Academic Standard

Algebra
Initiative: 
Tennessee Diploma Project
Set: 
Mathematics
Type: 
Standard
Code: 
3
Grade range: 
8
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?
 
Elements within this Standard
 
Grade Level Expectation
Recognize and generate equivalent forms for algebraic expressions.
Represent, analyze, and solve problems involving linear equations and inequalities in one and two variables.
Solve systems of linear equations in two variables.
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
Use slope to analyze situations and solve problems.
Compare and contrast linear and nonlinear functions.
Check For Understanding
Perform basic operations on algebraic expressions (including grouping, order of operations, exponents, square/cube roots, simplifying and expanding).
Represent algebraic relationships with equations and inequalities.
Solve systems of linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line.
Understand the relationship between the graph of a linear inequality and its solutions.
Solve linear inequalities in two variables (including those whose solutions require multiplication or division by a negative number).
Identify x- and y-intercepts and slope of linear equations from an equation, graph or table.
Analyze situations and solve problems involving constant rate of change.
Recognize a proportion as a special case of a linear equation and understand that the constant of proportionality is the slope, and the resulting graph is a line
Given a function rule, create tables of values for x and y, and plot graphs of nonlinear functions.
Distinguish quadratic and exponential functions as nonlinear using a graph and/or a table of values.
Distinguish between the equations of linear, quadratic, and exponential functions (e.g. function families such as y=x2, y=2x, and y=2x).
Understand how rates of change of nonlinear functions contrast with constant rates of change of linear functions.
Represent situations and solve real-world problems using symbolic algebra.
State Performance Indicator
Find solutions to systems of two linear equations in two variables.
Solve the linear equation f(x) = g(x).
Solve and graph linear inequalities in two variables.
Translate between various representations of a linear function.
Determine the slope of a line from an equation, two given points, a table or a graph.
Analyze the graph of a linear function to find solutions and intercepts.
Identify, compare and contrast functions as linear or nonlinear.