*For my assignment I will be acting out a lesson
plan as if I were teaching a class!
Hello Class! My name is Professor Paviglionite
and today we will be learning how to find the rate of change. The rate of
change is essentially the steepness of an increasing or decreasing straight line.
After today, my goal is for you guys to feel comfortable with finding the rate
of change, because there is a lot that we can do with it. Learning rate of
change is the beginning step to help determine the equation of a line, and can
help to graph a linear function. Rate of change can also be applied to many
real life situations, as you will see with my introductory example!! Enjoy!
In order to explain rate of change, I will begin
with a fun activity to find rate of change in a simple real life situation.
Everyone on their table should have a beaker, half filled with water, 10
plastic cubes of the same size, graph paper, a ruler, and a pencil. I am
passing this activity down, as I myself did it in math class in high school
when first learning this math concept.
This activity is based off of Aesop’s Fable, the
story of a raven. During a terrible, terrible drought, the raven was thirsty
and had to find a means of survival. Near his nest was a well; but the water
level was not high enough for the raven to reach with his beak. In this
activity the half-filled water beaker will represent the well. After days of
thirst, the raven had an idea…to drop pebbles into the well in order to raise
the water level so that he could reach it with his beak. The cubes on your
table will represent the pebbles.
What I would like everyone to do is to experiment
and record your results in a table. I want you to record the water level of the
beaker against the number of cubes that are dropped in. I then would like you
to graph your results and see what you come up with; see if you notice a
pattern in your graph.
(Students complete graph)
Now, what does everyone notice? What you should
have come up with is something that resembles this:
You should notice a linear relationship. As the
number of cubes dropped in increased, the water level rose. In this example our
y-axis, or output, was the water level, because it was dependent on the number
of cubes. The x-axis, or input variable, was number of cubes.
To determine rate of change, which is the goal of our class today, we
will do the following:
Rate of change=rise/ run
Or
Rate of change=y2-y1/x2-x1
Put more simply, we find the change in the y-value and divide it by the change
in the x-value. In the big picture this gives us the rate at which the linear
function is increasing or decreasing. So, for our raven example, I would like
everyone to give this a try. Find the rate of change, but try it with different
sets of numbers, they should all come to the same rate of change since this
function is linear.
(Students do their calculations)
Now, I would like everyone to come to the board
and share your results, I want to see your work!!!
As shown:
|
Water
Level (y)
|
3
|
3.5
|
4
|
4.5
|
5
|
|
Cubes (x)
|
2
|
3
|
4
|
5
|
6
|
3.5-3/3-2=.5
4-3.5/4-3=.5
4.5-4/5-4=.5
So as you can see from our
rate of change calculations, the rate of change should equal a .5 water level
increase for every one cube put into the water.
I hope that this simple real life example gave you guys a
better picture of how rate of change is determined and can be used. The rate of
change can also be called the slope. In the next class we will learn how the
slope and rate of change can be used within a linear equation! Now to end
class, given the following problems I would like you to find the rate of
change!
Practice Problems:
1.
Find
the rate of change of the line passing through the points (4,3) and (-5,-2).
Solution:
(3-(-2))/(4-(-5))=5/9
2.
Kevin's savings account balance changed from $1140 in
January to $1450 in April. Find the average rate of change per month.
Solution: (1450-1140/4-1)=310/3=$103.33
Works Cited
"Mathiness
Is Happiness." : Rate of Change. N.p., n.d. Web. 07 Apr. 2014.
04
Apr. 2014.
"Rate
of Change Practice Problems." Algebra-Class.com. N.p., n.d. Web. 07
Apr. 2014.
Your examples were great and easy to understand! I'm familiar with Aesop's fable so I really like how you utilized it. Plus the way you acted this out like a lecture was awesome! I think I'm going to use this to study for the final, thank you!
ReplyDeleteProfessor Nicole!
ReplyDeleteI loved your lecture! especially how you started off with an example at the beginning to make us all determine how we find the rate of change. I also liked how you had practice problems at the end of your lecture in order for us to practice! this was indeed really helpful
Thank you:)
nicole,
ReplyDeletereally nice lesson. i can tell you worked hard on it! i haven't used the beaker example for slope in a long time. thanks for reminding me of that activity for future use! one thing to note is to say what the units are for the water level.
good job.
professor little