An important part of the teacher's role is selecting the right problems. In some cases, it is possible to assign a problem that is appropriate for students of varying ability levels and that can be solved using different approaches. These problems are sometimes referred to as "low threshold, high ceiling" problems because all students can understand the problem and solve some part of it (low threshold), but even the highest-ability students in the class will not easily complete the problem (high ceiling). Such problems can often be extended to allow students to explore more challenging mathematics.

Students benefit from a few initial quiet moments to interpret and think about a problem, as well as from peer interaction. Students can be encouraged to model the use of comprehension strategies for classmates to ensure that everyone understands a problem before embarking on solution attempts. For example, students may restate the problem information and the question in their own words and make a quick diagram or sketch. They may also need to ask clarifying questions. Once the problem is understood, pairs or small groups can get to work. It is sometimes advantageous to strategically set up the groups, either to let students with similar experience with the topic work together, to let students with a variety of experience support and challenge one another, or to have the more advanced students work on a related challenge. At the end of the session, after various solutions are shared and discussed, the teacher can sum up by emphasizing the important discoveries that were made; new words, strategies, and examples that will be valuable to remember; and questions that need further investigation.

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