In this Warm-up, students use the order of operations to find the value of expressions involving square roots. Using their knowledge of order of operations is a form of looking for and making use of structure (MP7). In the associated Algebra 1 lesson, students will use the quadratic formula, so understanding the order of operations will be useful.

The purpose of the discussion is to remind students how square roots fit into the order of operations. Invite students to share their answers and clarify any understanding. Here are some questions for discussion:

• “Why is the last expression not equal to 7?” (The expression under the square root acts like an understood parentheses, so the values are squared and summed before the square root applies.)
• “Which is a greater value: or ? Explain how you know.” ( is greater, because the square root applies only to the 4 rather than to the sum of 4 and 5. and )

In this activity students rewrite quadratic equations into the form , then identify the values for and , then use those values to find . In the associated Algebra 1 lesson, students work with the quadratic formula. Identifying the values to be used in the quadratic formula and using the values to find the discriminant supports students to use the quadratic formula in its entirety. This practice familiarizes students with the structure of standard form quadratic equations and the quadratic formula (MP7).

In this activity, students are not told a specific method to use to solve quadratic equations. In the associated Algebra 1 lesson, students are introduced to the quadratic formula to solve quadratic equations. Here, students are reminded of the other methods, which can be more or less efficient for solving equations. When students are clear in their reasoning for the method they choose, they attend to precision (MP6).

Monitor for students who use these different strategies:

• Factoring
• Completing the square