Project 1: Loaf Problem

 https://docs.google.com/presentation/d/1_0E3hmz7vZBQ9JyVCCeeh1c3RUBB6E9eOz6LUo7mKkE/edit#slide=id.g308d529465f_1_3

For our project on Ahmed loaves, I learned a lot. I had almost forgotten what an arithmetic sequence was before doing this problem so it was a good refresher about this idea of a common difference. Moreover, when solving the ancient way, one of my challenges was wrapping my head around this idea that we had 2 unknowns at the beginning and so we had to assume either the initial loaf or the common difference. In the end, since the common difference can be obtained from the equation that we obtained from the problem itself then we need to assume the loaf and doing so by estimating a smallest share made sense since we are increasing. I also really enjoyed this idea of guess and check with our extension as I noticed a decrease of 2/7 it made sense to me how many groupings of 2/7 we would need to make the equation

  true. In my discussion with Raymond it became evident to me that this way of solving also involves no algebra so could be used with a lower lever class to get an estimation of the common difference.  We did struggle to find an extension problem. Initially, we were thinking of mentioning the idea of egyptians only writing fractions with 1 as a numerator and how that made bread cutting more convenient as there were less pieces to distribute; however, that problem seemed like more of an adapation than an extension and the trial and error (guess and check) approach illustrates that there are often more than one way to execute a problem. I think that in the classroom it’s always good to have multiple approaches and it is also important to prepare an extension because you will always have students that finish early so asking students to verify their solution or generally to assess whether their answer makes sense via estimation is a big takeaway I got from this exercise.

For the background, Raymond was responsible for looking into the ancient Egyptian mathematical developments that were necessary for the solving of this problem and presenting the problem description to the class. As for Zain, he was responsible for researching and presenting the solution that would've been possible with ancient Egyptian mathematics, as well as coming up with the extension which was a way to solve the problem by combining our understanding of linear systems with the ancient Egyptian strategy of false position. Finally, Carson was responsible for generating the toy example numbers, and writing and presenting the modern solution as well as linking it to the modern BC mathematics curriculum. He was also in charge of the artistic direction, which includes the artistic interpretation of the problem and the incredibly funny joke at the start of the presentation. All three members were involved in facilitating the toy example activity.

I felt the flow of the presentation was alright. Generally speaking, it was a learning experience to think ahead and anticipate what challenges and considerations/questions students may have. For example, one of the main questions students had was whether they could use fractions when solving to find the sum of 10 loaves. Also, we went a bit over time so it would be nice to receive some feedback on where we could cut time a little.

Thanks to everyone for listening and participating.