## Cool-Downs

Each lesson includes a cool-down (also known as an exit slip or exit ticket) to be given to students at the end of the lesson. This activity serves as a brief checkpoint to determine whether students understood the main concepts of that lesson. Teachers can use this as a formative assessment to plan further instruction.

What if the feedback from a cool-down suggests students haven't understood a key concept? Choose one or more of these strategies:

• Look at the next few lessons to see if students have more opportunities to engage with the same topic. If so, plan to focus on the topic in the context of the new activities.
• During the next lesson, display the work of a few students on that cool-down. Anonymize their names, but show some correct and incorrect work. Ask the class to observe some things each student did well and could have done better.
• Give each student brief, written feedback on their cool-down that asks a question that nudges them to re-examine their work. Ask students to revise and resubmit.
• Look for practice problems that are similar to, or involve the same topic as the cool-down, then assign those problems over the next few lessons.

Here is an example. For a lesson in Algebra 1, unit 2, the learning goals are

• Create and interpret graphs of inequalities in two variables.
• Write inequalities in two variables to represent situations.

A band is playing at an auditorium with floor seats and balcony seats. The band wants to sell the floor tickets for \$15 each and the balcony tickets for \$12 each. They want to make at least \$3,000 in ticket sales. 1. How much money will they collect for selling $$x$$ floor tickets? 2. How much money will they collect for selling $$y$$ balcony tickets? 3. Write an inequality whose solutions are the number of floor and balcony tickets sold if they make at least \$3,000 in ticket sales.
4. Use technology to graph the solutions to your inequality, and sketch the graph.

A number of students were able to write $$15x$$ to represent the money collected selling floor tickets and $$12y$$ to represent the money collected selling balcony tickets. However, they wrote the inequality $$15x+12y < 3,\!000$$ and sketched a graph corresponding to this incorrect inequality. You suspect that students interpreted “at least” to mean the same thing as “less than.” Here are some possible strategies:

• In the next four lessons, there are more opportunities to interpret the meaning of “at least.” When launching these activities, pause to assist students to interpret this correctly. For example, an activity reads, “He needs at least 9.5 yards of fabric altogether.” Ask students, “If he needs at least 9.5 yards, what kinds of numbers are we looking for?” [9.5 yards or anything more than 9.5 yards]. “Since he needs more than 9.5 yards, the amount of fabric needs to be less than 9.5 yards? or greater than 9.5 yards?” [greater than]
• Select the work of one student who answered correctly and one student whose work had the common error. In the next class, display these together for all to see (hide the students' names). Ask each student to decide which interpretation is correct, and defend their choice to their partner. Select students to share their reasoning with the class who have different ways of knowing that “at least \$3,000” means “more than \$3,000.”
• Write feedback for each student along the lines of “What are some different dollar amounts that would satisfy their wish to make at least \\$3,000?” Allow students to revise and resubmit their work.
• Look for practice problems in upcoming lessons that require students to correctly interpret the term “at least,” and be sure to assign those problems.