Imagine a brother and sister biking from their home to a nearby park. The brother starts off very quickly, but then gets tired and slows down. The sister bikes at the same speed the entire time. They arrive at the park at the same time.

A road map could show you the route and the distance that they traveled. But a distance–time graph can give you information about who was ahead and who was biking faster as they rode. In this lesson, you will learn how to read and interpret a distance–time graph.

Goals
Here are the big ideas you will learn about in this lesson:

• Distance and time can be represented on a graph.
• The steepness of a line segment on a distance–time graph can tell you how quickly an object was traveling during a certain period.

Strategies
You will be using many reading and writing strategies to complete this lesson. The key strategies that you will focus on are:

• Making inferences
• Determining important information
• Identifying and using text features
• Constructing summaries

• origin
• steepness
• vertical

A distance–time graph has two axes. The vertical axis (going up and down) shows the distance traveled, while the horizontal axis (going side to side) shows the time that has passed.

The two axes meet at a single point called the origin. As you move from the origin up the vertical axis, the distance traveled increases. As you move from the origin along the horizontal axis, the amount of time passed increases. People use distance–time graphs to see how far a person, bike, car, train—really, anything that moves—has traveled over a certain amount of time.

A single point on the graph can show where a moving object is at a certain moment. Look at the point on the graph to the left. It lines up with 1 hour on the horizontal axis and 5 miles on the vertical axis. So if this graph represented a person's trip, that person would have traveled 5 miles in 1 hour.

In this video, you will meet Harry, who is planning to ride his unicycle, a one-wheeled bike, to his grandmother’s house. Before he begins his trip, he creates a distance–time graph to show how far along he expects to be at different times during his ride. Harry knows he can ride 5 miles in 1 hour. He marks three points on his graph to predict how far he will be after 1, 2, and 3 hours of riding his unicycle. The straight line that he draws through the three points shows his expected distance at different times during the trip.

Click "View" on the left to watch the video. After watching, look at the graph of Harry's prediction on the left and then answer the question below.

Harry predicts that if he can cycle 5 miles in 1 hour, he can travel 20 miles in 4 hours. What do you think might be a problem with this prediction? Do you think that Harry can travel at the same speed for 4 straight hours? Why or why not? Write your answer in two to three sentences.

When you travel, your trip can take longer (or shorter) than you expected. For example, you might get stuck in traffic, stop for a snack, or find a shortcut.

Click “View” on the left to watch the beginning of Harry’s trip. After watching, keep reading below and answer the question.

In distance–time graphs, people often talk about the steepness of a line. A line gets steeper as it becomes more vertical. The steeper the line, the more quickly a person (or car, or bike) is traveling. Now look at the graph of the first part of Harry's trip on the left and then continue reading below.

Harry travels 8 miles in his first hour of riding. He shows his progress by placing a point that lines up with 8 miles on the distance axis and 1 hour on the time axis on his graph, and then he draws a red line from the origin to the point. The red line (his actual travel) is steeper than the blue line (his predicted travel), which means he went farther than expected in the first hour.

Notice that the point he adds to the graph is above the point he used to mark where he predicted he would be. This causes Harry to say, "I'm ahead of schedule!"

If Harry continues at this pace, do you think he will arrive at his grandmother’s house earlier, later, or at the expected time? Explain your answer in one to two sentences.

In the next part of the trip, Harry spends a lot of time talking on the phone, sitting down, and buying things at the store. When he checks his distance at the end of 3 hours, he finds he has traveled only a total of 10 miles.

Click "View" on the left to watch what happens during the second part of Harry’s trip. After watching, look to see the graph of the second part of Harry's trip on the left and then keep reading below.

The section between hours 0 and 1 is steeper than the section between hours 1 and 3. This means that after a fast start, Harry slowed down.

You can also look at the points on the graph to see how quickly he traveled. In the first hour, he cycled 8 miles. In the next 2 hours, he cycled only 2 miles. No wonder he says, “I’m 5 miles behind where I want to be!” at the 3-hour mark!

How does Harry realize he is 5 miles behind schedule? Use the graph to help you explain why he feels he is 5 miles behind. Explain your answer in two to three sentences.

Click “View” on the left to watch this video and see how Harry finished his trip. After watching, look at the graph of Harry's entire trip on the left and then keep reading below.

Harry arrives at his grandmother’s house at 4:00. The sections of the red line (his actual trip) that are above the blue line (his predicted trip) show when he is ahead of schedule. If the red sections are underneath the blue line, then he is behind schedule.

As you can see, the red line is steepest at the beginning and end of his trip. Describe Harry’s whole trip, making sure to explain what the steepness of the red line means at different points along his ride. Explain your answer in two to four sentences by using information from the graph.

The videos you have seen and the text you have read have helped you learn how to interpret distance–time graphs.

Now show what you have learned so far by answering these three questions. Be sure to save all your answers before you go to the next screen.

A distance–time graph can show you who is winning (or losing) a race at any point in time. Now read this passage to see how such a graph can tell the story of a whole race.

Click "View" on the left to begin the passage.

After you have finished reading the passage, answer this question in two to three sentences: During which section of the triathlon—swimming, biking, or running—were the racers going the fastest? How do you know? Use the idea of "steepness" in your answer.

You will now check your understanding of the vocabulary words for this lesson by placing them in sentences. Click "View" on the left to begin the activity.

Before moving to the next screen, choose two words from the vocabulary list and write a new sentence for each word.

Vocabulary words: axis, graph, horizontal, origin, steepness, vertical

Lilly wants to visit her friend. The trip usually takes about 30 minutes if Lilly walks, but today she decides to take her bike instead.

In this activity, you will see the distance–time graph of Lilly's trip, which includes two lines. A blue line shows her usual trip on foot, and a red line is the actual graph of her trip on a bike. You will now drag labels onto the red line to show what happened during Lilly's bike trip and compare it to her usual trip on foot. Click "View" on the left to begin the activity.

Then, before moving on to the final assignment, you may want to watch this lesson's videos again or reread the passage.

Using Points to Measure

Video: 0m 55s

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A Fast Start

Video: 0m 38s

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Slowing Down

Video: 0m 25s

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Looking at the Whole Trip

Video: 1m 24s

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Ahead or Behind?

Document

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In this lesson, you have learned how to express a distance–time relationship on a graph. You will now write an essay that explains what you have learned.

Begin by reviewing your notes. Click "review my work" above and view or print out the screen that pops up.

Final Assignment Instructions

• Click Graphing Distance and Time: Travel—Final Assignment (PDF).
• Choose one of the topics in the PDF and write an essay.
• Organize your response so that it includes at least three supporting details that you have learned from the reading passage, video(s), and other materials in this lesson.
• Use at least three vocabulary words (or a form of the words) as part of your supporting details. For example, for the word jump, you could use jumps, jumped, or jumping.