Students recognize a variety of expressions to differentiate between number and percentage, such as:

• Percentage, rate, relative amount
• Number, amount, absolute amount

Students turn ratios (fractions) into percentages, and percentages into ratios.  They have memorized common relationships between ratios and percentages, such as:

• 4/5 = 80%
  
• 3/4 = 75%
  
• 2/3 = about 67%
  
• 1/2 = 50%
• 2/5 = 40%
  
• 1/3 = about 33%
• 1/4 = 25%
• 1/5 = 20%
• 1/6 = about 17%
  

Students recognize that size feels quite different depending on whether they are estimating the absolute number or the percentage.

Students multiply fractions.

Change

Students calculate absolute change using subtraction.

Students calculate percent change using subtraction and division.

Students calculate a change in percentage points using subtraction.

Students recognize that each of these measures is important to a full picture of change over time.  Here's an example of how to use all three:

The population of France increased between 1960 and 2010 from 46.65 million to 65.03 million.  That's an increase of 18.38 million people, or 39.4 percent.  But as a percentage of the world population, the population of France decreased from 1.54 percent to .95 percent, a decrease of over half a percentage point.

Questions

If I earn a 75% on my first test, and the test is worth 30% of the course, can I still get an A in the course?

In 2012, 46.5 million people in the United States lived in poverty.  Approximately what percentage of people in the United States lived in poverty?  That is one out of how many people?

If there was an average mortality rate of 12% in the transatlantic slave trade and 12.5 million Africans began the journey from Africa to the Americas, about how many survived?

What is the difference between “50% of men immigrated to find a better job” and “50% of all immigrants who sought a better job were men”?

Is it more effective to increase car A’s gas mileage from 10 to 20 mpg, or car B’s gas mileage from 40 to 50 mpg?  Answer!

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