# Lesson 16

Posing Percentage Problems

## 16.1: Sorting the News (10 minutes)

### Launch

Arrange students in groups of 3--4. Provide each group with a set of newspaper clippings involving percentage increase and decrease.

Tell students to take turns sorting the clippings into the piles representing percentage increase and percentage decrease and explaining the decision. If there is a disagreement, partners should discuss their ideas to try to agree about the correct sorting of the item. If an agreement cannot be made, the clipping can be put to the side to be discussed after the activity.

### Student Facing

Your teacher will give you a variety of news clippings that include percentages.

1. Sort the clippings into two piles: those that are about increases and those that are about decreases.
2. Were there any clippings that you had trouble deciding which pile they should go in?

### Activity Synthesis

The purpose of the discussion is to discuss any issues students may have had determining the sorting as well as to discuss any interesting contexts from the clippings.

Ask students, "Were there any clippings that were not easy to sort? What made it difficult?" Work with the class to try to determine the correct sorting, if possible. Ask each group to read the important parts of their most interesting newspaper clipping and explain their reasoning behind sorting it where they did.

## 16.2: Investigating (10 minutes)

### Activity

In this activity, students use the examples of percentage increase and decrease that they sorted in the previous activity to pose questions that arise from the different situations. They ask and answer questions based on the information given and present this information graphically. In the next activity they will make a poster using one of their news items. Then students will go on a gallery walk and use sticky notes to ask questions about the information presented on each poster.

### Launch

Keep students in groups of 3–4. Display the following statement for all to see:

"Global human population growth amounts to around 75 million annually, or 1.1% per year."

Ask students what questions they could answer with this information. Sample responses:

• What were possible populations in the two years used to compute the annual increase?
• By how many people will the population grow next year?

Tell students they will use the clippings from the warm-up to write similar questions for different situations.

Representation: Internalize Comprehension. Activate or supply background knowledge about diagrams that can be used to represent situations of percent increase or percent decrease such as tape diagrams and double number line diagrams.
Supports accessibility for: Memory; Conceptual processing
Writing, Conversing: MLR5 Co-Craft Questions. Present a video or image that depicts population growth next to the display. Ask pairs of students to write possible mathematical questions about the situation. Then, invite pairs to share their questions with the class. This helps students produce the language of mathematical questions and talk about the relationships between the two quantities in this task (e.g., a quantity and percent increase or decrease) prior to being asked to create and solve questions based on their newspaper clippings.
Design Principle(s): Maximize meta-awareness; Support sense-making

### Student Facing

In the previous activity, you sorted news clippings into two piles.

1. For each pile, choose one example. Draw a diagram that shows how percentages are being used to describe the situation.

1. Increase Example:

2. Decrease Example:

2. For each example, write two questions that you can answer with the given information. Next, find the answers. Explain or show your reasoning.

## 16.3: Displaying the News (20 minutes)

### Activity

In this activity, students work in groups and make a poster in their groups using one of their news items. Next, students go on a gallery walk and use sticky notes to ask questions about the information presented on each poster. They practice critiquing the reasoning of others as they study information they have not themselves worked on. They then go back and study the feedback they received from their classmates and revise their own work.

### Launch

Keep students in the same groups of 3–4. Give students supplies to make posters. Tell them that they will choose one of their news clippings and make a visual display for the information they worked on in the previous activity. The posters should include all necessary information so that somebody who has not extensively worked with the same information should be able to understand the work.

Allow students 10 minutes to work on creating their display. Review group work as they finish.

After all groups have finished, display each group's work around the room for students to do a gallery walk. Tell students that they should leave feedback for each display on a sticky note attached to each group's work. Feedback can include questions about the display or information as well as compliments or critiques. Comments and questions should be constructive with the goal to help the groups who made the poster improve their work.

Tell each group which poster to start with and in which direction they should move.

As groups finish viewing the displays, allow them time to view the feedback left on their own display and, if necessary, time to improve their display based on the feedback.

Engagement: Develop Effort and Persistence. Provide prompts, reminders, guides, rubrics, or checklists that focus on increasing the length of on-task orientation in the face of distractions. For example, provide a task checklist which makes all the required components of the poster explicit.
Supports accessibility for: Attention; Social-emotional skills
Writing: MLR8 Discussion Supports. Provide sentence frames for students to use when asking questions about features of the visuals displays they do not understand. For example, “Why did you ____?” or “How did you ____?”
Design Principle(s): Support sense-making

### Student Facing

1. Choose the example that you find the most interesting. Create a visual display that includes:

• a title that describes the situation
• the news clipping
• your diagram of the situation
• an explanation of how you calculated each answer

2. Examine each display. Write one comment and one question for the group.

## Student Lesson Summary

### Student Facing

Statements about percentage increase or decrease need to specify what the whole is to be mathematically meaningful. Sometimes advertisements, media, etc. leave the whole ambiguous in order to make somewhat misleading claims. We should be careful to think critically about what mathematical claim is being made.

For example, if a disinfectant claims to "kill 99% of all bacteria," does it mean that

• It kills 99% of the number of bacteria on a surface?
• Or is it 99% of the types of bacteria commonly found inside the house?
• Or 99% of the total mass or volume of bacteria?
• Does it even matter if the remaining 1% are the most harmful bacteria?

Resolving questions of this type is an important step in making informed decisions.