Lesson 2

The purpose of this Math Talk is to elicit strategies and understandings students have for finding the percentage of a number. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to find the percentage of a number. 

Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

• “Who can restate [\(\underline{\hspace{.5in}}\)’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to \(\underline{\hspace{.5in}}\)’s strategy?”
• “Do you agree or disagree? Why?

The purpose of this activity is for students to practice calculating percentages of shapes that share a specific characteristic. In doing so, students consider the exact categories needed to calculate a percentage. Students must determine which rate is the appropriate one to represent as a percent based on the question. Monitor for students who create two-way tables to organize the shapes.

Allow students to work in pairs. Provide students with an example of how completed statements should look.

Example: 4 of the 24 shapes are gray. 17% of the shapes are gray.

The goal of this discussion is to highlight making a distinction between various categories to calculate a percentage. Allow students to share the percentages they calculated and how they calculated them. Discuss the processes that are used to compute the percentages in this activity. Here are sample questions to promote class discussion:

• “How do you know which numbers to use to find the percentage?” (First, I thought about the entire group of shapes included in the description and counted the number of shapes that fit it. Then, I considered the subgroup of shapes included in the description and counted the number of shapes that fit it. Then, I used the two numbers to calculate the percent.)
• “What strategy do you use to calculate the percentages?” (I set the two numbers up as a rate, and divide the first number by the second number. The quotient is a decimal and I multiply the decimal by 100 to get the percentage.)
• “What do you do about shapes that were a part of several categories?” (I focus on the characteristics that are described in the question. For example, when I count the number of quadrilaterals, I am not concerned with their colors or dots.)

The purpose of this activity is for students to practice calculating percentages from data, similar to what they encounter in the associated Algebra 1 lesson. In the previous activity, students practiced thinking about specific categories within groups before calculating a percentage. Here, students extend this thinking by applying it to data that are collected from their classmates.

Arrange students in groups of 2. Before starting the activity, ask students to answer the following questions: “Do you prefer sci-fi movies or dramas?” and “Do you prefer science or English class?”. Poll the class for students’ responses and display the values for all to see. Here's an example of how you can organize data:

Lin: science, drama

Andre: science, sci-fi movies

Diego: English, drama

Ensure that the data display you present to students includes both variables to help students see the connection between the two vaiables. Then, allow students to organize the class’ data into a two-way table.

Allow students to share the values they used to calculate each percentage and how they know to use those particular values. Here are sample questions to promote class discussion:

• “How do you know which two numbers should be used to calculate the percentage?” (If the question asks about a percentage of the class, I need to use the total number of people in the class. If the question specifies a smaller group such as, “Of the students who. . .” then I use the total for that column or row.)
• “Are there any patterns in the data?” (I notice that students who prefer dramas also tend to prefer English.)