They can correctly state the rule and write an equation using a variable. They can correctly solve both extension questions without building them. Students can then use a different method to solve the second problem, writing an equation with a variable to show their rule. Students can compare the two towers and explain how the two patterns relate to each other. They may not be able to solve the second problem in a different way and are unable to compare the two towers and come up with the above-stated relationship.
Students can solve the first problem at least two ways and explain their results.
They can help make a table and find the rule, but may or may not be able to write it as an equation using a variable. They can correctly solve at least one of the extension problems, using any method. They can solve the second problem using one of the same methods they tried on the first problem, but cannot discover the above-stated relationship. Students may or may not be able to solve either problem without help. They may be able to find the rule but cannot write it as an equation.