What do you notice? What do you wonder?

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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.

1. Lines u and v also show the positions of the two bugs. Which line shows the ladybug’s movement?

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Which line shows the ant's movement?

Explain your reasoning.

2. How long does it take the ladybug to travel 12 cm?

Do not include seconds (s) in your answer.

2. How long does it take the ant to travel 12 cm?

Do not include seconds (s) in your answer.

3. 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.

Draw your graph on paper, take a picture, and upload it using the image upload icon

If you do not have the ability to upload an image of your work type "Graph is on paper."

4. Mark and label the point on line * u* and the point on line

*that represent the time and position of each bug after traveling 1 cm.*

**v**

Draw your graph on paper, take a picture, and upload it using the image upload icon

If you do not have the ability to upload an image of your work type "Graph is on paper."

*Are you ready for more?*

How fast is each bug traveling?

Fill in the blank with your answer.

The purple bug (ant) is traveling at ___ cm/sec.

Do not include units (cm/sec) in your answer.

How fast is each bug traveling?

Fill in the blank with your answer.

The purple bug (ant) is traveling at ___ cm/sec.

Do not include units (cm/sec) in your answer.

2. Will there ever be a time when the purple bug (ant) is twice as far away from the start as the red bug (ladybug)?

Explain or show your reasoning.

Refer to the tick-mark diagrams and graph in the earlier activity when needed.

Imagine a bug that is moving twice as fast as the ladybug. On each tick-mark diagram, mark the position of this bug.

Draw your graph on paper, take a picture, and upload it using the upload icon

If you do not have the ability to upload an image of your work, type "Graph is on paper."

Plot this bug’s positions on the coordinate axes with lines and , and connect them with a line.

Draw your graph on paper, take a picture, and upload it using the upload icon

If you do not have the ability to upload an image of your work, type "Graph is on paper."

Write an equation for each of the three lines.