Stats & MBF 3C

Liisa kickstarted last week's class by giving us some statistics. She talked about the four different levels of math courses that the Ontario secondary schools offer in grade 11. They are offered at the university level (MCR 3U), college level (MBF 3C), mixed (MCF 3M), and everyday / workplace (MEL 3E). She then had us make an educated guess on what percentage of students we think took each course. To my surprise, my guesses were pretty much spot on! I split my pie chart up almost the exact same way as the data. Liisa's stats were only specific to the District School Board of Niagara but I would assume that the stats would be pretty close province wide. Of course SES and location are important factors that would affect the data but probably not by much.

Here was my prediction (I wrote the percentages in afterward when Liisa revealed the actual data):

I based my estimates on my previous experience in high school. At my high school, most of the students took university math since they were headed in that direction (because everyone thinks university is best...which for the record, I do not agree with), or simply because they wanted to "keep their options open". College was the next most popular because although everyone thought university was where all the "smart" people went, some knew it wouldn't be for them and they wanted to get into the trades so they went with the college route instead. And although mixed math can still get you to university, most people still took the U courses because mixed math can be limiting. For example, as the flow chart below demonstrates, one is able to take a U course in grade 12 if they took an M course in grade 11, but they are limited to the data management course at the U-level in grade 12. So, I can definitely see why students tend to take the U courses in order to "keep their options open", especially since some university programs require either advanced functions (MHF 4U) or calculus (MCV 4U) as a prerequisite. Due to this mentality, the M course always seems to be the underdog and no one expresses much interest, as the data above shows. And as I expected, the workplace course has the lowest enrolment. I'm assuming this is because there is a heavier emphasis on continuing education and most jobs require some sort of post-secondary education now, compared to 30 years ago when a high school diploma was sufficient.

Math Pathways

Exploring the college level math course was very exciting for me because I have never had any prior experience with it. I really enjoyed Tori's lesson. For her activity, she introduced the problem and recruited us to design a chocolate box. She gave us some restraints: 

1. The box had to fit 3 chocolates (or styrofoam spheres in this case!)

2. We had to try to limit the amount of excess space so that the chocolates wound't roll around too much and break, or in other words, minimize volume.

My group decided to challenge ourselves and add an additional constraint which was to try to conserve as much packaging as possible (minimize surface area). This would be great to tie in as it would become cross curricular and you can intersect it with business / marketing and a little bit of financial literacy as well!

Here was what we had come up with:

As you can see, we created an irregular hexagonal prism. At first, we planned to make a triangular prism, but we thought that if we cut off the vertices / corners of the triangle, we'd be saving space and surface area. It would reduce the amount of excess and unused room in the box, which would prevent the chocolates from moving around and potentially damaging the product! We also created a cylindrical prism but after doing the math, the hexagonal prism still won, with the least amount of volume and surface area!

My blog posts just don't seem complete without a joke at the end, so here's this week's joke:

Who invented the round table?

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Sir Cumference! 

Until next time,

- The Function(al) Teacher