Calculating The Unit Rate of A Ratio Situation

Calculating The Unit Rate of A Ratio Situation

Participate in Mathematical Discussions

Opening

Participate in Mathematical Discussions

Listening actively and asking questions during discussions are as important as the presentations.

To create a good math community, you should:

  • Focus on learning, not getting the answer right.
  • Help each other learn.
  • Be responsible for your own learning.

View the Hints during Ways of Thinking to read questions you can ask the presenter. Pick one or ask your own question.

Discuss the following with your classmates.

  • What can you as a listener contribute to improve your classroom math community?

Hint:

Here are ways listeners contribute to math discussions:

  • Clarify—Tell the presenter when you do not understand.
    “I did not understand. What do you mean by …?”
  • Critique—Challenge reasoning that is flawed.
    “How do you know that …?”
  • Connect—Explore how different strategies result in the same answer.
    “What you said is like … “
  • Compare—Describe similarities and differences.
    “Is that different from …?”
  • Notice Structure—Ask whether a conclusion is always, sometimes, or never true.
    “Is your conclusion always true for …?”

Rate Situations

Opening

Rate Situations

Discuss the following with your classmates.

In what types of situations would you see these rates?

  • Beats per minute
  • Dollars per kilogram
  • Gallons per hour

Math Mission

Opening

Explain how to calculate rates.

Cost of Groceries

Work Time

Cost of Groceries

Copy the top image.

  • Write a rate for the unit cost of each ingredient: 1 lb of potatoes, 1 can of tomatoes, 1 lb of carrots, 1 lb of celery, and 1 lb of dried beans.
  • The ingredients are used to make a stew that serves 12 people. What is the cost of each ingredient per serving? What does the stew cost per serving?
  • It is important you express your rates with a measurement unit? Explain why.

Hint:

  • What do you divide to find the unit cost of each ingredient?
  • What do you divide to find the rates per serving?
  • What is the measurement unit for each rate?
  • Are your quantities in the correct order?

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain how you calculated the rates.
  • Explain why it is important to use measurement units with your rates.
  • Identify any mistakes you made and what you learned from them.
  • Describe what you found most difficult about calculating rates.

Challenge Problem

Karen ran for 46 min. At the end of 45 min, her total distance was 3.75 mi. At the end of 46 min, her total distance was 3.85 mi.

  • Compare Karen’s average speed during the last minute of her run to her average speed during the first 45 min.
  • Did Karen run the last minute faster, slower, or at the same speed? Justify your answer mathematically.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about how your classmates’ strategies for calculating rates are similar to and different from yours.

Hint:

As your classmates present, ask questions such as:

  • What did you find most difficult?
  • What was the difference between finding the unit cost and finding the cost of each ingredient per serving?
  • Which ingredient was the most expensive? Least expensive?

Explain Rates

Formative Assessment

Summary of the Math: Explain Rates

Write a summary that explains what a rate is and why it always has a measurement unit.

Hint:

Check your summary.

  • Do you define rate?
  • Do you explain how to calculate a rate?
  • Do you explain why measurement units are important for rates?

Reflect On Your Work

Work Time

Reflection

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

Rates are related to ratios because…