In this partner activity, students take turns finding equations and their solutions. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

After sorting all the matches into two categories, students use observations about mathematical structure in the equations and solutions to generalize an algebraic solving strategy for equations of the form or (MP8). 

Ask students to study the group of equations that use addition.

• “How are these equations alike?”(They all start with a variable and add another number. The total is on the other side of the equal sign. The variable  plus a number equals a number.)
• “How are all of these equations solved?” (The number that is added to the variable is subtracted from both sides.) 

Ask students to study the group of equations that use multiplication. 

• “How are these equations alike?”(They all have a coefficient and a variable on one side of the equal sign and the total on the other. The variable x multiplied by a number equals a number.) 
• “How are all of these equations solved?” (Both sides of the equation are divided by the number that the variable is multiplied by.) 

Point out that the equations show that these solving strategies work when and are whole numbers, fractions, or decimals. 

The purpose of this activity is for students to practice solving equations. Some students may use the “do the same to each side” strategy they developed in their work with balanced hanger diagrams and formalized in the previous activity. Others may use strategies like substituting values until they find a value that makes the equation true, or asking themselves questions like “2 times what is 18?” As students progress through the activity, the equations become more difficult to solve by strategies other than “do the same thing to each side.”

Invite previously selected students to share how they used different strategies to solve the equations. Emphasize that no strategy is “better” than another. However, some strategies are more challenging to use when the equations involve fractions or decimals.

Display  the equation .

• “Which strategy would you use to solve this equation? Why?” (Divide both sides of the equation by because it would be difficult to draw a diagram for these fractions, and it would take too long to substitute values for the variable until one of the values makes the equation true.)

Consider describing and annotating the steps involved in dividing each side of the equation by . For example:

Display the solution for the equation as .

• “What does it mean that 6 is the solution to this equation? (When the variable is replaced with 6, the equation is true.)
• “How can we check that this solution is correct? (Replace the variable with 6 and see whether both sides of the equation have the same value.)

Demonstrate using substitution to check the solution. Encourage students to use this method to check their solutions for equations.