Lesson 13

Benchmark Percentages

Lesson Narrative

The goal of this lesson is to help students understand the connection between benchmark percentages and common fractions (MP7). In these materials, we have identified 10%, 25%, 50%, and 75% as primary benchmark percentages and multiples of 10% as secondary benchmark percentages.

It is common to say that \(25\% = \frac14\) or \(10\% = \frac{1}{10}\). In these materials we avoid this usage and say rather that 25% of a quantity is \(\frac14\) of that quantity, or that 10% of a quantity is \(\frac{1}{10}\) of that quantity.

This lesson builds on understanding of equivalent fractions, multiplying fractions, and dividing by unit fractions from grades 4 and 5.

Learning Goals

Teacher Facing

  • Explain (orally and in writing) how to solve problems involving the percentages 10%, 25%, 50%, and 75% by reasoning about the fractions $\frac{1}{10}$, $\frac14$, $\frac12$, and $\frac34$.
  • Generalize (orally) processes for calculating 10%, 25%, 50%, and 75% of a quantity.

Student Facing

Let’s contrast percentages and fractions.

Learning Targets

Student Facing

  • When I read or hear that something is 10%, 25%, 50%, or 75% of an amount, I know what fraction of that amount they are referring to.

CCSS Standards

Building On


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