This opening lesson invites students to experiment with expressions and equations to model a situation. Students think about relevant quantities, whether they might be fixed or variable, and how they might relate to one another. They make assumptions and estimates, and use numbers and letters to represent the quantities and relationships. The lesson also draws attention to the idea of constraints and how to represent them.
There is not one correct set of expressions or equations governing the potential quantities involved in the pizza party. The focus is on the modeling process itself—identifying relevant quantities, making assumptions, creating a model, and evaluating the model (MP4). Discussions are built in to foster an environment of collaboration and active thinking and listening. Encourage students to share their ideas and questions at these times.
In subsequent lessons, students will continue to write and interpret expressions, equations, and inequalities that represent situations and constraints.
Making internetenabled devices available gives students an opportunity to choose appropriate tools strategically (MP5).
Lesson overview
 1.1 Warmup: A Main Dish and Some Side Dishes (5 minutes)

1.2 Activity: How Much Will It Cost? (20 minutes)
 Includes "Are you Ready for More?" extension problem
 1.3 Activity: What are the Constraints? (10 minutes)
 Lesson Synthesis
 1.4 Cooldown: Ice Cream Party (5 minutes)
Learning goals:
 Comprehend the term “constraint” to mean a limitation on the possible or reasonable values a quantity could have.
 Use variables and the symbols \(=\), \(<\), and \(>\) to represent simple constraints in a situation.
 Write expressions with numbers and letters to represent the quantities in a situation.
Learning goals (student facing):
 Let’s write expressions to estimate the cost of a pizza party.
Learning targets (student facing):
 I can explain the meaning of the term “constraints.”
 I can tell which quantities in a situation can vary and which ones cannot.
 I can use letters and numbers to write expressions representing the quantities in a situation.
Glossary:
 constraint  A limitation on the possible values of variables in a model, often expressed by an equation or inequality or by specifying that the value must be an integer. For example, distance above the ground \(d\), in meters, might be constrained to be nonnegative, expressed by \(d \ge 0\).
 model  A mathematical or statistical representation of a problem from science, technology, engineering, work, or everyday life, used to solve problems and make decisions.
 Access the complete Algebra 1 glossary.
Standards:
 This lesson builds on the standard: CCSS.7.EE.AMS.7.EEMO.7.EEI.A
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