Academic Context and Connections
Finer grained standards that are part of this one
Make sense of problems and persevere in solving them.
In high school, students abstract and generalize about linear functions and how they compare and contrast to nonlinear functions. Students also reason about and solve systems of equations that include one or more nonlinear equations.
Look for and make use of structure.
How is it possible for an equation to have more than one solution? How is it possible for an equation to have no solution?
In previous grades, students reason about and solve one-step and two-step, one-variable equations and inequalities, use properties of operations to generate equivalent expressions, and solve real-world and mathematical problems using numerical and algebraic expressions and equations.
What is meant by a “solution” to a linear equation? What is meant by a “solution” to a system of two linear equations? How are these concepts related?
This expectation represents major work of the grade.
Why can’t a system of linear equations have a solution set other than one, zero, or infinitely many solutions?
In Grade 8, this expectation connects with understanding the connections between proportional relationships, lines, and linear equations and with investigating patterns of association in bivariate data.