Discrete Math - Day 10

Today I handed back the first draft of portfolio problems. Although everyone had revisions to make, many students had a good foundation to build upon. I re-emphasized that the paper needs to communicate their reasoning and processes and should make sense to anyone else in the class who would read it. I asked students to re-write and submit both their corrected version and their initial version.

My intent is to copy several of the revised versions to use as a mentor text for future classes. This will allow students to better see what a portfolio problem write-up should look like. It is always a challenge when doing things for the first time to have decent mentor text.

Most of the remainder of the class was taken by a quiz on figurate numbers. The quiz was a single question that contained three parts. The quiz focused on hexagonal numbers and was designed to see how much students absorbed and could apply of their learning.

I allow students to use notes and other materials that they have worked on, such as portfolio problems. I do this since the quizzes and tests I give are not a simple regurgitation of information. The problems exam knowledge and skill levels at different levels.

As I walked around I could see that many students were on the right track with the questions. I did notice a couple of students who obviously did not know what they were doing and hadn't actual done work on the problems that we worked on in class.

After the quiz we revisited the flag problem from the previous class. I put the results we had found so far and mentioned that we had answered the question of how many flags with at least 7 blue stripes existed. The issue now was how many flags with 6 blue stripes existed. We knew that there were 28 ways to position 6 blue stripes through 8 positions. We also knew that for the remaining two stripes that we had the following configurations: red-red, red-green, green-red, green-green.

Students were still stumped on how to proceed. I asked them how many flags with 6 blue stripes and two stripes that were red-red existed. After a few moments of thought a couple of people responded, somewhat hesitantly, that there were 28 flags. I then asked how many red-green flags would exist; again the response was 28. We then proceeded through the other two permutations and the responses both times were 28. I then asked how many total 6 blue striped flags existed. Students said 4 x 28 = 112.

Adding 112 + 16 + 1 = 129 gave us the total number of flags with at least 6 blue stripes.

We'll work on another flag problem next class.

Visit the class summary to see a student's perspective on the class.