Instructional Routines are designs for interaction that invite all students to engage in the mathematics of each lesson. They provide opportunities for students to bring their personal experiences as well as their mathematical knowledge to problems and discussions. They place value on students’ voices as they communicate their developing ideas, ask questions, justify their responses, and critique the reasoning of others.
As mentioned in the Design Principles, instructional routines have a predictable structure and flow. They provide structure for both the teacher and the students. A finite set of routines support the pacing of lessons as they become familiar and save time in classroom choreography, so students can spend less time learning how to execute lesson directions, and more time on learning mathematics. Some of the instructional routines, known as Mathematical Language Routines (MLRs), were developed by the Stanford University UL/SCALE team.
There are two types of Instructional Routines used in the materials: Warm-up Routines and Lesson Activity Routines. A list of the routines within each type is outlined in this table.
|Warm-up Routines||Lesson Activity Routines|
|Act It Out||Math Language Routines (MLRs)|
|Choral Count||MLR1: Stronger and Clearer Each Time|
|Estimation Exploration||MLR2: Collect and Display|
|How Many Do You See?||MLR3: Clarify, Critique, Correct|
|Notice and Wonder||MLR4: Information Gap|
|Number Talk||MLR5: Co-craft Questions|
|Questions About Us||MLR6: Three Reads|
|True or False?||MLR7: Compare and Connect|
|What Do You Know About _____?||MLR8: Discussion Supports|
|Which One Doesn’t Belong?||Other Lesson Activity Routines|
Each lesson begins with a Warm-up Routine intentionally designed to elicit student discussions around the mathematical goal of the lesson. The Lesson Activity Routines embed structures within the tasks of the lessons that allow students to engage in the content, and collaborate in ways that support the development of student thinking and precision with language. MLRs are written into each lesson, either as an embedded structure of a lesson activity in which all students engage, or as a suggested optional support specifically for English learners.
Notice and Wonder invites all students into a mathematical task with two low-stakes prompts: “What do you notice? What do you wonder?” By thinking about things they notice and wonder, students gain entry into the context and might have their curiosity piqued. Students learn to make sense of problems (MP1) by taking steps to become familiar with a context and the mathematics that might be involved. Note: Notice and Wonder and I Notice/I Wonder are trademarks of NCTM and the Math Forum and are used in these materials with permission.
The sequence of problems in a Number Talk encourages students to look for structure and use repeated reasoning to evaluate expressions and develop computational fluency (MP7 and MP8). As students share their strategies, they make connections and build on one another’s ideas, developing conceptual understanding.
Which One Doesn’t Belong fosters a need for students to identify defining attributes and use language precisely in order to compare and contrast a carefully chosen group of geometric figures, images, or other mathematical representations (MP3 and MP6).