Lesson 5

Solving Any Linear Equation

Lesson Narrative

The purpose of this lesson is to move towards a general method for solving linear equations. In the warm-up, students solve equations mentally, including equations with negative coefficients, prompting a discussion of multiplying or dividing each side of an equation by a negative number. In the first activity, students encounter several different structures of equations, and take turns suggesting moves for solving them. Then they apply their growing fluency in solving equations to constructing numbers puzzles of the sort they encountered in the first lesson in this unit. 

As students explain their reasoning for choosing a particular move while solving equations and critiquing the choice of their partner, they engage in MP3.

Learning Goals

Teacher Facing

  • Calculate a value that is a solution to a linear equation in one variable, and explain (orally) the steps used to solve.
  • Create an expression to represent a number puzzle, and justify (orally) that it is equivalent to another expression.
  • Justify (orally) that each step used in solving a linear equation maintains equality.

Student Facing

Let's solve linear equations.

Required Preparation

Print and cut up the Trading Steps blackline master for the matching activity. Prepare one set of cards for every 2 students.

Learning Targets

Student Facing

  • I can solve an equation where the variable appears on both sides.

CCSS Standards


Glossary Entries

  • term

    A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. For example, the expression \(5x + 18\) has two terms. The first term is \(5x\) and the second term is 18.

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