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.

A tape diagram showing 4 parts with each part worth 25% for a total value of 100%. The first piece is colored in.

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

Addressing

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.

    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