math – BC Physics 180

Day 92 – Barbie Bungee Jump

Math 8 – The Barbie Bungee Jump is a really nice activity that works in so many different settings in secondary school. I’ve used it in Math 10 for graphing linear relations/functions, I’ve used it in Physics 11 as a graphing warm-up and modeling example, and this year we’re using it in Math 8 for ratios and rates. In a few weeks we’ll come back to it, and tie it in with linear relations.

I’m working on this with my teacher candidate. Below is the handout that she developed and I tweaked (but just a little bit).

Math 8 Barbie Bungee Jump

Day 83 – Universal Gravitation, oh my!

Physics 11 – Today was the kids introduction to calculating gravitational forces. It was supposed to be a pretty straight forward skill since the students already covered the concepts of gravity. I even anticipated one problem from last year: students mistook the units for G as a formula. So I mentioned this to the kids.

And then chaos ensued. Basically it came down to how (un)comfortable students are with using symbolic representations.

Students can do this: $10=\frac{160}{x^2}$ but they can’t do this: $F_g=G\frac{m_1m_2}{r^2}$

They are fundamentally the same mathematical operation. For today, the one idea I gave students was to group the terms in their equation with a coefficient and variable. For example, when finding m2: $F_g = \left(\frac{Gm_1}{r^2}\right)m_2$

That helps to some extent but this is still confusing when finding r: $F_g = \left(Gm_1m2\right)\frac{1}{r^2}$
The solution to the above is to multiply both sides of the equation by the reciprocal of $Gm_1m_2$ and then take the inverse of $\frac{1}{r^2}$ , at which point I might was well be speaking Latin.

Somewhere in mathematics education we need to really, really emphasize that mathematics isn’t just about numbers and that mathematical rules apply to all sorts of things. This is a huge cognitive gap with most students.

To finish things off, I had over a dozen students ask me what N and m stand for in the equation for G, and that they didn’t know what to do with the equation. So my question for readers of this blog: next year do I omit the units for G, or simply suffer through more questions about the “equation for G”?

Day 31: Length, Area, Volume

Science 9 Most of my grade 9 students were away today, visiting one of their parents’ workplaces. I started off the class with the screenshot at the top. Here it is, a real life example of using math! I was asked this question the night before from a friend. I had the students address the prompt. The first thing they had to do was figure what question it was that they wanted to solve. Some chose length of books (books stacked), surface area of books, and volume of books. With the odd bit of help from me, we learned a few things. 350,000 books will reach a height of over 11 km if stacked. This is higher than Mr. Everest. Laid out on a soccer field, we would need 12 fields to contain all the books. Finally, we found out that we’d need 1.5 classrooms totally packed to hold all the books. Clearly the woman was exaggerating when she said she had 350,000 books at home…

Not all the kids were engaged but most were. It was another case of grabbing the students’ curiosity and running with it.