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.
Learning Targets
Student Facing
 I can use tape diagrams to solve different problems like “What is 40% of 60?” or “60 is 40% of what number?”
CCSS Standards
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%.