Summer SAVY, Session 4 Day 3, Mathematicians in History (3rd – 4th)
Hello SAVY Families,
Wednesday brought more deep mathematical thinking, connections, and perseverance to the SAVY mathematician in your family. Each day, the mathematicians continue to raise the standard, and I could not be prouder of their hard work today.
We started the day by reviewing the concepts we have learned this week and reminding ourselves of the historical importance of the mathematicians we have studied so far. Even though our Ancient Greek mathematicians lived over one thousand years before our Renaissance mathematicians, the SAVY mathematicians were quick to point out patterns, such as all of the mathematicians we have studied are men, and they all came from wealthy families. This prompted a discussion of why that may be the case, noting that the mathematicians we are studying were not the only people contributing to society during these time periods. We added other events to our class timeline, such as The Plague, The World Wars, and The Dark Ages. This history connection allowed the SAVY mathematicians to better contextualize what was happening in the world around the mathematicians we are studying. I let them know that we would be breaking some of these patterns as our studies continue.
The first historical mathematician that we studied today was Pierre de Fermat. Fermat is most well known for his work with prime numbers, square numbers, and number tricks. The SAVY mathematicians had to use their own knowledge of square numbers to see if they could find prime numbers that could be expressed as the sum of exactly two perfect squares. This was hard work, but the mathematicians showed the habits of a scholar to succeed. Fermat also discovered many number tricks. The SAVY mathematicians’ minds were blown when they tested out these tricks to see how well they worked. To end the lesson, the mathematicians had to come up with their own number trick using the patterns that we discovered from Fermat’s tricks. I was very impressed with their creativity in creating these tricks!
The second historical mathematician that we studied was Blaise Pascal. Pascal is remembered for his contributions to geometry but is most widely known for his discovery of Pascal’s triangle. We learned that there is a debate as to who first discovered this triangle, which brought us back to our discussion of whose work gets remembered. First, the SAVY mathematicians looked for their own patterns on the triangle. Then, we watched a video to learn about more patterns in the triangle. Finally, the SAVY mathematicians had to discover the sum of all numbers in 1 row, 2 rows, 50 rows, and the formula for the nth row of the triangle. The same process was repeated for finding the perimeter sum of parts of the triangle. The majority of our afternoon was spent unlocking the secrets of Pascal’s triangle. Pascal was also known for his work with probability. A fascinating problem from probability deals with birthdays: how many people do you have to ask before you find someone with the same birthday, month, and day? The SAVY mathematicians had to make a guess, and then we started to ask around. I told the SAVY mathematicians that they can continue this problem at home!
Questions for today:
- Who was Pierre de Fermat? Who was Blaise Pascal? What contributions did they make to the study of mathematics?
- How can we connect Fermat’s work and Pascal’s work to one of our generalizations about relationships?
- What connections or patterns have you noticed between all the mathematicians we have studied?
- How many people do you suppose you will have to ask before you find two people with the same birthday?
I hope the mathematicians can rest their brains tonight, as we have two full days of SAVY ahead of us. I look forward to working with all of them tomorrow!
Sincerely,
Ms. Gruchot