# Lesson 11

Using Equations to Solve Problems

### Lesson Narrative

This lesson brings together the skills and concepts that have been studied in the unit so far. Students solve problems that can be represented by equations of the form $$p(x+q) =r$$ and $$px+q = r$$. A bit of scaffolding is offered in the first activity to reactivate their understanding of tape diagrams, but after that no scaffolding is offered so that students can make sense of problems (MP1) and choose representations to use (MP5).

### Learning Goals

Teacher Facing

• Interpret and coordinate tape diagrams, equations, and verbal descriptions for situations involving signed numbers.
• Solve an equation of the form $px+q=r$ or $p(x+q)=r$ to determine an unknown quantity in a situation, and present the solution method (orally, in writing, and through other representations).
• Write an equation of the form $px+q=r$ or $p(x+q)=r$ to represent a situation involving signed numbers.

### Student Facing

Let’s use tape diagrams, equations, and reasoning to solve problems.

### Required Preparation

Decide if students will conduct group presentations or a gallery walk for the last activity. If so, prepare tools for creating a visual display and around 3 sticky notes per student. If not, these materials are not necessary.

### Student Facing

• I can solve story problems by drawing and reasoning about a tape diagram or by writing and solving an equation.