The purpose of this activity is to analyze a method of evaluating an expression involving exponents and negative numbers.

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 analyze a method of evaluating an expression involving exponents with negative numbers.

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.

• “Why did the solver put the -3 where the was in the expression?” (The problem asked the solver to evaluate the expression when is -3, so they substituted -3 for , since they are equal.)
• “In step 2, why is everything positive? What happened to the negative?” (The -3 was squared, or multiplied by itself. A negative number multiplied by a negative number is positive. So .)
• “How could the solver check their work to make sure they are correct?” (They could write an equation with the expression on one side of the equals sign and their solution on the other side. Then they could solve for and see if , in which case they have the right answer. In this case, it would be . Subtracting 7 from each side gives . The final step is taking the square root of each side, which gives two possible answers, 3 and -3.)

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). For example, solving the same problem but replacing the 9 in step 2 with -9.

In this activity, students use graphing technology to see how adjusting different parts of a linear equation affect its graph. This connects to the associated Algebra 1 lesson where students will look at similar effects to quadratic equations. When students vary the parameters in a linear function and record their observations, they have an opportunity to attend to precision through their word choices (MP6).

This activity is an opportunity to practice evaluating quadratic expressions for a negative value of the variable and choosing parameters of an equation that will result in its graph looking a certain way. Students’ repeated work with evaluating quadratic expressions involving negative values allows them to express regularity in repeated reasoning (MP8).