Lesson 21

Percentages and Tape Diagrams

Let's use tape diagrams to understand percentages.

21.1: Notice and Wonder: Tape Diagrams

What do you notice? What do you wonder?

Two equivalent diagrams. The top diagram solid orange, labeled 80. Bottom diagram partitioned into 4 parts. Three parts are blue and together labeled question mark %. The fourth part is white.

 

21.2: Revisiting Jada's Puppy

Jada has a new puppy that weighs 9 pounds. It is now at about 20% of its adult weight.

  1. Here is a diagram that Jada drew about the weight of her puppy.

    Tape diagram with five parts, each part 9. One part colored blue and indicated 20%.

    1. The adult weight of the puppy will be 45 pounds. How can you see that in the diagram?

    2. What fraction of its adult weight is the puppy now? How can you see that in the diagram?

  2. Jada’s friend has a dog that weighs 90 pounds. Here is a diagram Jada drew that represents the weight of her friend’s dog and the weight of her puppy.

    Tape diagrams. Top diagram, 10 parts each labeled 9. Bottom diagram, one box labeled 9.
    1. How many times greater is the dog’s weight than the puppy’s?
    2. Compare the weight of the puppy and the dog using fractions.
    3. Compare the weight of the puppy and the dog using percentages.

21.3: 5 Dollars

Noah has $5.

    1. Elena has 40% as much as Noah. How much does Elena have?
    2. Compare Elena’s and Noah’s money using fractions. Draw a diagram to illustrate.
    1. Diego has 150% as much as Noah. How much does Diego have?

    2. Compare Diego’s and Noah’s money using fractions. Draw a diagram to illustrate.

21.4: Staying Hydrated

During the first part of a hike, Andre drank 1.5 liters of the water he brought.

  1. If this is 50% of the water he brought, how much water did he bring?
  2. If he drank 80% of his water on his entire hike, how much did he drink?


Decide if each scenario is possible.

  1. Andre plans to bring his dog on his next hike, along with 150% as much water as he brought on this hike.
  2. Andre plans to drink 150% of the water he brought on his hike.

Summary

Tape diagrams can help us make sense of percentages.

Consider two problems that we solved earlier using double number lines and tables: “What is 30% of 50 pounds?” and “What is 100% of a number if 140% of it is 28?”

Here is a tape diagram that shows that 30% of 50 pounds is 15 pounds.

A tape diagram divided into 10 parts, each labeled 5. The entire diagram is labeled 100 %. The first part is labeled 10 %. The first three parts are colored orange, the rest are colored white.

This diagram shows that if 140% of some number is 28, then that number must be 20.

A tape diagram with seven parts, each labeled 4. The first part is labeled 20%. Five parts are together labeled 100%.

Glossary Entries

  • percent

    The word percent means “for each 100.” The symbol for percent is %.

    For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.

    A quarter (coin)
    A diagram of two bars with different lengths.
  • percentage

    A percentage is a rate per 100.

    For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.

    a double number line