Percentages

Percent of Increase and Percent of Decrease

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Objective Students will solve percent of increase and decrease word problems by writing a percent expression, changing the expression to a fraction, and changing the fraction to a percent.

CA State Standard: NS 7.1.6 Calculate the percentage of increases and decreases of a quantity. 2

Purpose • • • •

Proficiency on CA State Standard: Gr. 7 Number Sense 1.6 CAHSEE prep Tests and quizzes A look at some post secondary career opportunities at the Port of Long Beach

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Every year thousands of cars are brought into the Port of Long Beach from overseas for sale in the United States. They are literally “parked” in the ship for the ride here.

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Every year thousands of cars are brought into the Port of Long Beach from overseas for sale in the United States. They are literally “parked” in the ship for the ride here. After arrival, the cars are driven off the ship. 6

In 2005, approximately 328,000 cars were brought into the Port of Long Beach. In 2006, approximately 426,000 were brought in. What was the percent of increase in the amount of cars from 2005 to 2006? 8

How does one answer this question?

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How does one answer this question?

First, let’s review percents by using containers of goods that are unloaded from ships at the port.

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How does one answer this question?

Remember - 1 container out of 5 means:

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or

or

or

1 5

also

1 5

.2 = 5 1.0 = 20%

similarly

similarly

2 5

.4 = 5 2.0

= 40%

which is the same as

2 is what % of 5? .4 2 = 5 2.0 = 40%

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Back to our question:

What was the percent of increase in the amount of cars brought into the Port of Long Beach from 2005 to 2006?

Or, the increase in cars is what % of the original amount of cars? 19

Remember:

In 2005, approximately 328,000 cars were brought into the Port of Long Beach. In 2006, approximately 426,000 were brought in.

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2005: 328,000 cars 2006: 426,000 cars

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What is the increase in cars? What is the original amount?

increase:

426,000 - 328,000 = 98,000

original amount:

328,000

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The increase in cars is what % of the original amount of cars? 98,000 is what % of 328,000 ? 98,000 328,000

≈ .298 ≈ 30%

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Check for Understanding On the count of three, call out the correct letter to the following question: When finding the percent of increase, the denominator of the fraction neededamount is the A) Original C) Original amount D) New amount E) Amount calculated from subtracting 23

Imports and exports continue to grow in the Port of Long Beach. In 2004, the Port moved more than 5.8 million twenty-foot container units (TEUs).

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one TEU

Imports and exports continue to grow in the Port of Long Beach. In 2004, the Port moved more than 5.8 million twenty-foot container units (TEUs). In 2005, the Port moved more than 6.7 million TEUs. What was the percent of increase? 26

2004: 5.8 million TEUs 2005: 6.7 million TEUs

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What is the increase in TEUs? What is the original amount?

increase:

6.7 – 5.8 = 0.9

original amount:

5.8

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The increase in TEUs is what % of the original amount of TEUs? 0.9 is what % of 5.8 ? 0.9 5.8

≈ .155 ≈ 16%

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Check for Understanding On the count of three, call out the correct letter to the following question: When finding the amount of increase, the new amount is added to the original amount C) True D) False B) False - it is subtracted from 29

Guided Practice From 2004 to 2005, the Port saw more “calls,” ships that docked at the Port, by the newest generation of ships: a megaship which holds 8,000 TEUs.

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Guided Practice From 2004 to 2005, the Port saw more “calls” by the newest generation of ships: a mega-ship which holds 8,000 TEUs. In 2004, the Port container count was approximately 2.94 million TEUs. In 2005, the count was approximately 3.3 million TEUs. What was the percent of increase in the overall inbound containers? 32

Guided Practice 2004 – 2.94 million TEUs 2005 – 3.3 million TEUs Work the problem in your notes, then write the answer on your white board. Wait for the count of three, before holding up your board.

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Guided Practice

1. 3.3 – 2.94 = 0.36 2. 0.36 is what % of 2.94 ? 3. 0.36/2.94 4. Divide 2.94 into 0.36 5. 12% 34

The Port of Long Beach is committed to improving the environment.

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Cargo-handling equipment as seen here…

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Cargo-handling equipment as seen here… has been part of the emissions reduction program at the Port. The amount of NOx (nitrogen oxide) emissions went from approximately 36 grams/ton of cargo in 2002 to 21 grams/ton in 2005. What is the percent of decrease? 37

2002: 36 grams/ton 2005: 21 grams/ton

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What is the decrease in tons? What is the original amount?

decrease:

36 - 21 = 15

original amount:

36

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The decrease in tons is what % of the original amount of tons? 15 is what % of 36 ? 15 36

≈ .416 ≈ 42%

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Check for Understanding TELL YOUR NEIGHBOR A’s tell B’s: How is finding the percent of decrease different than finding the percent of increase? B’s tell A’s: How is finding the percent of decrease similar to finding the percent of increase?

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The Port of Long Beach monitors the daily Air Quality Index (AQI). AQI tells how clean or polluted the air is. Five major air pollutants regulated by the Clean Air Act are calculated: 1) ground-level ozone 2) particle pollution (also know as particle matter) 3) carbon monoxide 4) sulfur oxide 5) nitrogen dioxide 41

This chart was shown on the Port’s web site on Thursday, August 2, 2007

http://polb.airsis.com/SummaryYesterday.aspx

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AQI Highs for Thursday, August 2, 2007

http://polb.airsis.com/SummaryYesterday.aspx

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The information is collected every hour.

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Find the percent of decrease from 12:00 A.M. to 9:00 A.M.

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Guided Practice 12:00 A.M. – 0.023 ppm 9:00 A.M. – 0.005 ppm Work the problem in your notes, then write the answer on your white board. Wait for the count of three, before holding up your board.

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Guided Practice

1. 0.023 – 0.005 = 0.018 2. 0.018 is what % of 0.023 ? 3. 0.018/0.023 4. Divide 0.018 into 0.023 5. 78% 47

Write in your notes:

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A summary of how to find the percent of increase A summary of how to find the percent of decrease Check your notes with your neighbor and adjust yours if needed

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