Fundamental Problem Solving Concepts

Fundamental Problem Solving Concepts

Lightning and Thunder Video

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Lightning and Thunder Video

Watch the video.

  • Estimate how many miles away the lightning is.
  • What would you have to know to find out how far away the lightning is?

VIDEO: Lightning and Thunder

Math Mission

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Analyze the following problem: "How many miles away is the lightning?"

Represent the Situation

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Represent the Situation

The next step in analyzing the problem is to represent the situation. One approach is to first try to represent the situation using easy numbers.

  • How far away is the lightning if there are 5 seconds between the lightning and the sound of the thunder?
  • How far away is the lightning if there are 10 seconds between the lightning and the sound of the thunder?

Understand the Situation

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Understand the Situation

Do you remember the last time you watched the sky glow with streaks of lightning and listened to the resonating claps of thunder? You may have wondered how far away the lightning was from where you stood.

There is a simple rule that says: "The distance of lightning in miles is the time in seconds between the appearance of the lightning and the sound of the thunder, divided by 5." Watch the video again to count the seconds between the lightning and thunder.

To analyze this problem of how far away the lightning is, you need to start by understanding the situation. Think about these questions:

  • What does the rule tell you about the type of problems you will be solving?
  • What information does this rule provide?
  • What are the quantities that vary (that is, what are the variables)?
  • How are these variables related?
  • Which variable is the dependent variable and which is the independent variable?

VIDEO: Lightning and Thunder

Hint:

A quantity is an amount that can be measured. What can you measure in this situation?

Represent the Situation Mathematically

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Represent the Situation Mathematically

Now that you have used some easy numbers to represent the situation, it's important to make a general representation of the situation that will work for any numbers.

  • Make a ratio table showing the relationship between time and distance.
  • How could you use your completed ratio table to make a graph?
  • Write a formula that shows the relationship between time and distance.
  • Make a graph of this formula. How would you label the x-axis (independent variable) and the y-axis (dependent variable)?
  • Make a graph of the formula for distances up to 20 miles.

Hint:

Use the pairs of numbers in your ratio table as points on your graph.

Answer Questions about the Situation

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Answer Questions about the Situation

Use your formula and graph to answer this question about the situation.

  • How far away is the lightning if there are 12 seconds between the lightning and the sound of the thunder?

Hint:

  • Make sure you answer the question in the problem.
  • Give your solution as a complete sentence.

Check That Your Answer Makes Sense

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Check That Your Answer Makes Sense

Think about the last time you observed lightning and thunder. Then look back at your answer to the question about how far away the lightning is when the time between the lightning and thunder is 12 seconds.

  • Does your answer make sense based on your observations?

Hint:

Replay the video to see whether your answer also makes sense for the situation in the video.

A Different Question

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A Different Question

Here is a different question about the same situation.

  • If lightning is 7 miles away, what is the time between the lightning and the sound of the thunder?

Hint:

  • Can you use your ratio table to help you solve this problem?
  • Is the ratio for this problem the same as the ratio in your table?

Prepare a Presentation

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Prepare a Presentation

In this lesson, you went through a problem-solving process:

  • Understand the Situation
  • Represent the Situation
  • Answer Questions about the Situation
  • Check That Your Answer(s) Makes Sense

How did following that process help you solve any problems about how far away the lightning is in miles?

Support your explanation with examples from your work.

 

Challenge Problem

Light travels at a speed of approximately 180,000 miles per second. Thus, you see lightning almost instantaneously after it strikes.

However, sound travels more slowly, which is why you hear thunder only after you have already seen the lightning (generally—it’s possible that you might sometimes hear thunder without having seen any lightning). The differences in the speed of light and the speed of sound account for this occurrence. The greater the distance of the lightning, the greater the delay between the appearance of the lightning and the sound of the thunder.

  • What is the speed of sound?


Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes about the strategies and tools that your classmates discuss in their presentations.
  • As you listen to the presentations, think about the ways that each classmate used the steps of the problem-solving process. Which step(s) do you think were the most helpful for each individual in solving the problem?

Hint:

As your classmates present, ask questions such as:

  • Can you explain how you made your graph?
  • How did you decide which measurement units to use for time and distance?
  • How did you know your answer was reasonable?
  • What tool did you find to be the most helpful for solving the problem? Why?
  • What did you do to understand the situation?
  • Did you have any errors in your thinking? If so, what were they and how did you correct them?
  • How does knowing the time relationship between lightning and thunder help you calculate the distance of lightning from you?
  • What mathematical strategies are the most useful in solving a problem in which you are given a relationship between variables and are asked to make predictions?

Reflect On Your Work

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Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

When I think about lightning and thunder, I see these connections …