Lesson 23

Solving Percentage Problems

Lesson Narrative

In previous lessons, students saw that a percentage is a rate per 100. They were provided with double number line diagrams to develop this understanding and to solve problems involving percentages. In this lesson, students solve similar problems but with less support. Because double number lines are not provided, students have opportunities to choose approaches that seem appropriate. Drawing a double number line is still a good strategy, but students may opt for tables or even more abbreviated reasoning methods. Understanding the connections among different representations and using them strategically (MP5) is an important part of this lesson.

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. 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

• Determine what information is needed to solve a problem involving percentages. Ask questions to elicit that information.
• 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 more percentage problems.

Required Preparation

You will need the Music Devices Info Gap blackline master for this lesson. Make 1 copy for every 4 students, and cut them up ahead of time.

Student Facing

• I can choose and create diagrams to help me solve problems about percentages.
• I can solve different problems like “What is 40% of 60?” by dividing and multiplying.

Building On