The purpose of this activity is to shift the focus from solving an equation to thinking about what it means for a number to be a solution of an equation. Students inspect each equation, looking at the structure, the signs, and the operations in it to decide if the solution is positive, negative, or zero. The last two questions have a similar format, so students can take advantage of their thinking from one problem to the next.

The purpose of this discussion is for students to practice talking about equations and the operations within them and to use logical thinking. There is no need to try to formally generalize student thinking for all cases at this time. In later grades, students will continue the work started here looking for structure in equations.

For each equation, invite groups to share how they decided if the solution was positive, negative, or zero. After each group shares, ask if any other group reasoned about the problem in a different way, and invite them to share their reasoning.

Invite students to suggest ways that knowing the sign of a solution to an equation is helpful. Ensure that students understand that it can help in checking their solution and can often be done quickly mentally when working problems on their own.

The purpose of this activity is for students to think about what they see as “least difficult” and “most difficult” when looking at equations and to practice solving equations. Students also discuss strategies for dealing with “difficult” parts of equations.

The purpose of this discussion is for students to discuss strategies for solving different types of equations. Some students may have thought that an equation was in the “least difficult” category, while others thought that the same equation was in the “most difficult” category. Remind students that when you feel confident about the strategies for solving an equation, it may move into the “least difficult” category, and recognizing good strategies takes practice and time.

Poll the class for each equation as to whether they placed it in the “most difficult” category, “least difficult” category, or if it was somewhere in the middle. Record and display the results of the poll for all to see.

For equations with a split vote, have a group share something that was difficult about it and something that made it seem easy. If there are any equations that everyone thought would be more difficult or everyone thought would be less difficult, ask students why it seemed that way. Ask students, “Were there any equations that were more difficult to solve than you expected? Were there any that were less difficult to solve than you expected?”

Consider asking some of these questions to further the discussion:

• “For equation A, what could we do to eliminate the fraction?” (Multiply each side by the common denominator of 6. Then the terms will all have integer coefficients.)
• “Which other equations could we use this strategy for?” (Any equations that had fractions, such as B, C, E, and G.)
• “What steps do you need to do to solve equation D? Which other equations are like this one?” (There is a lot of distributing and collecting like terms. F and H also have to distribute several times.)
• “What other strategies or steps did you use in solving the equations?”