Lesson 16
Posing Percentage Problems
16.1: Sorting the News (10 minutes)
Launch
Arrange students in groups of 34. 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.
 Sort the clippings into two piles: those that are about increases and those that are about decreases.
 Were there any clippings that you had trouble deciding which pile they should go in?
Student Response
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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 warmup to write similar questions for different situations.
Supports accessibility for: Memory; Conceptual processing
Design Principle(s): Maximize metaawareness; Support sensemaking
Student Facing
In the previous activity, you sorted news clippings into two piles.

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

Increase Example:

Decrease Example:

 For each example, write two questions that you can answer with the given information. Next, find the answers. Explain or show your reasoning.
Student Response
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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.
Supports accessibility for: Attention; Socialemotional skills
Design Principle(s): Support sensemaking
Student Facing

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
 the two questions you asked about the situation
 the answers to each of your questions
 an explanation of how you calculated each answer
Pause here so your teacher can review your work.
 Examine each display. Write one comment and one question for the group.
 Next, read the comments and questions your classmates wrote for your group. Revise your display using the feedback from your classmates.
Student Response
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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.