The Next Week...

Discussion after discussion after discussion.  That's all we've done this entire week.  Now, I like discussing as much as the next guy, but sometimes it can become a little too much.

 For our discussion, we decided to talk about a packet we did last week for homework.  The title is Proportional Reasoning, and let me tell you I was a little skeptical of it.  I'm not the best at reasoning.  I can do it, but sometimes I write a little too much.  It just goes on and on unless I stop myself because I feel the need to make sure the reader of my work understands exactly what I'm saying.  I think this comes from the need to get a good grade, but I'm not exactly sure.  At least I'm working on it.

Anyway, the packet was about understanding proportions, converting to different units, and understanding different types of graphs.  From my standpoint, I was pretty okay with the proportions and conversions part. I had learned about both in math and science last year so I had them pretty down pat.  The thing that really tripped me up was the different types of graphs.  I knew I had learned it before but it was still hazy in my head.  It was probably the same for everyone, because my teacher decided to talk about that part the most.

I do remember talking about the answers of the packet with my group first to compare what we got.  There were some varying answers every few questions or so, but overall my group had pretty similar results.  This was mostly for the proportions and converting part.  However, when we came to the graphs, we were all stumped.  Some of us thought one thing while the rest of us thought another, and we didn't know what to do.

Later in the week, we did a Socratic Circle to talk about the graph questions.  For those of you who don't know what a Socratic Circle is, it's when the class is divided into two circles; the inner circle and the outer circle.  The inner circle actually talks about the topic at hand, while the outer circle observes the inner circle and comments on what the group did well and what they did not-so-well.  The circles then switch, and they discuss again.  This was our first one in physics, so it wasn't fantastic.  However, we did come up with some ideas.
For the equation y=a/(bx^2) :

• When a is doubled, keeping b and x constant, y also doubles.
• When b is doubled, keeping a and x constant, y halves.
• When x is doubled, keeping a and b constant, y quarters.
• Plugging in numbers works best.
• When the number doubling is in the numerator, y increases.
• When the number doubling is in the denominator, y decreases.
• You should plug in simple constants.

When x is halved...

• In the equation y=kx, y is halved.
• In the equation y=k/x, y us doubled.
• In the equation y=k/x^2, y is quartered.

The last time we met for class this week, we had a class discussion about different types of graphs in our packet.  Those different types were linear, direct, directly proportional, indirect, and inversely proportional. We discussed the meaning of these words, and drew graphs to see what they would look like.  We decided that:

• Linear- A straight line.
• Direct- When x goes up, y goes up or when x goes down, y goes down (they both have to do the same thing).
• Directly Proportional- x to y is the same ratio (Example: If you double x, you have to double y), the slope is always constant, and the line has to go through the origin.
• Indirect- Not direct. x and y do opposite things (Example: if x goes up, y goes down).  Also, anything not direct is indirect (Example: vertical and horizontal lines).
• Inversely Proportional- When x doubles, y halves (y is like the reciprocal of y).  Also, sometimes inverse can be indirect depending on the situation.
• Not all curved lines are exponential.
• Proportional lines cannot have y-intercepts.
• y=kx is direct, linear, and directly proportional.
• y=kx+b is linear and direct.
• y= -kx+b is linear and indirect.

Reflection

This week was a very interesting one with no labs.  Just continuous talking and reviewing topics.  I think I need to make sure that it is known when I have an idea or that I need to raise my hand more.  I have to say thanks to my teacher because he actually asked if I had an opinion on the topic multiple times.  I think he knew that I had something to say.  I also think that I am grasping the concept.  I don't find this too hard and I think that at the very least I understand it at the basic level.  I wonder what we will do next week.