# Lesson 12

Percentages and Tape Diagrams

### Lesson Narrative

In previous lessons students used double number lines to reason about percentages. Double number lines show different percentages when a given amount is identified as 100%, and emphasize that percentages are a rate per 100. In this lesson they use tape diagrams. Tape diagrams are useful for seeing the connection between percentages and fractions. For example, this tape diagram shows that 25% of a whole is the same as $$\frac14$$ of that whole by showing that 25% of the whole is one part when 100% of the whole is divided into four equal parts.

Tape diagrams are also useful in solving problems of the form $$A$$ is $$B\%$$ of $$C$$ when you are given two of the numbers and must find the third. When reasoning about percentages, it is important to indicate the whole as 100%, just as it is important to indicate the whole when working with fractions (MP6).

### Learning Goals

Teacher Facing

• Choose and create diagrams to solve problems such as A% of B is ? and A% of ? is C.
• Draw and label a tape diagram to represent a situation involving percentages.
• Interpret tape diagrams that represent multiplicative comparisons and express such comparisons using fractions and percentages.

### Student Facing

Let's use tape diagrams to understand percentages.

### Student Facing

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

Building Towards

### 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%.