Lesson 21Percentages and Tape Diagrams

Learning Goal

Let’s use tape diagrams to understand percentages.

Learning Targets

  • I can use tape diagrams to solve different problems like “What is 40% of 60?” or “60 is 40% of what number?”

Lesson Terms

  • percentage

Warm Up: Notice and Wonder: Tape Diagrams

Problem 1

What do you notice? What do you wonder?

A yellow tape diagram with "80" written in it and below it a diagram of the same size divided into 4 segments. 3 are colored blue with a "?$" below them.

Activity 1: Revisiting Jada’s Puppy

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

Problem 1

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

A tape diagram with 5 segments all labeled 9. The first segment is blue and is labeled 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?

Problem 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.

A tape diagram with one row of 10 segments and a second row of 1 segment. All segments are marked "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.

Activity 2: 5 Dollars

Noah has $5.

Problem 1

  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.

Problem 2

  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.

Activity 3: Staying Hydrated

Problem 1

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?

Are you ready for more?

Problem 1

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.

Lesson 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 of 10 segments with 3 yellow and 7 white. All are marked with "5". The entire diagram is labeled 100% and the first segment is labeled 10%.

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

A tape diagram of 7 blue segments each labeled with a 4. The first segment is labeled 20%. The first 5 segments are labeled as 100%.