big Ideas Essential Questions
    Fundamental Theorem of Algebra
    1 - Know (Fundamental Theorem of Algebra)
    2 - Show (Fundamental Theorem of Algebra true for quadratic polynomials)
    1 - I can know the Fundamental Theorem of Algebra.
    2 - I can show that the Fundamental Theorem of Algebra is true for quadratic polynomials.
    A. The Fundamental Theorem of Algebra applies to quadratic polynomials.
    A. How is the Fundamental Theorem of Algebra used?

Comments

Be the first to comment below.

Please enter a Registration Key to continue.