The purpose of this Warm-up is to elicit the idea that a variable represents an unknown number in an equation or diagram, which will be useful when students identify solutions for equations in a later activity. While students may notice and wonder many things about these equations, the fact that the variable represents the number 6 is the most important discussion point.

This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is that the number 6 in the first equation is replaced by the letter in all the other equations. They may also notice in the last three equations that replacing each with 6 makes the equations true. 

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the equations. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the fact that the number 6 is replaced by the letter does not come up during the conversation, ask students to discuss this idea. Explain that a letter used to stand in for a number is called a variable. Throughout this unit, students will have many chances to understand and use this term.

Students may wonder about the in the last two equations since it’s likely that this is their first experience with “next to” notation. Explain that means the same thing as , and we will frequently use this notation from now on. Explain that in the expression , the number 3 is called the coefficient. Use this term throughout the lesson when the need naturally arises to name it.

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.