In this section, students recall how to write expressions and equations from situations that can vary or have unknown quantities. They begin by modeling situations using self-defined variables and constraints that fit the situation. Then, they use tables to examine patterns of values and use those to write equations. They recall what it means for a value to be a solution to an equation and then graph the equations to look at several solutions.

Use the Check Your Readiness to assess students’ incoming understanding of manipulating expressions and equations. If there is a solid understanding, feel free to move quickly through the optional lessons or skip them to save time.

Graph of a line, origin O. Horizontal axis, pounds of beans, scale is 0 to 100, by 20’s. Vertical axis, pounds of rice, scale is 0 to 280, by 40’s. Line starts at 0 comma 240, passes through 10 comma 200, 30 comma 120 and 60 comma 0. Points 20 comma 80 and 70 comma 180 are shown but not on the line.

In the final section, students have the opportunity to apply their thinking from throughout the unit. Because this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions.

In this section, students make use of equivalent equations to solve for variables. Initially, students solve equations for an unknown quantity, then later solve for a variable in terms of another variable to reinterpret situations and find values more efficiently. Then, students draw closer connections between graphs and equations in both standard and slope-intercept form.

In this section, students revisit systems of equations and develop algebraic methods for finding any solutions. In earlier grades, students explored solving systems using graphs and substitution methods. In addition to revisiting these concepts, students use what they have learned in previous sections about writing equivalent equations to solve systems by using elimination methods.

After looking at solutions to systems on a graph, students use substitution and elimination methods to solve the systems. They see that equivalent equations have different graphs, but continue to intersect the other graphs at the solution to the system. The final lesson of the section looks, graphically as well as algebraically, at linear systems that have no solution or infinitely many solutions.