CCSS.Math.Content.6.EE.B.5

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

CCSS.Math.Content.6.EE.B.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

CCSS.Math.Content.HSA.REI.B.4

Solve quadratic equations in one variable.

This task asks students to connect solving higher order functions with exponential functions. With the task students are guided toward seeing how substitution can be implemented to simplify exponential functions into quadratic and cubic functions that are more easily solved.

Within this process students will be able to decontextualize by simplifying the exponential functions back to the more easily solved higher order functions. The use of substitution will show that the student knows and is flexible in using different properties of operations to solve higher level problems. Students are likely to struggle to see the substitution initially. However, I would encourage this concept to be taught as it has many benefits in later math courses.

As a method of ensuring success within this activity. Guided notes could be given on examples similar to the problems within the activity. As a way to lead students that are struggling into these problems we could start with more simplified exponential functions and build toward this level of solving.