The purpose of this Warm-up is to elicit the idea that equations are used to represent situations and relationships, which will be useful when students create equations from a situation in a later activity. While students may notice and wonder many things about the equation, how it describes a relationship between two quantities and the meaning of a solution are the important discussion points.

When students articulate what they notice and wonder about the equation, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

Listen to the language that students use to describe the equation. Do they refer to 12 as “the answer”? Do they see the operations of multiplication and addition in the expression ? Do they see a relationship between and ? Do students think about possible values for and ?

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 equation. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the ideas of what the equation represents, the meaning of its solutions, and possible values for and do not come up during the conversation, ask students to discuss these ideas.

If students’ answers included phrases like “” or “ plus ,” tell students that you are going to remind them of another way to describe and . Say, “ is the product of 2 and .” Remind students that they noticed that 2 was multiplied by , and connect the word product to their noticing of the term and the idea that 2 and are multiplied.

Say, “ plus  is the sum of and .” Remind students that they noticed the addition, and connect the word sum to their noticing of the + sign and addition.

The mathematical purpose of this lesson is to prepare students to make sense of equations in the form . The work of this lesson connects to previous work done in grade 8, when students explored linear relationships expressed as . This lesson prepares students to begin the work in their Algebra 1 lesson by supporting them to make sense of contexts that can be represented with equations in the form , and to building up a sense of the relationship between and in these contexts as well as the operations represented by .

Students express regularity in repeated reasoning as they find the total of many different combinations of raffle tickets and school logo pins, and then generalize when they represent the relationship between tickets purchased, pins purchased, and total cost with an equation (MP8).

In this activity, students get a chance to practice applying their skills in representing situations symbolically, and finding and interpreting solutions.

The structure of a row game supports students to check their thinking because their partners should get the same answer to different questions. When students’ answers disagree, they must make sense of each other’s questions and thinking to figure out whose answer is correct.

The practice prepares students to solve equations and solve for one variable in terms of another in their Algebra 1 lessons.

Monitor for students:

• Calculating some specific values before generating an equation
• Analyzing the quantities and relationships in the text
• Looking for and using mathematical structures, such as or

Students can look for and make use of the structure of linear equations to solve these problems (MP7).