In this activity, students consider what it means for an equation to be true or false. They also practice substituting values for a variable and evaluating expressions with addition and multiplication.

This discussion should focus on the idea that an equation can be either true or false, and that the truth of an equation with variables depends on the values of those variables. If needed, remind students that the equal sign shows that the two expressions on its two sides are equal to each other.  

Invite students to share their values for true and false equations. To support students in expressing their ideas about equations, consider asking:

• “What makes an equation true?” (The expressions on both sides of the equal sign have the same value.)
• “What makes an equation false?” (The expressions on each side have different values.)
• “How can we tell if an equation without variables is true or false?” (Find the value of the expression on each side and see whether or not those two values are equal.)

• “How can we tell if an equation with a variable is true or false when we are given a value for the variable?” (Replace the variable with the given value, find the value of each side, and see whether or not those two values are equal.)

Emphasize that the equation   can be understood as a mathematical statement that is not true instead of something that is “wrong” or “a mistake.” 

In this activity, students look for solutions to equations and determine which value from a given set makes an equation with a variable true. Since so many values are given, students may realize that using only substitution is not the most efficient method for finding a solution. As a result, students may use the structure of the equations and given values to eliminate some of the values as possible solutions (MP7).

If students only use substitution to identify the solution for each equation, consider asking:

• “How did you find a solution for this equation?”
• “How could you use the structure of the equation to eliminate some of the possible solutions?”

Encourage students to use words to express the relationship represented by the equation. For example, the equation can be stated as “When a number is subtracted from 1,000, the difference is 400.” This process will help students know that the value of must be less than 1,000. Some might also recognize that it means must be a whole number.

The goal of the discussion is to ensure that students understand what “a solution to an equation” means. To guide the discussion, consider doing the following:

• Solicit or display correct solutions.
• Choose a few equations and ask students to explain how they know a solution is correct.
• Highlight correct uses of the new terms “variable,” “solution,” and “coefficient.”
• Demonstrate substituting an identified solution in the equation to verify that it makes the equation true. Emphasize that this substitution method can always be used to check a solution to an equation.