# 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.

### 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.

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.

• 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%.