The purpose of this activity is to give students an opportunity to practice checking whether a particular value is a solution to an equation, and to recall properties of operations and equality that preserve the solution set of an equation.

This will be useful, in the associated Algebra 1 lesson, when students consider when and why equations have the same solution. Developing multiple approaches to determining if a value is a solution allows students to reason abstractly and quantitatively (MP2).

Monitor for students who use these different approaches:

• Check the value of in only one expression and reason about the second expression

• Identify properties by name, such as “commutative,” “distributive,” and “associative”

• Identify properties informally, such as “changing the order doesn’t matter” or “you can add first and then multiply, or multiply first and then add” or “you can multiply three or more terms in any order” or “you can add the same thing to each side”

• Manipulate the expressions

• Graph one or both expressions

Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).

The goal of this discussion is for students to share methods of determining if a pair of equations share a solution.

Display 2–3 approaches from previously selected students for all to see. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “How are checking the -value in each equation and manipulating the equations the same? How are they different?”
• “Are there any benefits or drawbacks to one representation compared to another?”

The purpose of this activity is for students to practice generating equivalent equations. The structure of taking turns and justifying your thinking to your partner supports students to check their work as they go, and the class has a chance to check for equivalence when the total score is recorded.

Students also have to justify, whether formally or informally, why each move keeps the equation equivalent. This will be helpful for students, in an associated Algebra 1 lesson, when they must determine what moves are acceptable to make to an equation without changing its solution. As students justify the equivalence of the equations, they are reasoning abstractly and quantitatively (MP2).

Monitor for students who solve the equation first and then work to create new equations with the same answer, and for students who simply create new equivalent equations from the given equation. Monitor for students who add or multiply by the same number on each side of an equation and students who use properties of operations (distributive, commutative, associative).

The goal is to review the work students did to create equivalent equations and the moves they could do to equations that wouldn’t change the solution.

Make a semi-permanent display of “moves that won’t change the solutions to equations.” Sort the list by moves that are done to each side, and moves that are done to one side. Use students’ language, adding formal language if that is an emphasis in your school.

Possible list:

• Add the same value to each side.

• Subtract the same value from each side.

• Multiply each side by the same value (but not zero!).

• Divide each side by the same value (but not zero!).

• Change the order of terms (on one side) being added or multiplied (commutative property).

• Change the grouping of terms (on one side) being added or multiplied (associative property).

• Distributive property: .