Units Resulting From Rate Calculations

Units Resulting From Rate Calculations

What Do the Numbers Mean?

Opening

What Do the Numbers Mean?

You can get a new unit by dividing two other units. In fact, that is what defines a rate. For instance, if you divide 10 meters by 2 seconds, you get 5 meterssecond. The new unit is “meters per second.”

When multiplying and dividing units, you can cancel them out as shown here.

inches · centimetersinches= centimeters12 in. · 2.54 cmin.= 30.48 cm

 

  • Discuss with your partner why units cancel out.
  • What would be the correct unit for this equation?

30.48 cm • 0.3937incm = 12 ___

Math Mission

Opening

Accurately place units and show how units are changed when multiplied or divided.

Focus On the Units

Work Time

Focus On the Units

Watch the video. Then read the problem below.

Emma has been running laps around the track. (A lap is a quarter mile.) Her coach recorded how many minutes she ran. After Emma’s run, her coach wrote these calculations on his clipboard:

30 ÷ 15 = 2 and 15 ÷ 30 = 0.5

The coach forgot to include the units with his calculations.

  • Determine what the numbers mean. Explain your thinking.

VIDEO: Emma Running

Hint:

  • What two units were mentioned in the video?
  • What is the relationship between those units?
  • Which of those units goes with the larger number (30)?

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation that explains your reasoning in finding the units. Which rate do you think the coach might use and when?

 

Challenge Problem

Write an explanation about how to determine which units to use in the answer to a rate problem. Consider the unit of the quotient when you are dividing to find a rate and the unit of a product when you are using a rate.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about other students’ presentations. Make sure you are able to understand each solution in terms of the units rather than just the numbers.

Hint:

As students present, ask questions such as:

  • Where do you see the number of laps, the time, and the speed in your solution to the problem about Emma?
  • Why couldn’t you change the numbers for laps and time?
  • How did you make sense of Emma’s situation?

Working With Units

Work Time

Working With Units

Understanding what the units mean when you find a rate or use a rate is just as important as calculating correctly.

Write the appropriate unit for each statement.

  1. Divide a quantity in minutes by a quantity in laps.
  2. Divide a quantity in beats by a quantity in minutes.
  3. Divide a quantity in miles by a quantity in hours.
  4. Multiply the answer from (c) by a quantity in hours.

Hint:

  • When you divide to find a rate, the unit of the quotient is expressed in the form A per B .
  • Think of 30 minutes ÷ 5 laps. What would the unit in the answer be?

Units of Rates

Formative Assessment

Summary of the Math: Units of Rates

Summarize what you have learned about rate problems by concentrating on the units.

Hint:

Check your summary

  • Does your summary explain how to express the unit of the quotient when dividing to find a rate?
  • Does your summary explain how to express the unit of the product when multiplying by a rate?

Check Your Knowledge of Rates

Formative Assessment

Check Your Knowledge of Rates

Now take some time to check how much you know about rates. For these problems, do not calculate the exact answers. Instead, do the following for each problem:

  • 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?

Hint:

Make sure you write the unit of the answer.

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 and units is …