# Modeling with Percents

## Objective

SWBAT draw percent equivalents using reasoning.

#### Big Idea

The Big Idea of this lesson is that students will use reasoning and modeling to find percent representation.

## Launch

5 minutes

Students will complete this Problem of the Day when they enter the class: After grading the math exam, Mrs. Keys discovered that 2/3 of the students who had taken the exam earned A’s or B’s. Of those students, 1/5 had earned 100% on the exam. If Mrs. Keys has 180 students, how many earned 100% on the exam?

After the problem is finished, as a class, we will talk about not only the answer to the problem, but how students solved the problem. Highlighting different approaches and the reasoning behind the approach will be a perfect segue into the next activity. During the next activity, students will create models of percents and using different aproaches will be beneficial.

## Explore

30 minutes

Students will work in pairs or groups of three to draw representations of all of the percents in the activity. The only numbers included in each of the problems is the percentage given and the percentage desired. This activity is valuable becaue part of the thinking that students have to do requires them to decide how to determine the representation of different percentages. Do they need to find 100% first? Or 50%? Using some benchmark percentages help them make their decisions. The discussions between partners are good as well. If partners are approaching the problem differently it is good to hear the resulting conversations about the next steps. Providing justification supports students' reasoning as they create their models.

When the pairs finish, volunteers will model the answers on the SMART board and discuss their thinking. How did they decide what the picture would look like? Did partners approach the problem differently? Did ther students take a different approach? Is there an alternative way to determine the answer? We will also explore the proportionality of their drawings.

## Summary

5 minutes

Exit Ticket: Create a picture representing a percentage then create another picture that models another percentage that relates to the initial picture. Explain the relationship.

Looking at the responses, I will be able to see what they understand about creating models. Can they originate a model and makes changes to it that represent different percents? What percent equivalents are the using? Have students moved away from the benchmarks like 50% and 100%?