Unit 3: Lesson 1: Understanding Proportional Relationships

Q1: 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.

Q2: How long does it take the ladybug to travel 12 cm? The ant?

Q3: 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.

Q4: Mark and label the point on line u and the point on line v that represent the time and position of each bug after traveling 1 cm.

Q1: Ladybug: line u ; Ant: line v

Q2: Ladybug: 6 seconds, ant: 4 seconds

Q1:

 $Equation\ for\ Ladybug\ y=\frac{1}{2\ }x$  

 $Equation\ for\ Ant\ y=\ \frac{1}{3}x$  

 $Equation\ for\ new\ bug\ y=\ \frac{1}{4}x$  ; (twice as fast as ladybug).

Where  represents the distance traveled and  represents elapsed time.

1.On the same axes, draw a line for a third turtle that is going half as fast as the turtle described by line g.

2.Explain how your line shows that the turtle is going half as fast.

1.A line through (0,0), (1,1), (2,2) , etc.

2.Looking at the values for 2 seconds, turtle g moves 4 cm and the third turtle moves only 2 cm. This third turtle covers half the distance in the same amount of time.