Number and Operations
Tennessee Diploma Project
9 to 12
Conceptual StrandThe Number and Operations Standard describes deep and fundamental understanding of, and proficiency with, counting, numbers, and arithmetic, as well as an understanding of number systems and their structures.Guiding QuestionHow do students develop number sense that allows them to naturally decompose numbers, use particular numbers as referents, solve problems using the relationships among operations and knowledge about the base-ten system, estimate a reasonable result for a problem, and have a disposition to make sense of numbers, problems, and results?
Course Level Expectation
Understand the hierarchy of the complex number system and relationships between the elements, properties and operations.
Connect numeric, analytic, graphical and verbal representations of both real and complex numbers.
Use appropriate technology (including graphing calculators and computer spreadsheets) to solve problems, recognize patterns and collect and analyze data.
Understand the capabilities and limitations of technology when performing operations, graphing, and solving equations involving complex numbers.
Check For Understanding
Understand that to solve certain problems and equations, the real number system needs to be extended from real numbers to complex numbers.
Define and give examples of each of the types of numbers in the complex number system.
Identify and apply properties of complex numbers (including simplification and standard form).
Add and subtract complex numbers.
Multiply complex numbers.
Define and utilize the complex conjugates to write the quotient of two complex numbers in standard form.
Graph complex numbers in the complex plane and recognize differences and similarities with the graphical representations of real numbers graphed on the number line.
Solve quadratic equations over the complex number system.
Understand the capabilities and limitations of technology. Make estimations without a calculator to detect potential errors.
Select and use appropriate methods to make estimations without technology when solving contextual problems.
Analyze and evaluate contextual situations involving any type of number from the complex number system.
State Performance Indicator
Describe any number in the complex number system.
Compute with all real and complex numbers.
Use the number system, from real to complex, to solve equations and contextual problems