3.1 Understanding Proportional Relationships (Extra Lesson)UNIT 3 • LESSON 1 UNDERSTANDING PROPORTIONAL RELATIONSHIPS[list][*][url=https://hcpss.instructure.com/courses/93828/pages/3-dot-1-understanding-proportional-relationships-extra-lesson?module_item_id=2557378#kl_panel_0_content]Setting the Stage[/url][/*][*][url=https://hcpss.instructure.com/courses/93828/pages/3-dot-1-understanding-proportional-relationships-extra-lesson?module_item_id=2557378#kl_panel_1_content]1.1: Notice and Wonder: Two Graphs[/url][/*][*][url=https://hcpss.instructure.com/courses/93828/pages/3-dot-1-understanding-proportional-relationships-extra-lesson?module_item_id=2557378#kl_panel_2_content]1.2: Moving Through Representations[/url][/*][*][url=https://hcpss.instructure.com/courses/93828/pages/3-dot-1-understanding-proportional-relationships-extra-lesson?module_item_id=2557378#kl_panel_3_content]Are You Ready For More?[/url][/*][*][url=https://hcpss.instructure.com/courses/93828/pages/3-dot-1-understanding-proportional-relationships-extra-lesson?module_item_id=2557378#kl_panel_4_content]1.3: Moving Twice as Fast[/url][/*][*][url=https://hcpss.instructure.com/courses/93828/pages/3-dot-1-understanding-proportional-relationships-extra-lesson?module_item_id=2557378#kl_panel_5_content]Summary[/url][/*][/list][img]https://hcpss.instructure.com/courses/93828/files/10865572/preview[/img][br]adybug and ant move at constant speeds. The diagrams with tick marks show their positions at different times. Each tick mark represents 1 centimeter.[img width=601,height=338]https://hcpss.instructure.com/courses/93828/files/10865105/preview[/img][img]https://hcpss.instructure.com/courses/93828/files/10865818/preview[/img][list=1][*]Lines uu and v also show the positions of the two bugs. Which line shows the ladybug’s movement? Which line shows the ant’s movement? Explain your reasoning.[/*][*]How long does it take the ladybug to travel 12 cm? The ant?[/*][*]Scale the vertical and horizontal axes by labeling each grid line with a number. You will need to use the time and distance information shown in the tick-mark diagrams.[/*][*]Mark and label the point on line u and the point on line v that represent the time and position of each bug after travelling 1 cm.[/*][/list]Refer to the tick-mark diagrams and graph in the earlier activity when needed.[list=1][*]Imagine a bug that is moving twice as fast as the ladybug. On each tick-mark diagram, mark the position of this bug.[/*][*]Plot this bug’s positions on the coordinate axes with lines uu and vv, and connect them with a line.[/*][*]Write an equation for each of the three lines.[/*][/list]Here is a graph that could represent a variety of different situations.  [img width=418,height=530]https://hcpss.instructure.com/courses/93828/files/10865870/preview[/img] [list=1][*] Write an equation for the graph.[/*][*]Sketch a new graph of this relationship.[/*][/list][img]https://hcpss.instructure.com/courses/93828/files/10864962/preview[/img]You teacher will give you 12 graphs of proportional relationships.[list=1][*]Sort the graphs into groups based on what proportional relationship they represent.[/*][*]Write an equation for each [i]different[/i] proportional relationship you find.[/*][/list][color=#2d3b45][br][/color]Two large water tanks are filling with water. Tank A is not filled at a constant rate, and the relationship between its volume of water and time is graphed on each set of axes. Tank B is filled at a constant rate of 12 liters per minute. The relationship between its volume of water and time can be described by the equation v=12t, where t is the time in minutes and v is the total volume in liters of water in the tank.[br][br]The graph of a very slight curve representing the volume of the tank in liters versus time in minutes[br]The graph of a very slight curve representing the volume of the tank in liters versus time in minutes[br][br]Sketch and label a graph of the relationship between the volume of water v and time t for Tank B on each of the axes.[br]Answer the following questions and say which graph you used to find your answer.[br]After 30 seconds, which tank has the most water? [br]At approximately what times do both tanks have the same amount of water? [br]At approximately what times do both tanks contain 1 liter of water? 20 liters?