IM 8.3.1 Lesson: Understanding Proportional Relationships
What do you notice? What do you wonder?
A ladybug and ant move at constant speeds. The diagrams with tick marks show their positions at different times. Each tick mark represents 1 centimeter. On the graph, lines u 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?
In the applet below,
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 and the point on line that represent the time and position of each bug after traveling 1 cm.
How fast is each bug traveling?
Will there ever be a time when the ant is twice as far away from the start as the ladybug? Explain your reasoning.
Refer to these tick-mark diagrams and graph from the earlier activity when needed.
Plot this bug’s positions on the coordinate axes with lines u and v, and connect them with a line.
Write an equation for each of the three lines.