U3L1

Multiple Choice

What is the significance of studying graphs in mathematics and real life?

• Graphs help visualize data and relationships, making complex information easier to understand.

• Graphs are only used in mathematics and have no real-life applications.

• Graphs are mainly used for artistic purposes.

• Graphs are not useful for problem-solving.

Open Ended

When you look at two different graphs, what kinds of things do you notice and wonder about?

Multiple Choice

Which of the following best describes the difference between the lines labeled 'g' and 'f' in the left graph?

• Line g represents a bug moving slower than line f.

• Line g represents a bug moving faster than line f.

• Line g and line f represent bugs moving at the same speed.

• Line g represents a bug that stops moving.

Open Ended

What do you notice about the two graphs showing elapsed time versus distance traveled?

Open Ended

What are the things you noticed and wondered about the graphs?

Fill in the Blank

A ladybug and an ant move at constant speeds. The diagrams show their positions at different times. After 6 seconds, the ladybug has traveled ___ centimeters.

Multiple Choice

Based on the diagrams, which bug moves faster: the ladybug or the ant?

• Ladybug

• Ant

• Both move at the same speed

• Cannot be determined

Open Ended

Which line on the graph represents the movement of the ladybug, and which represents the ant? Explain your reasoning.

Open Ended

How long does it take the ladybug to travel 12 centimeters? The ant?

Multiple Choice

If the ant travels 12 centimeters in 6 seconds, what is its average speed?

• 2 cm/sec

• 1 cm/sec

• 3 cm/sec

• 6 cm/sec

Fill in the Blank

The slope of a distance vs. time graph represents the bug's ___.

Open Ended

Will there ever be a time when the ant is twice as far away from the start as the ladybug? Explain or show your reasoning.

Open Ended

How fast is each bug traveling?

Multiple Choice

Which of the following graphs best represents a bug moving twice as fast as the ladybug?

• A graph with a line steeper than u

• A graph with a line parallel to v

• A graph with a line less steep than v

• A graph with a line identical to u

Multiple Choice

Which bug traveled at a faster rate according to the graph?

• Bug u

• Bug v

• Both bugs traveled at the same rate

• Cannot be determined

Multiple Select

Select all statements that correctly describe how different representations (graphs, equations, tables) can show the same information about rates.

• They all show the relationship between distance and time.

• Only graphs can show who is faster.

• Equations can be used to predict future outcomes.

• Tables cannot show rates.

Open Ended

How does the slope of the line show up in each equation?

Fill in the Blank

Kiran can ride 4 miles every ___ minutes.

Multiple Choice

If Kiran and Mai start a bike trip at the same time, how far apart are they after 24 minutes?

• 1 mile

• 2 miles

• 3 miles

• 4 miles

Open Ended

Who rides faster?

Fill in the Blank

The graph shows that the turtle described by line g travels ___ cm in 6 seconds.

Multiple Choice

Based on the graph showing the positions of two turtles in a race, which turtle is moving faster, the one represented by line f or line g?

• The turtle represented by line f

• The turtle represented by line g

• Both turtles are moving at the same speed

• There is not enough information

Open Ended

How does the constant of proportionality help you compare the pace of different animals in a race?

Fill in the Blank

Graphs are useful for representing and analyzing ___.

Open Ended

What is one thing you learned about graphs today that you found interesting or surprising?