Color or Black/White both ok, just make sure face clearly visible/in focus.
(Need even more review of slopes? Try this CoolMath.com very "entry-level" review of lines and slopes)
I. QL Skills, Lessons, and Themes for Week 1
DISCLAIMERS: The outline below is not complete, it is only a starting point (and future weeks' outlines may not be given in as much detail) to help you start organizing the material in and out of class. Anything mentioned in class, discussed in class, or related to work in class or outside of class, is fair game on tests; this list is offered as a helping start. So please go beyond this list. Use it just as a launching point. Also don't just memorize it: think up of your own examples, illustrations, expansions/generalizations, etc, and the analytic skills, and quantitative reasoning skills you are expected to be developing- Lines and Slopes
- Review of Cartesian Plane and Definition of Slope
- Calculating Slopes given formula or exact numbers (rise/run)
- Estimate Slope between 2 pts by estimating x&y coords of each
(then finding Δy and Δx and taking quotient)
Note: Δy just means y2-y1 and likewise for Δx - Estimate slope of already-drawn (e.g. hand-drawn) line
- Lines and Avg. Rates of Change
- Lines and Linear growth: constant rate of change
- Slopes of line-segments between 2 pts = average rate of change between the two (physical or temporal) points
- Ex. is average speed. How to find your car's avg speed
- Why it's meaningless to ask for "average" speed unless question specifies two times (starting and ending pts)
- Likewise with any "find the average rate of change" question
- Tangent lines/ Instantaneous rates of change/ How different
from avg. (average) rates of change
- Definition of a Tangent line
- The fact that a tangent line (or more accurately, its slope: the slope of a tangent line) represents an instantaneous rate of change (e.g. instant. speed) instead of representing an average rate of change. If you're driving your car and a compute shows time on x-axis and distance travelled on y-axis, and if the graph is drawn by the computer, then what is the slope of the tangent line equal to if you draw a tangent line to the curve above x=4? It's equal to whatever your speedometer was at time equal to t=4. This is a bit complicated so review it but realize we will get to see these concepts again to solidify them)
- Secant lines: given any two points in the x-y-plane which are on the graph of a function, we can connect those two lines and draw out the (unique) line one gets that goes through both of those points: it is the secant line between those two points.
- Secan lines (if we use the right ones) can approximate a tangent
line. The basic idea:
Basic
After you fully understand the above (review also your class notes) repeatedly view the graphic below too which has more detail (the notation Δy, or "delta-y" stands for the difference you get when you subtract the second y-value from the first y-value; similarly for Δx. Ignore the "f &prime(x0)" part at the end) see below:
- Another good and short review with visuals of avg. versus instant. speed is on this page at the Canadian Space Agency website. If instead of "distance" on the y-axis we had some other quantity like "population of bacteria in the dish in the laboratory" then we could have not average speeds but "average rate of change" (average rate of growth, if the change is positive; otherwise, avg. rate of decrease or avg. rate of deline) versus the instant. rate of increase.
- What if y-axis was temperature? Pressure? CO2 concentration? In all cases we can ask what the avg. rate of change is during a period with a starting time and ending time, or we can ask what the instantaneous rate of change is at one point in time. It does not make sense to ask what the "average" rate is at a single point in time, nor to ask what "the" instant. rate is "Between these two points"
- The units for the number representing the slope of a line (or the slope of line segment connecting two points on the graph of a function that isn't a line) is simply the quotient of the units represented on the y-axis, divided by the units represented on the x-axis (recall "average speed (in miles per hours) example: the y-axis has "miles" as the units and x-axis has "hours" as units so what are the units behind whatever number "m", the slop of a line, is? Answer: "miles per hour")
- Advantages of numerical tables over graphs (precision)
- Advantages of graphs over numerical tables (several advantages, as discussed in class)
- Definitions of QL (Quantitative Literacy) - see link to First-day overhead.
- Outside of Class
- Google Calculator: Arithmetic
- Google Calculator: Units Conversions
- Google Calc: Getting comfortable with Large Numbers
Modeling and Estimating: Definitions of each.- Modeling and Estimating: Gaining some comfort with
(In Screening Mammography you let a sphere 'model' a tumor; in CO2-Slopes you used estimation) - Expository quantitative writing: be specific and precise, and clear while still concise.
- Visualization of large numbers, a first
look: Two
separate videos on size of planets and stars.
- Tests will not assume you have looked at every link in "In Context" or "On the Web" etc sections in this and future weeks, but will assume you have looked at, and given careful thought to, some of them.
II. In context
The Mauna Loa Observatory (MLO) is an atmospheric baseline station on Mauna Loa volcano, on the big island of Hawaii. Since 1957 MLO has been continuously monitoring and collecting data relating to atmospheric change, and is known especially for their continuous monitoring of atmospheric carbon dioxide (CO2) levels. The observatory is under the Climate Monitoring and Diagnostics Laboratory (CMDL) which is part of the National Oceanic and Atmospheric Administration (NOAA).The high elevation (11,000+ feet high) helps avoid most local, time dependent CO2 release issues distorting the data (e.g. a lot of traffic on some days, less traffic on other days). But since volcanoes can release CO2 isn't this a problem?Mauna Loa Observatory (MLO) has activities at five sites. The primary observing site is located at the 11,135 ft (3397 m) level on Mauna Loa north slope...Mauna Loa was originally chosen as a CO2 monitoring site because, being isolated in the middle of the Pacific, the air is exceptionally pure. Being high, it is above the inversion layer. There was also already a convenient road to the summit built by the military. [about Mauna Loa Observatory]
"The purity is good as long as there is no contamination from local volcanic sources - this is detected and removed" [Wikipedia There is a blog run by PhD climate scientists, see comment by notable science history expert Spencer Weart
So the scientists are of course well aware of this. In addition, the CO2 readings at Mauna Loa can also be checked against other observatories around the world. And, sure enough, while there are minor variations (since CO2 is not at completely identical levels but differs a bit from one place to another), the data match very closely so the famous Mauna Loa data is a very good match, that is, it is confirmed elsewhere like the Barrow CO2 data, Samoa, etc (notice the red and dark blue dots are almost identical, and the other two (Barrow, Alaska and South Pole differ a bit but stay in the same narrow distance 'band' in the graph
(Notice that the yellow and pink are methane readings ;the first four colors are CO2 at various stations around the world. Notice also how this graph/data set being much more condensed it's harder to read the precise year to year increases, while overall 1970-2006 trend is visible)
See also here for CO2 data from Barrow (Alaska).
Speculation that government ministers are far more concerned about a future supply crunch than they have admitted has been fuelled by the revelation that they are canvassing views from industry and the scientific community about "peak oil". The Department of Energy and Climate Change (DECC) is also refusing to hand over policy documents about "peak oil" ...under the Freedom of Information (FoI) Act, despite releasing others in which it admits "secrecy around the topic is probably not good". Experts say they have received a letter from David Mackay, chief scientific adviser to the DECC, asking for information and advice on peak oil amid a growing campaign from industrialists such as Sir Richard Branson for the government to put contingency plans in place to deal with any future crisis.
"A study by a German military think tank has analyzed how 'peak oil' might change the global economy. The internal draft document -- leaked on the Internet -- shows for the first time how carefully the German government has considered a potential energy crisis...According to the German report, there is 'some probability that peak oil will occur around the year 2010..'The Bundeswehr prediction is consistent with those of well-known scientists who assume global oil production has either already passed its peak or will do so this year."
III. On the Web