## Calculus 2: Using the Infinite

Student exploration of series in a Calculus 2 class. The class had 25 students and met two times a week for 75 minutes each and one time for 50 minutes.

Student exploration of series in a Calculus 2 class. The class had 25 students and met two times a week for 75 minutes each and one time for 50 minutes.

This video was taken in a mathematics for liberal arts class with 15 honors students. It met two times a week for 75 minutes each.

Students have been exploring the 3a+5b problem: Determine all possible values generated by the Diophantine equation 3a+5b when a,b≥0 (see the blog 3a+5b Proofs which contains a complete video of her explanation).

Even though the proof is still incomplete, I comment that the proof idea is beautiful. Next, I ask: Does it make sense to you? Are there questions? Normally I would give wait time here but since class is almost done, I use a show of hands to monitor understanding.

For homework, students were trying to find an equation that connects two whole numbers, their least common multiple and their greatest common factor.

The video begins with one student sharing her findings. I revoice and represent her thinking. In her explanation, the student has made a distinction between the larger and the smaller number. Even though I know that that is unnecessary, I go along with her thinking. Another student asks "Does it matter?" and again I give that question back to the class without evaluating.