options: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Recognize and represent proportional relationships between quantities.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Optional activity
In this activity, students make a visual display of their scenarios from the previous activity (after sharing their rough draft with another group and getting some feedback).
When the posters are complete and displayed around the room, students view each others' work and use sentence starters to give feedback and to critique the reasoning of others (MP3).
Launch
Keep students in the same groups. Tell them that they should incorporate the feedback they received when making their posters.
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
Student Facing
Create a visual display of your two situations that includes all the information from the previous activity.
Student Response
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Activity Synthesis
When the posters are complete, hang them around the room. Provide students with these sentence starters, and give them an opportunity to view their classmates’ work and write their responses. This provides a structured way for students to critique the reasoning of others (MP3).
The most surprising combination of things was ____________________ because ______________________________________________________________.
The group _______________________________ should check their work where they ___________________________________________________________________.
I really liked when the group ____________________________ did this __________________________________ because _______________________________________.
Representing, Reading, Writing: MLR7 Compare and Connect.
Use this routine when students share their visual displays. Direct attention to the different ways pairs explained quantities and their relationships and justified whether the relationship was proportional (e.g., distance traveled in yards and time elapsed in minutes, for every one minute they traveled 5 yards, the relationship is proportional because the graph of the line passes through the origin). Emphasize the language used to describe the proportional relationships and justify whether the relationship was proportional. These exchanges strengthen students' mathematical language use and reasoning of proportional relationships.
Design Principle(s): Maximize meta-awareness


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