Lesson 15

Finding This Percent of That

Lesson Narrative

Students have practiced solving three different types of percentage problems (corresponding to finding \(A\), \(B\), or \(C\) respectively when \(A\%\) of \(B\) is \(C\)). This lesson focuses on finding “\(A\%\) of \(B\)” as efficiently as possible. While the previous lesson used numbers that students could calculate mentally, the numbers in this lesson are purposefully chosen to be difficult for students to calculate mentally or to represent on a double number line diagram, so as to motivate them to find the simplest way to do the calculation by hand.

The third activity hints at work students will do in grade 7, namely finding a constant of proportionality and writing an equation to represent a proportional relationship.

Learning Goals

Teacher Facing

  • Choose and create diagrams to calculate A% of B, and explain (orally) the solution method.
  • Generalize a process for finding A% of B and justify (orally) why this can be abstracted as $\frac{A}{100} \boldcdot B$.
  • Identify equivalent expressions that could be used to find A% of B and justify (orally) that they are equivalent.

Student Facing

Let’s solve percentage problems like a pro.

Learning Targets

Student Facing

  • I can solve different problems like “What is 40% of 60?” by dividing and multiplying.

CCSS Standards

Building On

Addressing

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