Lesson 22Benchmark Percentages

Learning Goal

Let’s contrast percentages and fractions.

Learning Targets

  • When I read or hear that something is 10%, 25%, 50%, or 75% of an amount, I know what fraction of that amount they are referring to.

Lesson Terms

  • percent
  • percentage

Warm Up: What Percentage Is Shaded?

Problem 1

What percentage of each diagram is shaded?

  1. tape diagram broken into ten parts with one part shaded.
  2. tape diagram divided into two parts with one part shaded.
  3. tape diagram divided into four parts with three parts shaded.

Activity 1: Liters, Meters, and Hours

A tape diagram showing a segment labeled "10", a similar size segment below it labeled "2,000". A third row with a similar segment divided in half labeled "?" It is shown as 50%

Problem 1

  1. How much is 50% of 10 liters of milk?

  2. How far is 50% of a 2,000-kilometer trip?

  3. How long is 50% of a 24-hour day?

  4. How can you find 50% of any number?

Problem 2

  1. How far is 10% of a 2,000-kilometer trip?

  2. How much is 10% of 10 liters of milk?

  3. How long is 10% of a 24-hour day?

  4. How can you find 10% of any number?

Problem 3

  1. How long is 75% of a 24-hour day?

  2. How far is 75% of a 2,000-kilometer trip?

  3. How much is 75% of 10 liters of milk?

  4. How can you find 75% of any number?

Activity 2: Nine Is …

Problem 1

Explain how you can calculate each value mentally.

A tape diagram with 2 segments with the first segment marked as 9 and labeled as 50%. The entire diagram is labeled with a "?"

  1. 9 is 50% of what number?

  2. 9 is 25% of what number?

  3. 9 is 10% of what number?

  4. 9 is 75% of what number?

  5. 9 is 150% of what number?

Activity 3: Matching the Percentage

Problem 1

Match the percentage that describes the relationship between each pair of numbers. One percentage will be left over. Be prepared to explain your reasoning.

  1. 7 is what percentage of 14?

  2. 5 is what percentage of 20?

  3. 3 is what percentage of 30?

  4. 6 is what percentage of 8?

  5. 20 is what percentage of 5?

  1. 4%

  2. 10%

  3. 25%

  4. 50%

  5. 75%

  6. 400%

Are you ready for more?

Problem 1

  1. What percentage of the world’s current population is under the age of 14?

  2. How many people is that?

  3. How many people are 14 or older?

Lesson Summary

Certain percentages are easy to think about in terms of fractions.

A double number line with 5 evenly spaced tick marks. The tick marks on the top number line are labeled 0, one fourth times x, one half times x, three fourths times x, and x. The tick marks on the bottom number line are labeled 0 percent, 25 percent, 50 percent, 75 percent, and 100 percent.

  • 25% of a number is always of that number.
    For example, 25% of 40 liters is or 10 liters.

  • 50% of a number is always of that number.
    For example, 50% of 82 kilometers or 41 kilometers.

  • 75% of a number is always of that number.
    For example, 75% of 1 pound is pound.

  • 10% of a number is always of that number.
    For example, 10% of 95 meters is 9.5 meters.

  • We can also find multiples of 10% using tenths.
    For example, 70% of a number is always of that number, so 70% of 30 days is or 21 days.

A double number line with 11 evenly spaced tick marks. For the top number line the number 0 is on the first tick mark, one tenth times x on the second, seven tenths times x on the eigthth, and x on the eleventh. The remaining tick marks are blank. On the bottom number line starting from the first tick mark, zero percent, 10 percent, 20 percent, 30 percent, 40 percent, 50 percent, 60 percent, 70 percent, 80 percent, 90 percent, and 100 percent are labeled.