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Lesson Plans (1) A detailed description of the instruction for teaching one or more concepts or skills. Classroom Resources (1)


ALEX Lesson Plans  
   View Standards     Standard(s): [MA2015] AL2 (9-12) 5 :
5 ) (+) Extend polynomial identities to the complex numbers.

Example: Rewrite x2 + 4 as (x + 2i)(x - 2i). [N-CN8]

[MA2015] ALT (9-12) 5 :
5 ) (+) Extend polynomial identities to the complex numbers. [N-CN8]

Example: Rewrite x2 + 4 as (x + 2i)(x - 2i).

Subject: Mathematics (9 - 12)
Title: Complex Numbers Solutions
Description:

This lesson is designed to teach the students that some quadratic equations will have imaginary solutions. The lesson will examine the concept of complex numbers in terms i. The student will use the quadratic formula to solve the equations and write the the solutions in the form a +bi.

This lesson results from the ALEX Resource Gap Project.




ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] AL2 (9-12) 5 :
5 ) (+) Extend polynomial identities to the complex numbers.

Example: Rewrite x2 + 4 as (x + 2i)(x - 2i). [N-CN8]

[MA2015] AL2 (9-12) 6 :
6 ) (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [N-CN9]

[MA2015] PRE (9-12) 13 :
13 ) (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal's Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.) [A-APR5]

[MA2015] ALT (9-12) 5 :
5 ) (+) Extend polynomial identities to the complex numbers. [N-CN8]

Example: Rewrite x2 + 4 as (x + 2i)(x - 2i).

[MA2015] ALT (9-12) 6 :
6 ) (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [N-CN9]

[MA2015] PRE (9-12) 37 :
37 ) (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. [G-GPE3]

[MA2015] PRE (9-12) 38 :
38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]

Subject: Mathematics (9 - 12)
Title: Precalculus and Advanced Topics Module 3, Topic A: Polynomial Functions and the Fundamental Theorem of Algebra
URL: https://www.engageny.org/resource/precalculus-and-advanced-topics-module-3-topic-a-overview
Description:

Module 3, Topic A brings students back to the study of complex roots of polynomial functions.  Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both complex numbers and to general polynomial functions. Students use polynomial identities to find square roots of complex numbers. The binomial theorem and its relationship to Pascal’s Triangle are explored using roots of unity. The topic concludes with students’ use of Cavalieri’s principle to derive formulas for the volume of the sphere and other geometric solids.

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses of Study.



ALEX Classroom Resources: 1

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