In this activity, students solve quadratic equations that can be written as a perfect square equal to a constant. In the associated Algebra 1 lesson, students recognize patterns of quadratic equations that can be written as perfect squares. The work of this activity supports students in solving those equations after they have been written as perfect squares. As students strategize how to approach each problem they make sense of problems and persevere in solving them (MP1).

The purpose of the discussion is to remind students of methods for solving quadratic equations that can be written as a perfect square equal to a constant. Select students to share their solutions and reasoning. Here are some questions for discussion:

• “Compare the equations in this activity to an equation like . What is the same? What is different?” (They are all quadratic and can be written as an expression equal to a constant. The ones in the activity, though, can be written as something squared equal to a constant.)
• “Why are there two solutions to each of these equations?” (Since they involve , there are usually 2 values that can square to the same number, which provides a second solution.)

In this activity, students work to write simpler versions of expressions. All of the expressions in this row game can be written as a perfect square. Students work in pairs, and each partner is responsible for answering the questions in either column A or column B. Although each row has two different problems, they share the same answer. Ensure that students work their problems out independently and collaborate with one another when they do not arrive at the same answers. Students construct viable arguments and critique the reasoning of others (MP3) when they resolve errors by critiquing their partner’s work or explaining their reasoning. In the associated Algebra 1 lesson, students look for quadratic expressions that can be written as perfect squares. Recognizing a perfect square in different forms will support students for the Algebra 1 lesson.

The purpose of the discussion is for students to recognize some different forms of expressions that can be written as perfect squares. Select groups to share their solutions and methods for rewriting the expressions. Record the simplified expressions for all to see. Here are some questions for discussion:

• “What do you notice about all of the solutions?” (They are all written as perfect squares.)
• “Expand the last two expressions into standard form. Do you notice anything that might help you recognize them as quadratic expressions that could be written as something squared?” ( and . I noticed that, when written in standard form as , and are perfect squares. (It is ok at this stage if students notice patterns that are specific to these examples, rather than ideas that are more general. In the associated Algebra 1 lesson, students will start to recognize these patterns.)