# Lesson 2

Writing Equations to Model Relationships (Part 1)

### Lesson Narrative

This is the first of two lessons where students write equations to model various situations. The work here progresses in two ways—in terms of the complexity of the relationships and in terms of the amount of scaffolding built into the prompts.

Students begin by revisiting ways to calculate a given percentage of a given number, in preparation for computations they'll need to do in the lesson. Then, they look at a geometric context where three quantities can be related by addition and subtraction. Next, they look at a couple of contexts on spending, earning, and sales tax, which involve multiplication, multiplication and addition, and increasing a number by a percentage.

In each case, students begin by creating models where the values of the quantities are known (or mostly known), and move toward models where the quantities are unknown or can change. The repeated reasoning allows students to practice looking for and expressing regularity (MP8). As they interpret verbal descriptions and write equations, students develop their understanding of equations as a way to represent constraints and practice reasoning quantitatively and abstractly (MP2).

### Learning Goals

Teacher Facing

• Given a description of a situation or an equation, identify quantities that vary and quantities that don’t.
• Understand that letters can be used to represent both quantities that vary and those that are constant.
• Write equations with numbers and variables to describe relationships and constraints.

### Student Facing

• Let's look at how equations can help us describe relationships and constraints.

### Student Facing

• I can tell which quantities in a situation can vary and which ones cannot.
• I can use letters and numbers to write equations representing the relationships in a situation.

Building On

### Glossary Entries

• 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 non-negative, 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.

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