Unit 2, Lesson 21
What Are Percentages?
Accelerated 6
Preparation
Lesson Narrative
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 reason about percentages when the value for 100% is known (such as finding 75% of \$10) and about the value of 100% when a percentage is known (such as finding a weight given that 10% of that weight is 9 pounds). The percentages in all problems are limited to multiples of 10% and 25%.
Blank or partially labeled double number line diagrams are provided to support students in their reasoning. This is done for several reasons:
- Using a double number line diagram involves identifying the value that corresponds to 100%, reinforcing the idea of a percentage as a rate per 100.
- The equal intervals on the two number lines encourage students to reason about equivalent ratios.
- Thinking about how to extend or further partition the given intervals to represent a situation also prompts students to look for and make use of structure (MP7).
It is perfectly acceptable, however, for students to choose other representations or use other strategies for solving percentage problems.
- Comprehend the word “percentage” (in written and spoken language) and the symbol “%” (in written language) to mean a rate per 100.
- Explain (orally) how to use a double number line diagram to solve problems such as $A%$ of $B$ is ? and $A%$ of ? is $C$.
- Interpret statements about percentages and identify the quantity that corresponds to 100%.
Let’s use double number line diagrams to understand percentages.
Required Materials
Activity 3
Required Preparation
None
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. A quarter is worth 25% of a dollar.
A diagram of two bars with different lengths. The top bar is labeled 1 Quarter and 25 cents is labeled inside the bar. The bottom bar is labeled 1 Dollar. It is 4 times longer than the top bar and 100 cents is labeled inside the bar.
A percentage is a rate per 100.
For example, a fish tank can hold 36 liters. There are 27 liters of water in the tank. The percentage of the tank that is full is 75%.