Functions LT: I will be able to explain the graph with a real-life scenario Think of three things you can do to help insure your success in this class I can … I can… Today’s Agenda Success Criteria I can create graphs to explain a real-life scenario Do Now Lesson Activity

Graphing in Two Dimensions Speed Time

Two Dimensional Graphs Two dimensional graphs show the relationship between two variables. For example, a graph could show a person’s distance from an object as he moves around during a specified period of time. Can you think of any other relationships that could be graphed? The next few slides give examples to illustrate what these graphs look like.  

A train pulls into a station and lets off its passengers. Speed Speed Time Elapsed Time Elapsed Discussion topics Time is independent (continues without interruption) Speed is dependent constant, decreasing, increasing Top left; constant speed and then slow down instantly and gone: not a function because time stopped Top right: correct Bottom left: increasing and decreasing speed over time Bottom right: constant speed, then crash to complete stop in an instant (not good and not a function) Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7 Speed Speed Time Elapsed Time Elapsed

A man takes a ride on a ferris wheel. Distance from ground Distance from ground Time Elapsed Time Elapsed Discussion topics Time is independent (continues without interruption) Distance is dependent Top left; going back in time (not a function) Top right: correct Bottom left: up and down, but never back to the top Bottom right: going back in time (not a function) Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7 Distance from ground Distance from ground Time Elapsed Time Elapsed

A woman climbs a hill at a steady pace and the starts to run down one side Speed Speed Time Elapsed Time Elapsed Discussion topics Time is independent (continues without interruption) Speed is dependent: constant, decreasing, increasing Top left: correct constant speed and then speeds up down Top right: speeds up and then slow down (would be a graph of height vs time) Bottom left: increasing and then constant speed Bottom right: increases then decreases and then increases forever All are functions, can someone explain why they are all functions? Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7 Speed Speed Time Elapsed Time Elapsed

A child swings on a swing. Distance from ground Distance from ground Time Elapsed Time Elapsed Discussion topics Time is independent (continues without interruption) - Distance is dependent All are functions, explain to your partner why all are a function Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7 Distance from ground Distance from ground Time Elapsed Time Elapsed

A child climbs up a slide and then slides down. Speed Speed Time Elapsed Time Elapsed Discussion topics Time is independent (continues without interruption) Speed is dependent: constant, decreasing, increasing Top left: increasing speed, constant, decreasing Top right: not a function, why Bottom left: correct Bottom right: constant speed, then decreasing speed Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7 Speed Speed Time Elapsed Time Elapsed

Students pick to be Sully or Mike They are asked to graph the distance from the entrance with respect to time. (one part of the movie does not show the 2 characters so tell students to assume both characters keep walking away from the door) Remind students that their pencil/pen should keep moving across the graph because time continues Might need to show the clip 2 to 3 times so students can try, then think through the second time, and then make their final version the 3rd time

How far from the entrance? Distance from door Time Have a few students present and talk through what is happening Remember creating functions so moving away from entrance, standing still, or moving toward entrance

They are asked to graph the speed of Dash during the race. Remind students that their pencil/pen should keep moving across the graph because time continues Might need to show the clip 2 to 3 times so students can try, then think through the second time, and then make their final version the 3rd time

How fast does Dash run? Speed Time Speed: increasing, decreasing, constant

How far above the ground are Wesley’s feet? Wesley is the character with the mask

How far above the ground are Wesley’s feet? Height Started up and ended lower: so if started at (0,0) quadrant 1 and 4 or if started up at time 0 then only need quadrant 1 What about the loop around the branch? (remember no going back in time) Time

Students will be asked to graph height vs time Or Speed vs time

Watch Spidey go! Height vs. Time Speed vs. Time Speed Height Time Time

Height of Neville above the ground vs time

How high is Neville? Height above ground Time