Teaching Pascal's to some Rascals

I taught my lesson plan to the same group of students who I did my pre-assessment with. The students attend Cabrillo College and are in an intermediate algebra class. Before I began to implement my lesson, I discussed the KWL charts that the students turned in to me in our prior meeting. During the week, in between our meetings, the students said that they had covered a lot of the things they were curious about in their “would like to know” section. After briefly discussing their KWL charts, I began with my pre-assessment for using Pascal's Triangle to understand Binomial Theorem.

I began by giving the students ten minutes to research Pascal’s triangle and expanding polynomials. I believe that recognizing patterns is a very effective tool in factoring. All of the students brought their laptop computers and went to work. I think that it is imortant to advocate use of technology in the classroom. But, occasionally teachers need to be careful. Computer are full of distractions and I made sure to stop them at ten minutes so that they couldn’t get distracted and start searching the web and going onto social media websites. Then I had each of the students share something that they learned during their research period and we had a discussion about their findings.

    The students shared that the first row of Pascal’s Triangle was the ones, the second row is the counting numbers, and the third row is the triangle numbers. I asked the students if they knew what the triangle numbers meant. They did not. I explained that they followed the formula:

 xn=n(n+1)/2

          They are called the triangle numbers because of the image below. I think of it as the stacking numbers, as if one was to make a pyramid of cans. After the discussion, I was able to determine that the student's understood the basic principle of Pascal's Triangle, but they hadn't had enough time to research the many uses of it (including binomial expansion).

          After the pre-assessment, I decided that a great starting point would be to have students fill out their own Pascal’s Triangle and to label the columns. I gave them a sheet with the first 15 rows blank and had them fill it out. This took about ten minutes and the students did the activity with very little help. Then, I discussed all the patterns that could be found in Pascal’s triangle, such as: the diagonals, horizontal sums, squares, the Fibonacci Sequence, and exponents of eleven. 

             Then, I showed how some binomial expansions worked. This part of the lesson I used direct instruction and I lectured them for approximately 15 minutes while using the white board. I showed how Pascal’s Triangle helped to explain Binomial Theorem. The students recognized the pattern and I did a couple of examples on the board and then had students try one on their own; then holding up their answer when they got the question. 

                 As my summative assessment I had a worksheet for the students to work on and fill in with my help. I remembered from when I did my test run pre-assessment that two of the students were slightly more advanced since it was their second time taking the course. This was there second time working with binomial expansion. I gave two of the students a harder sheet and the other two students an easier practice sheet. They worked on the questions and I walked around and provided help when I was needed. 

               Overall, I was pretty happy with the adjustments that I made to my lesson plan after turning in assignment 2A. I think that I did a good job of including technology and engaging the students into the curriculum. I think that I did a good job of differentiating my assessments (I didn’t do this as well in the pre-assessment). I found that assessing becomes a little easier once you get to know the students better. I think that students need to spend a lot of time practicing math (it’s a good form of assessment too) and that teachers need to give students more time to practice in class. I really liked the discussion that I had with the student’s as a pre-assessment. I don’t think that discussions are used nearly enough in mathematics. 

              I only had about 50 minutes to work with the students. If I had more time I would have given the students a lot more time to research Pascal’s Triangle. It is one of the most interesting tools in mathematics, and I think the students would find it interesting and it would be a valuable use of time. I had a really good time doing the lesson plan and I am working on finding ways to differentiate all of the assessments that I use in and out of the classroom.