The purpose of this activity is to remind students of a strategy for multiplying using binomials.

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 clarify using a diagram to solve multiplication problems by rewriting the factors as binomials.

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.

• “In the first step, the solver changes the two numbers into expressions related to 10. Why did the solver use 10?” (10 is a number that most people know the multiples of without much thinking, so it makes the math more accessible.)
• “Why did the solver put on the top of the diagram?” (The solver made a choice, but could go on top or on the side.)
• “After completing the diagram, how did the solver know when to add and subtract each number?” (All of the numbers are being added, but adding a negative number is the same as subtracting. The last step could have been written as .)

Ask partners to compare their responses to each question to 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 learn and practice a method for multiplying two values of the form . Through the discussion, students should begin to recognize that two of the terms from the expanded form are opposites. In the associated Algebra 1 lesson, students examine quadratic expressions that can be factored into the form . Using diagrams supports students as they look for and make use of structure (MP7).

In this activity, students find missing parts of a multiplication diagram. This strategy will be useful in the associated Algebra 1 lesson when they factor polynomials. Students look for and make use of structure (MP7) when they use tables to understand the relationships between 2 numbers.