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Title: Classifying Complex Numbers
Description:
This lesson helps students distinguish between strictly complex numbers, strictly real numbers and strictly imaginary numbers while learning that real numbers and imaginary numbers are subsets of the set of complex numbers.
Standard(s): [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4] [MA2013] AL2 (912) 1: Know there is a complex number i such that i^{2} = 1, and every complex number has the form a + bi with a and b real. [NCN1] [MA2013] ALT (912) 1: Know there is a complex number i such that i^{2} = 1, and every complex number has the form a + bi with a and b real. [NCN1] [MA2013] MI1 (912) 4: Explain the development and uses of sets of numbers, including complex, real, rational, irrational, integer, whole, and natural numbers. (Alabama) [MA2013] PRE (912) 1: (+) 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. [NCN4]
Subject: Mathematics (9  12)
Title: Classifying Complex Numbers
Description: This lesson helps students distinguish between strictly complex numbers, strictly real numbers and strictly imaginary numbers while learning that real numbers and imaginary numbers are subsets of the set of complex numbers.
Thinkfinity Lesson Plans
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Title: Approximations of Pi
Description:
This student reproducible, from an Illuminations lesson, provides information about and several examples of approximations for the constant pi.
Standard(s): [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (8) 1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8NS1] [MA2013] (8) 2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^{2}). [8NS2] [MA2013] GEO (912) 35: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [GGMD1] [MA2013] MI1 (912) 4: Explain the development and uses of sets of numbers, including complex, real, rational, irrational, integer, whole, and natural numbers. (Alabama) [MA2013] AM1 (912) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)
Subject: Mathematics Title: Approximations of Pi
Description: This student reproducible, from an Illuminations lesson, provides information about and several examples of approximations for the constant pi. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Caesar Cipher
Description:
In this lesson, one of a multipart unit from Illuminations, students investigate the Caesar substitution cipher. Text is encoded and decoded using inverse operations.
Standard(s): [MA2013] MI1 (912) 4: Explain the development and uses of sets of numbers, including complex, real, rational, irrational, integer, whole, and natural numbers. (Alabama) [MA2013] MI1 (912) 8: Solve problems from nonEuclidean geometry, including graph theory, networks, topology, and fractals. (Alabama) [MA2013] MI1 (912) 10: Determine the mathematical impact of the ancient Greeks, including Archimedes, Eratosthenes, Euclid, Hypatia, Pythagoras, and the Pythagorean Society. (Alabama)
Subject: Mathematics Title: Caesar Cipher
Description: In this lesson, one of a multipart unit from Illuminations, students investigate the Caesar substitution cipher. Text is encoded and decoded using inverse operations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

