This Math Talk focuses on fluency with multi-digit multiplication. It encourages students to think about and rely on the properties of operations to mentally solve problems. The strategies and understanding elicited here will be helpful later in the associated Algebra 1 lesson when students solve multistep equations.

To compare different representations of the same multiplication problem, students need to look for and make use of structure (MP7).

The goal of this discussion is to review students’ strategies for solving expressions, particularly when the distributive property can be used. To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

As you record, consider using notation that makes properties of operations, such as the associative and distributive properties, visible. For example, if a student evaluates  and describes it as an extension of evaluating , record that as  and ask students if your recording matches the student’s thinking. Ask students how they know that . It’s fine if students don’t name the distributive property, as long as they recognize that you can multiply 10 and 3 by 3 separately and add the results, or add first and then multiply. 

The purpose of this activity is to help students focus on not just the what, but the why and how of moves that are made when solving equations. Students who struggle often have a hard time seeing the steps that are taken to solve an equation as purposeful moves and struggle to understand the choices made. Focusing on the why and the justification will help students when they work to make sense of solving systems of equations and solving equations with multiple variables for one of the variables. As students discuss different methods of solving equations, they have the opportunity to construct viable arguments and critique the reasoning of others (MP3).

Monitor for students who make different choices in solving the equation in the second problem—either distributing first, or multiplying or dividing to get rid of the coefficient of the quantity in parentheses.

In this activity, students get a chance to practice working with formulas and writing them in equivalent forms, or expressing regularity in repeated reasoning as they find the values of unknown quantities in the formulas (MP8).

The practice will pay off in the associated Algebra 1 lesson when they solve formulas and equations to isolate chosen variables.

Monitor for students who come up with steps or algorithms or even write rules or formulas that they use for each of the problems. Let students know that they will be asked to share their algorithm, rule, or process, and that they should be prepared to explain it to the class.

This is the first time Math Language Routine 3: Critique, Correct, Clarify is suggested in this course. In this routine, students are given a “first draft” statement or response to a question that is intentionally unclear, incorrect, or incomplete. Students analyze and improve the written work by first identifying what parts of the writing need clarification, correction, or details, and then by writing a second draft (individually or with a partner). Finally, the teacher scribes as a selected second draft is read aloud by its author(s), and the whole class is invited to help edit this “third draft” by clarifying meaning and adding details to make the writing as convincing as possible to everyone in the room.

Typical prompts are: “Is anything unclear?” and “Are there any reasoning errors?” The purpose of this routine is to engage students in analyzing mathematical writing and reasoning that is not their own, and to solidify their knowledge and use of language.