Understands and applies number operations and properties
There are many important types of numbers, operations on numbers, and properties of numbers that students need to understand and apply. For example, prime numbers (numbers divisible only by 1 and themselves) are used in encrypting credit card numbers in online e-commerce transactions, the commutative property (e.g., 2 x 3 = 3 x 2) is true when multiplying real numbers but not when multiplying matrices, and the property that ab = 0 implies a = 0 or b = 0 is useful for solving equations.
As problem situations become more sophisticated in high school, the need arises to build on and expand students' understanding of number, operations on numbers, properties of number, and different number systems. Students should solve problems with solutions involving natural numbers, whole numbers, integers, rational numbers, real numbers, and complex numbers. Students should understand and apply the properties of the operations (add, subtract, multiply and divide) within the number systems.
Students should use mental, pencil-paper, and technology-based computation techniques. Given a variety of situations, students should determine the reasonableness of computation results. Students should develop skills in estimating, approximating, and judging the size and appropriateness of numbers.