Students begin the lesson by digging into what it means for an equation to be true or not true. They expand previouslyheld understandings of equations by thinking about the assumption that equations are always true. Students learn that a letter standing in for a number is called a variable. Students learn that, for an equation with a variable, a value of the variable that makes the equation true is called a solution of the equation. They find solutions to equations by using tape diagrams or reasoning about the meaning of "solution" once an equation is written.
This lesson is where "next to" notation is introduced (for example, \(10m\) means \(10⋅m\)).
Lesson overview
 2.1 Warmup: Three Letters (10 minutes)
 2.2 Activity: Storytime (15 minutes)

2.3 Activity: Using Structure to Find Solutions (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 2.4 Cooldown: How Do You Know a Solution is a Solution? (5 minutes)
Learning goals:
 Comprehend the word “variable” to refer to a letter standing in for a number and recognize that a coefficient next to a variable indicates multiplication (in spoken and written language).
 Generate values that make an equation true or false and justify (orally and in writing) whether they are “solutions” to the equation.
 Use substitution to determine whether a given number makes an equation true.
Learning goals (student facing):
 Let's use equations to represent stories and see what it means to solve equations.
Learning targets (student facing):
 I can replace a variable in an equation with a number that makes the equation true, and know that this number is called a solution to the equation.
 I can match equations to real life situations they could represent.
Glossary:
 coefficient  A coefficient is a number that is multiplied by a variable. For example, in the expression \(3x+5\), the coefficient of \(x\) is 3. In the expression \(y+5\), the coefficient of \(y\) is 1, because \(y=1 \cdot y\).
 solution to an equation  A solution to an equation is a number that can be used in place of the variable to make the equation true. For example, 7 is the solution to the equation \(m+1=8\), because it is true that \(7+1=8\). The solution to \(m+1=8\) is not 9, because \(9+1 \ne 8\)
 variable  A variable is a letter that represents a number. You can choose different numbers for the value of the variable. For example, in the expression \(10x\), the variable is \(x\). If the value of \(x\) is 3, then \(10x=7\), because \(103=7\). If the value of \(x\) is 6, then \(10x=4\), because \(106=4\).
 Access the complete Grade 6 glossary.
Standards:
 This lesson builds towards the standard:CCSS.6.EE.B.6MS.6.EE.6
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.