The purpose of this activity is to show a way to find the value of expressions involving absolute value.

This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.

The purpose of this discussion is to highlight the things students should remember when evaluating expressions involving absolute value.

Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.

• “What part of the original expression did the solver do first? Why?” (The solver started by finding the value of the expression inside of the absolute value signs. When solving expressions or equations, absolute value signs act like parentheses or other grouping symbols.)
• “In step 2, why did the 9 become positive?” (Absolute value is the distance a number is from 0, and distance is always a positive measurement. If 0 and -9 were on a number line, they would be 9 units apart.)
• “How did the solver know to keep going after they finished with the absolute value signs? How did they know when to stop?” (This problem has more steps than just the absolute value. The expression also includes multiplication and division. To find the value of the expression, all of the mathematical steps must be completed, leaving a number [and sometimes variables, but not in this case].)

Ask partners to compare their responses to each question and decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.

If time allows, consider displaying a second worked example next to the first that either:

• Shows a different method of solving a similar problem that students can compare and contrast with the first example (MP7).
• Shows the same method with an error that students can critique and correct (MP3).

In this activity students recall the notation for absolute value presented in grade 6 by explaining the meaning of absolute values in a situation and then comparing values using absolute value. Students reason abstractly and quantitatively when interpreting the meaning of absolute value (MP2). In the associated Algebra 1 lesson, students build on the understanding from grade 6 by thinking of the absolute value function as a piecewise function.

In this activity, students get more familiar with how to use the absolute value by reviewing its place in order of operations. In the associated Algebra 1 lesson, students examine absolute value as a piecewise function. This activity helps familiarize students with absolute value as an operation before they understand it as a function.

In this activity, students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).