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Which three go together? Why do they go together?
A
B
C
D
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology they use, such as “terms,” “coefficient,” “combine,” or “distribute” and to clarify their reasoning as needed. Consider asking:
In this activity, students encounter typical errors with signed numbers, operations, and properties. They are tasked with identifying which strategies are correct. For those that are not, students must describe the error that was made.
Since students are contrasting and critiquing different approaches, they are critiquing the reasoning of others (MP3).
Ensure students understand the task: first they decide whether they agree with each person's strategy, but they also need to describe the errors that were made. Give 5 minutes quiet work time followed by a whole-class discussion.
Some students are trying to write an expression with fewer terms that is equivalent to
Noah says, “I worked the problem from left to right and ended up with
Lin says, “I started inside the parentheses and ended up with
Jada says, “I used the distributive property and ended up with
Andre says, “I also used the distributive property, but I ended up with
The purpose of this discussion is to help students recognize some common missteps when rewriting expressions.
Invite students to share the errors they identified in the activity. Point out that since each given work in this activity contains at least two steps, students can use the steps to identify where the error occurs—where the expressions are no longer equal for a value of the variable.
Consider displaying these examples and asking student to explain the error each illustrates:
Review the useful approach of rewriting subtraction operations as adding the opposite. If desired, demonstrate such an approach for the expression
Help us improve by sharing suggestions or reporting issues.
Match each expression in column A with an equivalent expression from column B. Be prepared to explain your reasoning.
A
B
For the second and third rows, some students may not understand that the subtraction sign in front of the parentheses applies to both terms inside that set of parentheses. Some students may get the second row correct, but not realize how the third row relates to the fact that the product of two negative numbers is a positive number. For the last three rows, some students may not recognize the importance of the subtraction sign in front of
Students might write an expression with fewer terms but not recognize an equivalent form because the distributive property has been used to write a sum as a product. For example,