Discrete Math - Day 3

We started the day summarizing what was learned about triangular and square numbers from last class. Since this was a Monday morning class I thought it would be a good idea to have students re-engage in their thinking and notes before tackling the next set of problems.

We wrote out the formulas for T_n and S_n, the values of the nth triangular and square numbers, respectively. It was interesting that students struggled with the formula for S_n = n², since we didn't explicitly discuss this last week. They were much more comfortable reciting the Gaussian summation formula for triangular numbers, T_n = n(n+1)/2.

Students tackled the next three problems related to triangular numbers. The purpose of these are to get students comfortable working through problems. I warned students that part e was a tougher pattern to see. Students made slow progress on these but did identify the patterns for d and f. For part d, we have

         T_n-1 + T_n = n².

For part f we have T²_n-1 + T²_n = n³.

After having students present results I wrote out the associated formulas for both problems. There wasn't much progress on part e, so I asked students to write out the first eight terms and to look for a pattern.

Visit the class summary page to get a student's perspective on the day's activities and to view slides of the lesson.

We'll work with these tomorrow, along with looking at pentagonal numbers. I intend on the pentagonal numbers to be the first portfolio problem.