What: This routine can appear as a Warm-up or in the Launch or the Activity Synthesis of an instructional activity. Students are shown some media or a mathematical representation. The Notice and Wonder routine invites all students into a mathematical task, with two low-stakes prompts: “What do you notice?” and “What do you wonder?” Give students a few minutes to think of, and share with a partner, the things they notice and the things they wonder. Then ask several students to share the things they noticed and the things they wondered, and record these for all to see. At opportune times, steer the conversation to wondering about the mathematics on which the class is about to focus.

Why: The Notice and Wonder routine makes a mathematical task accessible to all students, using two approachable questions. By thinking about them and responding, students gain entry into the context and may have their curiosity piqued. By taking steps to become familiar with the context and the mathematics involved, students learn to make sense of problems (MP1). Note: Notice and Wonder and I Notice/I Wonder, trademarks of the National Council of Teachers of Mathematics (NCTM) and the Math Forum, are used in these materials with permission.

What: Students are presented with four figures, diagrams, graphs, or expressions with the prompt “Which three go together?” Typically, each option for a group of three “go together” for a different reason, and the similarities and the differences are mathematically significant. Students are prompted to explain their rationale for deciding why their group of three goes together and given opportunities to make their rationale more precise. Encourage students first to identify why all four representations go together and then to look closely at how the representations are alike and how they are different while being as specific as they can in their responses. 

Why: Which Three Go Together? fosters a need for students to define terms carefully and to use words precisely (MP6) in order to compare and contrast a group of geometric figures or other mathematical representations.