This lesson introduces students to percent and percentages. They learn that percent means “per hundred” and that it describes the ratio of a quantity to 100.

Students begin with gridded 10-by-10 squares that each represent an area of 100 square units. They use “percent of the large square” to describe the shaded region in each diagram and are prompted to articulate their initial interpretation of the term “percent.”

Next, students explore percentages as rates per 100 with money as the main context. They use their knowledge that there are 100 cents in a dollar to express the values of coins as percentages of a dollar. For example:

• The value of a nickel is 5 percent of a dollar because there are 5 cents in a nickel to 100 cents in a dollar.
• The value of 6 quarters is 150 percent of a dollar because there are 150 cents in 6 quarters to 100 cents in a dollar.

Double number line diagrams are used to develop the idea of a percentage as a rate per 100 and to make the connections to equivalent ratios. A double number line diagram can help students see, for instance, that when we refer to a percentage “of a dollar,” \$1 is “100 per 100” or 100 percent of a dollar. Students can then reason that \$0.50 is “50 per 100” or 50 percent of a dollar, \$1.25 is 125 percent of a dollar, and so on.

In this lesson, 100% corresponds only to 100 units of a quantity (100 square units of area) and to 1 dollar (understood as equivalent to 100 cents). In upcoming lessons, students will explore percentages in which 100% corresponds to other values.