Defining Rate Discussion

Defining Rate Discussion

Using Mathematical Definitions

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Using Mathematical Definitions

Attending to precision is an important mathematical practice. One of the most important parts of attending to precision is developing and using clear definitions. In this lesson, you will write a definition of rate and then apply the definition to see if it is precise enough to be useful.

Think about and use this mathematical practice of attending to precision in this class, in other math classes that you take, and as you use mathematics in your life.

  • Read the conversation.
  • How is the conversation an example of attending to precision?

Math Mission

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Write a precise and usable definition of rate.

Define Rate

Work Time

Define Rate

Think about the different rates you have worked with in previous lessons. Use what you know about rates to write a definition of the term rate.

Hint:

  • What does a rate compare?
  • What word is usually used to express a rate?
  • Does a rate involve subtraction, multiplication, or division?

Identify Rates

Work Time

Identify Rates

Look at the situations cards and sort them into the following categories:

  • Situations that describe rates
  • Situations that do not describe rates
  • Situations in which you are not sure whether or not it describes rates

HANDOUT: Card Sort

Hint:

  • Sort the cards into the appropriate categories.
  • For each situation, explain your thinking to your partner.
  • If a situation describes a rate, check it against your definition.
  • If the situation does not describe a rate or if it is not possible to tell, explain why not.
  • Use your definition of rate to help you decide whether or not each situation describes a rate. If your definition is not helpful, revise your definition.

Define Rate

Work Time

Define Rate

Think about the situations that you categorized as describing a rate. What do these situations have in common?

By identifying things that these situations have in common, you can make your definition of rate more precise.

  • Review your initial definition of rate. Then, using what you have learned from the previous task, refine your definition to make it more precise.

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation about your work.

  • Write your revised definition of rate.
  • Select one situation that you are sure describes a rate, and explain why it fits your definition.
  • Select one situation that you are sure does not describe a rate, and explain why your definition excludes it.
  • Select one situation that you are not sure about to discuss with the class.

Challenge Problem

Read the definition of rate in the Glossary. Then go back and review your solutions with this definition in mind.

  • Would you categorize the situations in the same way?
  • Can you think of any situation that does describe a rate using your definition but does not describe a rate using the Glossary definition?
  • Can you think of any situation that does describe a rate using the Glossary definition but does not describe a rate using your definition?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Share your presentation.

  • Be ready to defend your solutions by using your definition of rate.
  • As other students present, challenge answers that differ from your own by presenting your ideas.

Hint:

As your classmates present, ask questions such as:

  • Why did you put this card in the “describes a rate” category? What makes the situation a rate situation?
  • Why did you put this card in the “does not describe a rate” category? What makes this situation not a rate situation?

A Final Definition of Rate

Formative Assessment

Summary of the Math: A Final Definition of Rate

  • Write a final definition of rate.

Hint:

Check your summary

  • Does your definition provide enough specific information to be useful, but enough general information so that it can be applied to a variety of situations?

Reflect On Your Work

Work Time

Reflection

Reflecting on your work is another way to solidify your understanding of a mathematical concept.

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

What I learned about defining rate is …