Part 1 Presentation & Guided Practice Slide 2 Learning
Targets: I can locate and graph points on the coordinate plane
system I can find slope and relate it to rate of change I can
identify and describe situations with constant and non-constant
rates of change and compare and contrast them I can identify
domain, range and solutions sets I can represent relations as
ordered pairs, tables and graphs Slide 3 What is a graph? In some
cases there are an infinite number of possible coordinate pairs
that make an equation true or relate two variables in a scenario.
Since we can never list all of the solutions in a table, we often
create a graph to give a visual of the solution set. In the
examples that follow, the number of ordered pairs generated by each
video clip is infinite since time is continuous. Let's just try to
identify key points. Then we can make a graph to represent each
clip. Slide 4 Part 1a Good Puppy Let the x-axis be time (seconds)
Let the y-axis be Reese's distance from the first cone (feet) Start
by filling in the table of values on your worksheet. Plot the
points to help make the graph and find the required slopes
http://www.youtube.com/watch?v=1IdDZ3KVl yc Slide 5 Part 1a Good
Puppy Discussion Questions: When Reese is sitting still, what
should the slope of the graph be? For which part of the graph
should the slope be the steepest? Why? Slide 6 Part 1a Good Puppy
Reese waits at the starting point for 8 seconds The slope of this
line segment is zero, which makes sense since she isn't moving
Slide 7 Part 1a Good Puppy The slope of this line segment: (40 0) =
up 40 feet, (13 - 8) = over 5 seconds, tells us that Reese is
trotting towards her treat at 8 ft/sec. From t = 8 to t =13, Reese
runs forward 40 feet Slide 8 Part 1a Good Puppy Reese's position
remains the same for the last 7 seconds of the clip, the slope of
this segment is also zero. Reese enjoys her treat and some praise
at d = 40 for the last 7 seconds of the clip. Slide 9 Part 1b - The
Eye of the Puggle Let the x-axis be time (seconds) Let the y-axis
be Reese's distance from the first cone (feet) Start by filling in
the table of values on your sheet. Plot the points to help make the
graph and find the required slopes
http://www.youtube.com/watch?v=OTwVJgA26 gY Slide 10 Part 1b - The
Eye of the Puggle Discussion Questions: For which parts of the
graph should the slope be zero? Why? How should the slope at t =10
compare to the slope at t = 16? Why so? Slide 11 Part 1b - Eye of
the Puggle Reese waits 2 seconds, then is led on a walk The slope
of this portion of the graph is zero, the y-value remains the same
from t=0 up to t=2. Slide 12 Part 1b - Eye of the Puggle Over the
next ten seconds, Reese walks 30 feet. From (2,0) to (12,30) Slope?
30 0 = up 30 feet, 12 2 = over 10 seconds. Reese is walked at 3
ft./sec on her leash. Slide 13 Part 1b - Eye of the Puggle Reese
waits for the next three seconds as her leash is removed No change
in distance over this time means a slope of zero Slide 14
Connecting (15,30) and (18,60) A steeper slope for the run than for
the walk. Reese is running at 30 ft./ 3 sec. Or 10 ft/sec during
this part of the clip Slide 15 The last 2 seconds of the clip are
spent at d = 60. Since distance (the y-coordinate) isn't changing,
the slope is zero Slide 16 Part 1c - Fetch Let the x-axis be time
(seconds) Let the y-axis be Reese's distance from the first cone
(feet) Start by filling in the table of values on your sheet. Plot
the points to help make the graph and find the required slopes
http://www.youtube.com/watch?v=Rb-jlxKsv0s Slide 17 Part 1c - Fetch
Discussion Questions: How do the slopes at t = 4, t = 5 and t = 5.9
compare? For which parts of the graph is the slope negative? Why?
Slide 18 Reese waits with anticipation for two seconds, until the
ball is thrown Even though she is excited, Reese's distance didn't
change until the ball was thrown, the slope of the first segment is
zero. Slide 19 Reese covers 60 feet in 4 seconds, moving from (2,0)
to (6,60). Slope = 15ft/sec. Though in reality, the ends of this
line segment would curve due to her acceleration and deceleration.
Slide 20 Reese is quick, but it did take her about one second to
stop, pick up the ball and turn around. During this time her
distance does not change. Connecting (6,60) with (7,60) Slide 21
Reese returns with the ball over the next 5 seconds. This segment
connects (7,60) with (12,0). Slope = -12ft/sec. In this case, the
negative sign indicates direction. Back towards d = 0. Slide 22
Reese is showered with praise for the last 8 seconds of the clip.
Her distance doesn't change, so we see a flat line with a slope of
zero to complete the graph Slide 23 Are all graphs lines?
Discussion Questions: What is true about the slope of any line
segment? What types of scenarios might generate graphs that are not
linear? ? Slide 24 Part 1d - Reese vs. the Chew Rope Let the x-axis
be time (seconds) Let the y-axis the height of Reese's head (feet)
While standing, Reese's head is about 1 foot off the ground Watch
for both low jumps and high jumps from Reese.
http://www.youtube.com/watch?v=PUaSgZwCeEg Slide 25 Part 1d - Reese
vs. the Chew Rope Discussion questions: When Reese's feet are on
the ground, what should the graph look like? Each time Reese jumps,
what will we see on the graph? Slide 26 Reese runs up and makes a
quick short jump at the rope within the first second and a half.
Slide 27 Just before the 2 second mark, Reese jumps up to about the
4 foot cone. Slide 28 Reese makes another big jump near the 3.5
second mark. Notice that her height is only at the crest (vertex)
for a split second. Slide 29 Reese regroups, and takes a low and
somewhat longer jump at the rope. Slide 30 She circles, then jams
on the breaks, thinking she's fooled me! Slide 31 Showing signs of
frustration, Reese lunges right at me! Reese actually did stay in
the air a little longer on this jump, trust me I got a good look.
Slide 32 Still off-balance, Reese makes another quick jump for the
rope. Cats may always land on their feet, but puggles don't. Slide
33 Now Reese decides to bide her time and wait until I blink. Then
she'll strike. Slide 34 With a mighty surge, the puggle springs up
and latches onto the rope! Slide 35 Now locked onto the rope, Reese
and I are engaged in a tug-of-war through the end of the clip
(which was edited to cut out before I lost to avoid embarrassment)
Slide 36 What's Next? Part A Discussions & Reflections Part 2
Creating Visuals from a graph Part 3 Creating Graphs from
Animations
