Converting with Percents

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Objective

SWBAT convert fractions and decimals to percents.

Big Idea

Students work with percents.

Do Now

10 minutes
Students previously worked on converting between fractions and decimals.  The Do Now is a review of this concept, applying it to word problems, and comparing amounts.
Do Now

1)  Last week, Jamal gave away 2/5 of his baseball cards.  This week he gave away 0.38 of his cards.  Which week did he give away more of his cards?
2)  Tia read .46 of the book assigned for class.  Kiana read 38 out of the 70 pages.  Who read more of the book?
After about 5 minutes, I will encourage students to discuss their strategy and answer with their group.  This is important because students may have chosen different strategies.  For example, for problem 1, one student may have chosen to change 2/5 to a decimal and compare the quantities, while another student may have changed 0.38 to a fraction.  Students should realize that regardless of the strategy the answer will be the same. 

Mini Lesson

15 minutes

Students will develop algorithms for converting between fractions, decimals and percents.  

What is a percent?  If you earned a 90% on a test, what does this mean?

Students should understand that percents are "out of 100", so a 90% would mean they earned a 90 out of 100.

I will give students a formal definition of percents.

Percent - a ratio of a part of a whole divided into hundredths to 100

This will lead us into changing fractions to percents.

Fractions and Percents

Example 1 - Write 11/20 as a percent

How can we apply the definition of percents and use a proportion to find our answer?

Students should set up a proportion with a denominator of 100 and use their knowledge of equivalent fractions to find the numerator.

Decimals and Percents

Example 2 - Write 5/8 as a percent

Students may notice that although I've mentioned that we will change from decimals to percents, I've given them an example with a fraction.

Can we easily use a proportion to convert 5/8 to a percent?  Why not?

Students should realize that since 8 can not be easily divided into 100, the proportion method will be difficult.

How can we change 5/8 to a decimal? 

Students should use their previous knowledge and convert 5/8 to 0.625.

I will explain that to change the decimal 0.625 to a percent, we need to multiply by 100, giving us 62.5%

We will try another example together.

Example 3 - Write 4/7 as a percent.

What is the better strategy to use for this fraction?

Students should suggest that we change the fraction to a decimal and then multiply the decimal by 100.

Instead of multiplying the decimals by 100, is there a shortcut?

Students may notice that we would arrive at the same answer if we moved the decimal point 2 places to the right.

Group Work

10 minutes

Once students develop the algorithms for converting fractions and decimals to percents, students should be able to develop the algorithms for converting from percents.  I will give students a few examples to discuss with their group and they will develop an appropriate algorithm.

 

Ex. 4 - Write 45% as a fractions 

Ex. 5 - Write 135% as a fraction

Ex. 6 - Write 4% as a decimal

Ex. 7 - Write 175% as a decimal

 

 After 10 minutes, groups will share their algorithms with the class.

Percents to Fractions

Students should realize that since a percent is out of 100, they can write the percent as a ratio with a denominator of 100.  I will remind students that they have to reduce the fraction, if possible.

Percents to Decimals

Students should realize that since the algorithm for changing a decimal to percent was to multiply by 100, then they should perform the inverse operation of dividing by 100.

Is there a shortcut, rather than dividing by 100?

Students should realize that they can move the decimal point two places to the left.

 

Independent Practice

10 minutes

Students will have 10 minutes to work independently on the problems below.  If they should finish early, I will encourage them to try the challenge problems.  After 10 minutes, students will discuss their work and answers with their group.  If students disagree on an answer, they should verify that they've simplified their fractions correctly.

Independent Practice

Write as a fraction.

1)  17%

2)  8%

3)  110%

Write as a decimal.

4)  12%

5)  40%

6)  375%

Challenge:

Write as a fraction.

7)  88% 

8)  940% 

9)  695% 

Write as a decimal.

10)  19994% 

11)  9.2% 

12)  0.81%

Lesson Summary

5 minutes

For a lesson review, I will ask students questions to assess and deepen their understanding of converting between fractions, decimals, and percents.

To change a decimal to a percent, why does the shortcut work?

When performing division to change a fraction to a decimal, how can we eliminate the remainder?

How can something be more than 100%?

I will randomly select students to share their thoughts and answers with the class.