Hey guys! Long time no blogging! I am going to cover what we have learned so far in Relations and Patterns. It's obvious that as a class we struggled with this unit, especially while Mr. P was away. Now Mr. P is back (yay!) and we're finally getting the hang of it with his help. Hopefully my post will help you guys with anything you still don't understand!
Now, lets start from the beginning.
From what I noticed, we did very well with representing patterns with written equations. But to refresh your memory here is this short and sweet video on the subject here!
What we struggled with most was the difference between an independent and dependent variable. Here are the definitions to both and i'll also throw in an example!
Independent Variable: It stands alone and is never changed by other variables you are trying to calculate and measure.
Dependent Variable: A variable that depends on other factors, sometimes it can be dependent on the independent variable, on other factors, or on both!
For example, Mr. P jogs every morning at 6 AM. Each morning, he runs further and for a longer amount of time.
DISTANCE TIME
200 2 min
600 5 min
1200 10 min
1600 13 min
1800 15 min
2200 19 min
2400 20 min
Now before we even begin to graph this, we need to figure out what our independent variable is (which would go on our x axis) and our dependent variable (which would go on our y axis)
Ask yourself, which of these two variables, distance and time, can be changed due to whatever reason? Obviously, time can not be bent, and the distance Mr. P runs can be affected by any injuries, weather (if he is running outside) and for his own personal goals for his jog. But time will not change! So time would go on the x axis, because it is independent and distance would go on the y axis, because it is dependent on several different factors. Graphing the data is now the easiest part! Make sense?
For this unit, our best friends are these two equations: y = mx + b and y2-y1
x2-x1
The first represents the equation for a linear pattern. (Dependent Variable= Slope x Independent Variable + Fixed value)
The second equation would calculate the slope of any linear equation. Voila~
As a class, we did this cool experiment in which we measured our height and our arm length. With Christian having the longest arm length, at 181 cm and Angela (me!) with the shortest, at 155 cm.
After measuring everyone in the class, we made a scatter plot with our data. Very simple, no one struggled with scatter plots and we all had a fun time doing the experiment.
With calculating slope, which is the steepness of a line, there are two ways of calculating it. The equation and simply counting the rise and the run. Both are quite simple! But you can choose your preferred method. I found this awesome (and short) video which covers both methods! The answers you seek are here.
Lastly, here is a video which goes more in depth on how y= mx + b can be put into use and how rise/run works!
Hopefully I covered anything that seemed confusing or frustrating. In summary, the hardest part to graphing is collecting your data and creating a correct table of values, which with some practice, isn't hard at all. Graphing the data will be the easiest part! For calculating slope, make sure you use the method you are most comfortable with (try to get use to using both!) and double check to make sure that your slope matches with the graph.
Good luck to you all and have an awesome weekend! The test for this unit is next Friday, January 17th.
-Angela
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