Finding Percents

Finding Percents

Introduction to Percent

Opening

Introduction to Percent

Discuss:

  • Most of the relationships you have looked at in this unit are part-part relationships.
    • For example, 60 students like action movies, and 40 students do not like action movies. The quantity 60 is one part, and the quantity 40 is the other part.
  • You can think about this situation in another way.
    • You can say that out of 100 students, 60 students like action movies. You can also say that out of 100 students, 40 students don't like action movies.
      In this way of expressing the relationships between the quantities, 60 and 40 are parts and 100 is the whole.

More About Percent

Opening

More About Percent

If there are 100 students and 60 of them like action movies:

  • You can say that 60100 or 610 or 35 of the students like action movies.
  • You can say that 0.60 or 0.6 of the students like action movies.
  • You can say that 60% (percent) of the students like action movies.

The percent symbol (%), as well as the word percent itself, indicates "per hundred" or "out of a hundred." (You can remember that cent means 100 because it takes 100 cents to make 1 dollar.) Thus, 60% means "60 per hundred" or "60 out of one hundred."

  • Using a 10x10 grid, and fill in 60% of the squares to represent the students who like action movies.
  • Write an equation that you could use to find 60% of a number.

Math Mission

Opening

Find percents of a given whole, and find a whole given a part and a percent.

How Much Is in the Bag?

Work Time

How Much Is in the Bag?

  • The label on the bag tells you how much money is in the bag. Take turns finding how much money is indicated by the given percentage.
  • Your partner should agree with your answer or challenge it if your explanation is not clear, correct, and complete. When you agree on an answer, enter it in the appropiate blank on the diagram.
  • Continue until you have filled in all the blanks.
  • What is 10% of the number on the bag?
  • Fill that number in the "10% is" box.

Find Percents and Whole Amounts

Work Time

Find Percents and Whole Amounts

In this diagram you are given a value that is 75% of the amount of money in the bag.

  • Find the amount of money that is in the bag, and enter the value in the 100% box.
  • Take turns finding how much money is indicated by the given percentage.
  • Your partner should agree with your answer or challenge it. When you agree on an answer, enter it in the appropriate blank on the diagram.
  • Continue until you have filled in all the blanks.

Ask yourself:

  • Find the value in the bag first.
  • Remember the given number is 75% of the value in the bag.

Jan’s and Martin’s Ideas

Work Time

Jan's and Martin's Ideas

  • Jan said that the same percent can represent different quantities. Is she correct? Explain.
  • Martin said that a single quantity can be represented by different percents. Is he correct? Explain.

Ask yourself:

  • When considering Jan’s statement, think about 50% of two different “wholes."
  • When considering Martin’s statement, think about this situation: you have $100 and your friend has $20, and each of you contributes $10 to your school library fundraiser.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain the strategy you used to find the percent of a given number. Provide an example.
  • Explain the strategy you used to find the whole when given a part and the percent. Provide an example.
  • Be prepared to present and justify your explanation about why Jan and Martin are either right or wrong.

Challenge Problem

  • What is 10% of 0.1?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the different approaches your classmates used to find percents and whole amounts.

As your classmates present, ask questions such as:

  • Do your strategies make use of any patterns? Can you explain the pattern?
  • Why did you use that operation to find the missing number?
  • Did you check that your answers make sense? If so, how?
  • Was it helpful for you to think of the decimal in the Challenge Problem as a monetary value?

Overview of Percent

Formative Assessment

Summary of the Math: Overview of Percent

Read and Discuss

  • A ratio of a number to the special denominator 100 is called a percent. Percent means "per hundred." The symbol for percent is %.
  • For example, if 6 teachers and 44 students went on a field trip, then there were 50 people on the field trip in all. The ratio of teachers to all of the people on the trip is 6:50 or 12:100.

teacherspeople on the field trip=650=12100

 

Therefore, 12% of the people on the trip were teachers.

Can you:

  • Explain what percent means?
  • Find the percent of a number?
  • Find the whole, given a part and the percent?

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.

Some connections that I see between decimals and percents are …