LAC 28:CXLII.1505. Algebraic Reasoning

A. Apply and extend previous understandings of arithmetic to algebraic expressions. 1. Understand, write, and evaluate numerical expressions involving whole-number exponents. a. Identify parts of exponential notation using mathematical terms base and exponent. b. Represent and evaluate powers using a whole number or fraction as the base and a whole number as an exponent, and evaluate numerical expressions. 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. b. Identify parts of an expression using mathematical terms sum, term, product, factor, quotient, and coefficient; view one or more parts of an expression as a single entity. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order of operations. 3. Apply the properties of operations to generate equivalent expressions, identify when two expressions are equivalent, and explain why two expressions are equivalent. B. Reason about and solve one-variable equations and inequalities. 1. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 3. Solve real-world and mathematical problems by writing and solving equations and inequalities of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. Inequalities will include >, <, ≥, and ≤. 4. Translate a real-world written description into an algebraic inequality in the form of x > c or x < c. Describe and interpret the infinitely many solutions for x>c or x<c and graph the solutions on a number line. C. Represent and analyze quantitative relationships between dependent and independent variables. 1. Use variables to represent two quantities in a real-world problem that change in relationship to one another. a. Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. b. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.