Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Understand meanings of operations and how they relate to one another
Compute fluently and make reasonable estimates
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number.
Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(24 - 1) = 45, 4|3 - 5| + 6 = 14; apply such simplifications in the solution of problems.
Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g., .
Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
Exploratory Concepts and Skills for Grades 9-10 and Single-Subject Courses
Analyze relationships among the various subsets of the real numbers (whole numbers, integers, rationals, and irrationals).
Explore higher powers and roots using technology.
Explore the system of complex numbers and find complex roots of quadratic equations.