Part 1 – Presentation & Guided Practice

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

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.

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 yc

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?

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

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

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.

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 gY

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?

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.

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.

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

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

The last 2 seconds of the clip are spent at d = 60. Since distance (the y-coordinate) isn't changing, the slope is zero

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

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?

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.

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.

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)

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.

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

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? ?

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.

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?

Reese runs up and makes a quick short jump at the rope within the first second and a half.

Just before the 2 second mark, Reese jumps up to about the 4 foot cone.

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.

Reese regroups, and takes a low and somewhat longer jump at the rope.

She circles, then jams on the breaks, thinking she's fooled me!

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.

Still off-balance, Reese makes another quick jump for the rope. Cats may always land on their feet, but puggles don't.

Now Reese decides to bide her time and wait until I blink. Then she'll strike.

With a mighty surge, the puggle springs up and latches onto the rope!

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)

What's Next? Part A – Discussions & Reflections Part 2 – Creating Visuals from a graph Part 3 – Creating Graphs from Animations