How Have I Learned Math?
- Think back over your math career. Could you describe a typical math class?
- What were your responsibilities?
- What was the teacher's role?
- Where/When did most of your learning take place?
Inquiry Based Learning
- When you see the title above, what do you think it has to do with this class?
Let's Work
Grab a partner. Then as a group of two, join with another group of 2. As a group of 4, claim some board space. Write your names on the board. Then alternately take turns acting as scribe for the group. Each time you finish a problem, pass the chalk. If you get stuck on a problem, remember that you are the scribe for your group and they can help you.
- In the small town of Coriander, the library can be found by starting at the center of the town square, walking 25 meters north ($\vec a$), turning 90 degrees to the right, and walking a further 60 meters ($\vec b$).
- Draw a figure showing the displacement vectors $\vec a$ and $\vec b$, as well as their sum $\vec v = \vec a+\vec b$.
- How far is the library from the center of the town square.
- Let $\vec i$ represent walking 1 unit east and $\vec j$ represent walking 1 unit north. We call these unit vectors because their length is 1 unit. Express $\vec a$, $\vec b$, and $\vec v$ in terms of $\vec i$ and $\vec j$.
- It turns out that magnetic north in Coriander is approximately 14 degrees east of true north. The directions above won't actually get you to library if you use a compass. Instead, you must walk 39 meters in the direction of magnetic north ($\vec A$), and then turn 90 degrees to the right and walk another 52 meters ($\vec B$).
- Draw a figure showing the displacement vectors $\vec A$ and $\vec B$, as well as their sum $\vec v = \vec A+\vec B$.
- How far is the library from the center of the town square.
- Let $\vec I$ represent a unit vector pointing towards magnetic east, and let $\vec J$ represent a unit vector representing magnetic north. Express $\vec A$, $\vec B$, and $\vec v$ in terms of $\vec I$ and $\vec J$.
- The above two computations are partly both incorrect, as they both forgot to take into account the fact that the library is actually 5 meters higher ($\vec c$) in elevation than the center of the town square.
- Construct a new drawing that relates $\vec a$, $\vec b$, and $\vec c$ to the context of this problem.
- How far is the center of the town square from the library.
- Let $\vec k$ represent a unit vector that points upwards toward the sky. How can you use this to revisit the problems above?
- Find the distance between $(2,1,0)$ and $(0,-1,1)$.
The problems above are an adaptation of the work from the physics department at Oregon State University. See http://physics.oregonstate.edu/portfolioswiki/doku.php?id=activities:main&file=vcnorth
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