Using Rates To Solve Problems

Using Rates To Solve Problems

Revise and Extend Your Work

Opening

Revise and Extend Your Work

Work with your partner to revise your work on the Self Check.

  • Explain what calculation the person can perform to find what he or she wants to know.
  • Explain what the unit of the answer is.
  1. At the store, Jason sees that the price of cherries is $3.00 per pound. What calculation can he perform to find the price of 5.75 pounds of cherries?
  2. Rosa knows that she can skate to the park in 1.5 hours. The park is 12 miles away. What calculation can she perform to find her speed?
  3. Denzel knows that 1 quart of paint will cover about 85 square feet of wall. He needs enough paint to cover 325 square feet of wall. What calculation can Denzel perform to find how many quarts of paint he will need?
  4. Mina ran a half marathon (13.1 miles) this weekend. She completed the run in 2.6 hours. What calculation can Mina perform to find her speed during this run?

Math Mission

Opening

Use what you know about rates to work through problems.

Distance, Time, and Speed

Work Time

Distance, Time, and Speed

In this problem, you will work with three quantities: distance, time, and speed.

Create a set of three numbers that shows the relationship among the quantities. For instance, if you chose a time of 3 hours and a speed of 25 miles per hour, the distance would be 75 miles.

  • Create your sets of three numbers in three different ways:
    • The first set contains any numbers.
    • The second set contains numbers greater than 10.
    • The third set contains decimal numbers.

INTERACTIVE: Distance, Time, and Speed

Price per Gallon

Work Time

Price per Gallon

In this problem, you will work with three quantities: gallons, total price, and price per gallon.

Create a set of three numbers that shows the relationship among the quantities.

  • Create your sets of three numbers in three different ways:
    • The first set contains any numbers.
    • The second set contains numbers greater than 10.
    • The third set contains decimal numbers.

INTERACTIVE: Price per Gallon

Dollars and Pesos

Work Time

Dollars and Pesos

In this problem, you will work with three quantities: dollars, pesos, and dollars per peso.

Create a set of three numbers that show the relationship among the quantities.

  • Create your sets of three numbers in three different ways:
    • The first set contains any numbers.
    • The second set contains numbers greater than 10.
    • The third set contains decimal numbers.

INTERACTIVE: Dollars and Pesos

Hours, Speed, and Miles

Work Time

Hours, Speed, and Miles

In this problem, you will work with three quantities: hours, speed, and miles.

Create a set of three numbers that show the relationship among the quantities.

  • Create your sets of three numbers in three different ways:
    • The first set contains any numbers.
    • The second set contains numbers greater than 10.
    • The third set contains decimal numbers.

Stack of Books

Work Time

Stack of Books

In this problem, you will work with three quantities: the number of books in a stack, the height of the stack, and the thickness of each book (inches per book).

Create a set of three numbers that show the relationship among the quantities.

  • Create your sets of three numbers in three different ways:
    • The first set contains any numbers.
    • The second set contains numbers greater than 10.
    • The third set contains decimal numbers.

INTERACTIVE: Stack of Books

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation of your work.

  • The runner runs at a constant speed.
    • Does the table support this statement?
    • Complete the table.
    • Express the speed of the runner in kilometers per hour.

INTERACTIVE: Prepare a Presentation

Make Connections

Performance Task

Ways of Thinking: Make Connections

As you listen to other students present their work, find ways to understand how to think about rate.

Hint:

As your classmates present, ask questions such as:

  • Where is the rate in your numbers?
  • Where do you see the other two quantities?
  • How would you describe the relationship among the three numbers?

Reflect On Your Work

Work Time

Reflection

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

Something I still wonder about rates is …