Tennessee Diploma Project
Conceptual StrandThe Algebra Standard emphasizes relationships among quantities, including functions, patterns, ways of representing mathematical relationships, and the analysis of change.Guiding QuestionHow does algebra encompass the relationships among quantities, the use of symbols, the modeling of phenomena, and the mathematical study of change?
Grade Level Expectation
Recognize and generate equivalent forms for simple algebraic expressions.
Understand and compare various representations of relations and functions.
Understand the concept of function as a rule that assigns to a given input one and only one number (the output).
Use function notation where f(x) represents the output that the function f assigns to the input x.
Understand and graph proportional relationships.
Conceptualize the meanings of slope using various interpretations, representations, and contexts.
Use mathematical models involving linear equations to analyze real-world phenomena.
Use a variety of strategies to efficiently solve linear equations and inequalities.
Check For Understanding
Perform basic operations on linear expressions (including grouping, order of operations, exponents, simplifying and expanding).
Represent and analyze mathematical situations using algebraic symbols.
Identify a function from a written description, table, graph, rule, set of ordered pairs, and/or mapping.
Make tables of inputs x and outputs f(x) for a variety of rules that include rational numbers (including negative numbers) as inputs.
Plot points to represent tables of linear function values.
Understand that the graph of a linear function f is the set of points on a line representing the ordered pairs (x, f(x)).
Distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).
Understand slope as the ratio of vertical change to horizontal change.
Identify a function exhibiting a constant rate of change as a linear function and identify the slope as a unit rate.
Solve problems involving unit rates (e.g., miles per hour, words per minute).
Relate the features of a linear equation to a table and/or graph of the equation.
Use linear equations to solve problems and interpret the meaning of slope, m, and the y-intercept, b, in f(x)= mx + b in terms of the context.
Given a graph that exhibits the intersection of a line and the y-axis, write a linear function in slope-intercept form: y = mx + b.
Understand that when solving linear inequalities, multiplication or division by a negative reverses the inequality symbol.
State Performance Indicator
Evaluate algebraic expressions involving rational values for coefficients and/or variables.
Determine whether a relation (represented in various ways) is a function.
Given a table of inputs x and outputs f(x), identify the function rule and continue the pattern.
Interpret the slope of a line as a unit rate given the graph of a proportional relationship.
Represent proportional relationships with equations, tables and graphs.
Solve linear equations with rational coefficients symbolically or graphically.
Translate between verbal and symbolic representations of real-world phenomena involving linear equations.
Solve contextual problems involving two-step linear equations.
Solve linear inequalities in one variable with rational coefficients symbolically or graphically.