Fractional Exponents, Clip 2, 4:48

• The teacher creates the beginning of a table in this clip. For this class, a table has become a tool for noticing functional relationships (refer to proportional/linear videos). Thus she is reminding them of a tool they have used in the class before.
• The teacher collects several student solutions along with their reasoning. This creates an atmosphere where other students can judge and try to make sense of other students work. It is important that students have the opportunity to judge mathematical answers (along with justification) for correctness. This is a key component in the mathematical process.
• The teacher helps facilitate this discussion by writing their responses on the board. Another way this can be done is to have the students come up and put their solutions on the board themselves.
• Notice how the teacher does not let other groups off the hook. She makes them accountable by asking about the solutions that are on the board.
• This also gives her the opportunity to focus students' attention on some of the key components of exponential functions. Having a variety of answers can help her make different points.
• Finally she demonstrates how they could check their results with the table. It is important as a teacher to encourage students to check their answers to make sure they make sense.