In this activity, students continue working with exponential expressions with variables. They evaluate expressions when given a value for the variable. As students discuss and compare their thinking with others, they also deepen their understanding of the order of operations, such as when considering the difference between expressions like and . During class discussion, students also have opportunities to practice using mathematical vocabulary related to expressions, such as “coefficient,” “variable,” and “exponent.”

The purpose of the discussion is to ensure that students understand how to evaluate exponential expressions with variables for a given value of the variable. It is also an opportunity for students to practice interpreting and using vocabulary like “coefficient,” “variable,” “power,” and “exponent.”

Direct students’ attention to the reference created using Collect and Display. Ask students to share the steps they used to find the value of an expression. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional words or phrases.

If more than a few students multiply the coefficient and the variable in and then square the product, which results in a value of 900 when is 10 and when is , discuss the difference between and and how each expression should be evaluated based on the order of operations.

If time permits, consider asking questions such as: 

• "In each expression, what is the coefficient?" (3, 3, 3, , 1, 1.)
• "How is evaluating the expressions when is a fraction similar to when is a whole number? How is it different?" (It's similar because we're still just multiplying by itself a certain number of times. It's different because multiplying a fraction by a fraction is a bit more complicated than multiplying a whole number by itself.)

In this activity, students recall what is meant by a solution to an equation as they look to replace a variable with a number that makes two expressions equal. Here, one or both expressions in each equation contains an exponent.

Students are not expected to use algebraic methods to solve equations such as or in grade 6. Instead, they are to look for and make use of the structure to strategically choose and test values that could be solutions from a list, or by reasoning about the meaning of each expression. For example, to find the solution for , they may think: “What number, when squared, will give 64?”

Note that some of the equations also have solutions that are negative. Because operations on negative numbers are not part of grade 6 standards, students are only expected to consider positive values in this activity. 

The goal of the discussion should focus on how the meaning of the equal sign, exponent, and solution to an equation can help us find a value that makes each equation true. 

Invite students to share how they found the solution to each equation. Discuss questions such as:

• “What was your strategy when is by itself on one side of the equation?”
• “What was your strategy when is the number being multiplied or raised to a power?”
• “What was your strategy when x was the exponent?”
• “Did you reason about the last equation the same way you did with the first equation? What did you do differently, if anything?”