Students will understand, develop, and use computational skills and techniques, including estimation, mental math, paper-and-pencil, calculators, and computers, in problem-solving situations.

Elementary Level

Middle School Level

High School Level

• Demonstrates conceptual meanings for the four basic arithmetic operations
• Selects and uses a appropriate method for computing with whole numbers in problem-solving situations from among mental math, estimation, paper-and-pencil, calculator and computer methods
• Models, explains, and demonstrates proficiency with addition and subtraction facts, and with multiplication and division of numbers through 12
• Computes and estimates with whole numbers
• Understands the concept of commutative and associative properties

• Computes and estimates with whole numbers, fractions, decimals, integers, rational and irrational numbers
• Selects and uses an appropriate method for computing with commonly-used fractions and decimals, percents and integers from among mental math, estimation, paper-and-pencil, calculator and computer methods, and determines whether the results are reasonable
• Applies and describes a variety of different estimation strategies in problem-solving situations explaining why an estimate is acceptable in place of an exact answer
• Solves real-world problems involving ratios, proportions, percents, fractions, decimals, integers, exponents, rational and irrational numbers
• Knows and applies the standard algebraic order of operations (parenthesis, exponents, multiplication, division, addition, subtraction)
• Applies the associative, commutative, distributive, inverse, and identity properties
• Demonstrates an understanding of operational algorithms (procedures for adding, subtracting, etc.)
• Develops appropriate proficiency with facts and algorithms

• Uses addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions
• Develops an understanding of and uses the composition of functions and transformations
• Explores and uses negative exponents on integers and algebraic expressions
• Uses field properties to justify mathematical procedures
• Uses transformations on figures and functions in the coordinate plane
• Uses rational exponents on real numbers and all operations on complex numbers

• Uses appropriate techniques including graphing utilities to perform addition and subtraction on matrices

**********

For students continuing their mathematics education, what they know and are able to do may include:

• Uses appropriate techniques, including graphing utilities to perform basic operations on matrices
• Combines functions using the basic operations and the composition of two functions