In this lesson, students apply what they have learned about solving an equation of the form to situations that involve percentages. Students learned about what percentages are and how to solve percentage problems in an earlier unit. However, they did not generalize the reasoning process for finding the value that corresponds to 100% when a percentage and its value is known, or for finding in “% of is ” given and . Students have an opportunity to generalize that process in this lesson.

Students begin the lesson by recalling that they can find % of by multiplying . They then use repeated calculations to extend this structure and write the equation  to represent percentage problems and solve for . An optional activity is included to allow students to practice solving such problems before they move on the main activity, an Information Gap activity.  There, students solve real-world percentage problems where is unknown.

Throughout the lesson students have opportunities to use and compare strategies based on arithmetic and those based on algebra. As needed, encourage students to use strategies from prior units (for example, using double number line diagrams) to make sense of problems and other solution strategies.