The only way I could think of to solve this question without using algebra was to draw out a table of values. I actually did this on Excel and I was thinking, well it's easy to figure out how many dishes based on guests but it's difficult to go the other way without using algebra. After 12 guests, the number of dishes always exceeds the number of guests so I was thinking you could also do trial and error by starting with (n-1) if n is the number of dishes
It definitely is beneficial to offer these kinds of math puzzles highlighting a diversity of cultures however I can't help but think of the concept that if someone is excluded, then someone is included. It's impossible to grasp all cultures in one problem. As a teacher, if I included a problem like this then there will certainly be students from other backgrounds that may feel excluded. Obviously as I introduce more puzzles as the school year continues, I would ensure all cultures represented in my classroom are presented. It's about patience and building that trust. I do remember as students we would get giddy when some of our names appeared on test questions and the teacher made sure to rotate and use all of us. Even if we weren't on one test, we knew eventually we would be represented, and that was important.
Personally, the reality of the question helps. I'm not too particular on imagery if the concepts are too farfetched - as we discussed in class, no, Susan will not be buying 83 watermelons. However, a good balance between imagery and reality, as well as representation always makes mathematics more fun.
Thanks, Sahl. I agree that using a table of values is an excellent strategy. I couldn't quite follow your logic of 61 guests sharing 65 dishes or how having 59 guests and 62 guests to satisfy this problem's requirement. Could you please clarify?
ReplyDeleteYour statement, "if I included a problem like this then there will certainly be students from other backgrounds that may feel excluded," caught my attention. Could we help our students develop an appreciation for other cultures so that they would not feel excluded whenever the course content is about another culture?
Hey Erica! For example, if there were 4 guests they would use 2 dishes of rice and 1 dish of each broth and meat. Similarly, 5 guests would use 2 dishes of rice and 1 dish of each broth and meat. 5 does not have a factor of 2, 3 or 4 so we would not be adding any extra dishes. However 6 guests would yield an additional rice and broth (since it has the factors 2 and 3). By this logic, 61 is a prime number and thus would not yield any extra dishes compared to 60 guests. I'm not sure if I understood the problem correctly but this is how I interpreted it, I hope this helps!
ReplyDeleteYour second question is an important point that I hoped to answer in the latter portion of that paragraph in my blog post. However, I did not consider your point of cultural appreciation to mitigate those potential feelings of some students. I agree, even spending a few minutes discussing some key features of said culture can illicit some curiosity in students and make them appreciate the example I show afterwards. Food for thought, for sure.
Thanks for your clarification, Sahl! I think the intention of the problem was that the number of guests would be a multiple of 2, 3, and 4; however, I can see how the question can be interpreted differently. Several of your classmates also found the wording of the problem ambiguous. It's not easy translating and interpreting an ancient Chinese text!
DeleteI think spending a few minutes to discuss some key features of the culture to spark some curiosity is a great idea! Of course, it might be harder for students if an activity is from a culture different from their own, but learning to appreciate other people's culture is important, too. I recall that many years ago a Caucasian student in my Math 8 class was enthusiastic about researching a Japanese mathematician for his project as he's fascinated by Japanese culture!