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 grade 6, unit 2, the learning goals are

• Understand that doubling, tripling, or halving a recipe yields something that tastes the same.
• Understand that “doubling, tripling, or halving the recipe” means “doubling, tripling, or halving each ingredient.”

The cool-down reads:

Usually when Elena makes bird food, she mixes 9 cups of seeds with 6 tablespoons of maple syrup. However, today she is short on ingredients. Think of a recipe that would yield a smaller batch of bird food but still taste the same. Explain or show your reasoning.

A number of students responded with 8 cups of seeds and 5 tablespoons of maple syrup, and did not provide an explanation or show their reasoning. Here are some possible strategies:

• Notice that this lesson is the first of several that familiarize students with contexts where equivalent ratios carry physical meaning, for example, the taste of a recipe or the result of mixing paint colors. Over the next several lessons, there are more opportunities to reason about multiple batches of a recipe. When launching these activities, pause to assist students to interpret this correctly. Highlight the strategies of any students who use a discrete diagram or other representation to correctly represent multiple batches.
• 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 representing that $$9:6$$ is equivalent to $$3:2$$, $$6:4$$, or $$4\frac12:3$$.
• Write feedback for each student along the lines of "If this recipe is 3 batches, how could you make 1 batch?" Allow students to revise and resubmit their work.
• Look for practice problems in upcoming lessons that require students to generate examples of different numbers of batches equivalent to a given ratio, and be sure to assign those problems.