Lesson 12
Percentages and Tape Diagrams
Let's use tape diagrams to understand percentages.
12.1: Notice and Wonder: Tape Diagrams
What do you notice? What do you wonder?
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12.2: Revisiting Jada's Puppy
Jada has a new puppy that weighs 9 pounds. It is now at about 20% of its adult weight.
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Here is a diagram that Jada drew about the weight of her puppy.
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The adult weight of the puppy will be 45 pounds. How can you see that in the diagram?
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What fraction of its adult weight is the puppy now? How can you see that in the diagram?
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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.
- How many times greater is the dog’s weight than the puppy’s?
- Compare the weight of the puppy and the dog using fractions.
- Compare the weight of the puppy and the dog using percentages.
12.3: 5 Dollars
Noah has $5.
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- Elena has 40% as much as Noah. How much does Elena have?
- Compare Elena’s and Noah’s money using fractions. Draw a diagram to illustrate.
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- Diego has 150% as much as Noah. How much does Diego have?
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Compare Diego’s and Noah’s money using fractions. Draw a diagram to illustrate.
12.4: Staying Hydrated
During the first part of a hike, Andre drank 1.5 liters of the water he brought.
- If this is 50% of the water he brought, how much water did he bring?
- If he drank 80% of his water on his entire hike, how much did he drink?
Decide if each scenario is possible.
- Andre plans to bring his dog on his next hike, along with 150% as much water as he brought on this hike.
- 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.

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

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.
- 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%.