Getting Started 
Misconception/Error The student is unable to write an equation that models the problem. 
Examples of Student Work at this Level The student:
 Attempts to solve the problem computationally and is unable to write an equation.
 Writes a linear function such as y = 2 + 3x.

Questions Eliciting Thinking What does it mean to write an equation? Suppose x represents the number of days and y represents the number of followers. Could you write an equation to show how x and y are related?
If a quantity is doubling every day, can a linear equation model the quantity? 
Instructional Implications Provide instruction on exponential functions that model simple problem situations. Make clear the meaning of the initial amount and the growth (or decay) factor and their roles in the equation. Assist the student in recognizing that the situation described on the Follow Me worksheet can be modeled by an exponential function. Guide the student to write the function. Relate each value in the equation to a specific feature of the problem (i.e., the growth factor andÂ the starting amount). If necessary, provide instruction on solving equations, and encourage the student to always assess the reasonableness of solutions. Guide the student to use the solution of the equation to explicitly answer any question asked in the problem.
Review with the student the differences between linear and exponential functions. Discuss that in a linear function, the change in the dependent variable is increasing or decreasing by a fixed number while in an exponential function the change in the dependent variable is increasing by a common factor (e.g., doubling, five times as much, or as much). Review with the student the general form of an exponential function, . Discuss with the student the similarities and differences between exponential growth and exponential decay.
Provide additional opportunities to write exponential functions that model both exponential growth and decay. 
Moving Forward 
Misconception/Error The student writes an exponential equation that containsÂ significant errors. 
Examples of Student Work at this Level The student:
 Confuses the starting amount and the growth factor.
 Writes the exponent as x instead of .

Questions Eliciting Thinking What is the general form of an exponential function? What is the starting amount in this problem? What is the growth factor?
What variables did you use to represent theÂ two related quantities in this problem?
How many followers does the school have on the first day? The second day? The third day? How is the number of followers changing each day? How can you represent this change in the equation?
I see that in your equation you wrote that the exponent is x. So when xÂ = 1, you found that yÂ = 6. Does that match with the information given in the problem? Were there 12 followers on day one? How can you adjust your equation to match the information given in the problem? 
Instructional Implications Review the general form of an exponential function. Make clear the meaning of the initial amount and the growth (or decay) factor and their role in the equation. Ask the student to identify the growth factor and the initial amount in his or her equation. Then, have the student compare these amounts to information given in the problem. Ask the student to revise his or her equation as needed.
If the student wrote the exponent incorrectly, use a table of values to explain that the exponent is always one less than the number of days. Assist the student in writing the exponent correctly in his or her equation.
Provide additional opportunities to write exponential functions that model both exponential growth and decay. 
Almost There 
Misconception/Error The student makes errors when solving a correctly written equation. 
Examples of Student Work at this Level The student correctly writes the equation where x is the number of days and y is the total number of followers but:
 Fails to put parentheses around the 10  1 when using a calculator.
 Cannot correctly use algebraic properties to solve the equation (e.g., multiplies two and three and then raises six to the ninth power or multiplies three by nine instead of raisingÂ three to the ninth power).

Questions Eliciting Thinking There is a minor mistake in your work. Can you find it?
What was your first step in trying to solve this problem? Did you follow the order of operations? 
Instructional Implications Provide the student with additional opportunities to solve exponential equations in problem contexts. Encourage the student to always review the problem to be sure the question asked was answered. Remind the student to always check the reasonableness of solutions in the context of the problem. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly writes the equation where x is the number of days and y is the total number of followers. The student substitutes 10 for x and determines that on the 10th day, the school would have 39,366 followers on Twitter. 
Questions Eliciting Thinking Can you describe how the graph of this function would look?
Could you have solved this problem without writing an equation? How?
When would writing an equation be a better option than making a table of values? 
Instructional Implications Provide the student with more complex problem situations to model with equations.
Consider using other tasks for ACED.1.1 if not used previously. 