Instructional Routines

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
5 Practices
Card Sort

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.

Warm-up Routines

Act It Out
Act It Out is a kindergarten routine that allows students to represent story problems (MP4). Students listen to a story problem and act it out, connecting language to mathematical representations. This routine provides an opportunity for students to connect with the storytelling tradition, typically found in ethnically diverse cultures. 

Choral Count
While Choral Counting offers students the opportunity to practice verbal counting, the recorded count is the primary focus of the routine. As students reflect on the recorded count, they make observations, predict upcoming numbers in the count, and justify their reasoning (MP7 and MP3).

Estimation Exploration
Estimation Exploration encourages students to use what they know and what they can see to problem-solve for a rough evaluation of a quantity rather than giving a “wild guess.” The estimates can be in the context of measurement, computation, or numerosity—estimating about a large group of objects (MP2).

How Many Do You See?
How Many Do You See helps early math learners develop an understanding of counting and quantity through subitizing and combining parts of sets to find the total in a whole collection. In later grades, this routine encourages students to use operations and groupings that make finding the total number of dots faster. Through these recorded strategies, students look for relationships between the operations and their properties (MP7).

Notice and Wonder

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.

Number Talk

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.

Questions About Us
Questions About Us is a kindergarten routine that allows students to consider number concepts in a familiar context. Students analyze data collected about the students, and answer questions such as: “What do you notice? What do you wonder?” Using data that represents students helps them to see math in the world around them. 

True or False
The True or False routine structure encourages students to reason about numerical expressions and equations using base-ten structure, meaning and properties of operations, and the meaning of the equal sign. Often, students can determine whether an equation or inequality is true or false without doing any direct computation (MP7).

What Do You Know About _____?
The What Do You Know About _____? routine elicits students’ ideas of numbers, place value, operations, and groupings through visuals of quantity, expressions, and other representations. It is an invitational prompt that could include such things as understanding where students see numbers embedded in various contexts or how students compare and order numbers.

Which One Doesn’t Belong?

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).

Other Instructional Routines

5 Practices
Lessons that include this routine are designed to allow students to solve problems in ways that make sense to them. During the activity, students engage in a problem in meaningful ways and teachers monitor to uncover and nurture conceptual understandings. During the activity synthesis, students collectively reveal multiple approaches to a problem and make connections between these approaches (MP3). 

Card Sort
A card sorting task gives students opportunities to analyze representations, statements, and structures closely, and make connections (MP2 and MP7). As students work, teachers monitor for the different ways groups choose their categories, and encourage increasingly precise mathematical language (MP6).

MLR1 Stronger and Clearer Each Time
Provides students with a structured and interactive opportunity to revise and refine both their ideas and their verbal and written output. Embedded in grades 3–5.

MLR2 Collect and Display
Captures a variety of students’ oral words and phrases into a stable, collective reference. Output can be organized, revoiced, or explicitly connected to other languages in a display that all students can refer to, build on, or make connections with during future discussion or writing. Embedded in grades K–5.

MLR3 Clarify, Critique, Correct
Gives students a piece of mathematical writing that is not their own to analyze, reflect on, and develop. Embedded in grades 3–5.

MLR4 Information Gap
Creates an authentic need for students to communicate. Partners or team members are given different pieces of necessary information that must be used together to solve a problem. Embedded in grades 3–5.

MLR5 Co-craft Questions
Allows students to get inside a context before feeling pressure to produce answers, and creates opportunities for students to produce the language of mathematical questions. Embedded in grades 2–5.

MLR6 Three Reads
Supports reading comprehension, sense-making, and meta-awareness of mathematical language. Students take time to understand mathematical situations and story problems, and plan their strategies before finding solutions. Embedded in grades K–5.

MLR7 Compare and Connect
Fosters students’ meta-awareness as they identify, compare, and contrast different mathematical approaches, representations, and language. Embedded in grades K–5.

MLR8 Discussion Supports
Includes a large variety of teacher moves that support rich discussions about mathematical ideas, representations, contexts, and strategies. Embedded in grades K–2.