TERMS IN COMMON 
EVERYDAY LANGUAGE OK 
I DON’T GET IT
PRINCIPLE: Academic language promotes 
precise thinking. Mathematically proficient students comprehend and produce mathematical representations (symbolic expressions, graphs, tables, number lines, etc.) that are embedded in ordinary and academic explanations and justifications. Students comprehend and produce the paragraphs, sentences, phrases and words characteristic of justifications, explanations and word problems typical for their grade level.
PROVIDE LANGUAGE SCAFFOLDS
FORTIFY STUDENT STATEMENTS
Student Vital Actions
THE VALUE OF PRECISE LANGUAGE
Students use general and discipline-specific academic language.
MOVES TO SUPPORT THIS STUDENT VITAL ACTION
IN OTHER WORDS
TERMS IN COMMON
Why does this matter?
Next
Students use academic language.
Most frequently used: during the initial phases of a lesson. when the whole class is discussing the mathematics.
Most frequently used:
PROVIDE LANGUAGE SCAFFOLDS The problem:  Inocorporating a mathematical term into academic discourse can be challenging if a student is not familar with the language that typically accompanies the term.  The move: Before beginning small group work, give students sentence frames and probing questions that feature important terms. Teacher Tip:  This move can provide a scaffold for students to use the desired terms in meaningful discussion. Have posters for the classroom that can prompt all students to use terms accurately. 
Previous
EVERYDAY LANGUAGE OK TO START The problem:  Some students don’t feel qualified to join a discussion about math, even though there should be no prerequisites for talking about math. Anyone should be able to share ideas.  The move: Accept students’ everyday way of talking as a starting point for joining the math conversation. Teacher Tip:  There is a balancing act to be done between encouraging precision and allowing students to feel comfortable talking.  Consistent and prolonged engagement in discussions will lead to the addition of new vocabulary and discourse practices.
Most frequently used: during the initial phases of a lesson. during the "last third" of a lesson. within small groups. when the whole class is discussing the mathematics.
Most frequently used: during the initial phases of a lesson. during the "last third" of a lesson. when the whole class is discussing the mathematics.
IN OTHER WORDS The problem:  Students are rarely invited to explore correspondences and differences between everyday language and mathematical symbols. The move: Students translate from symbols to words, from images to words, and from words to images and symbols, and identify correspondences between representations. Teacher Tip:  Students will typically use everyday language, such as “goes up” instead of increases or ascends, and “goes down” rather than declines, descends, or has a negative slope. Initially you may want to restate using academic language. Over time you can ask the student if he or she can restate using academic language. 
I DON'T GET IT The problem:  Students offer a muddled response or do not use academic language when communicating a mathematical idea.   The move: Play as if you do not understand student talk when the language used is imprecise in order to give students the opportunity to improve their explanations.  Teacher Tip:  By taking what students say at face value, teachers can create a light-hearted joke that prompts the student to use more precise language.
Most frequently used: during the initial phases of a lesson. during the "last third" of a lesson. when the whole class is discussing the mathematics. after a classroom culture is established (advanced move).
Examples:
TEACH THE VALUE OF PRECISE LANGUAGE The problem:  Students can resist learning unfamiliar language when they don’t see the value of it.  The move: Recognize and appreciate conciseness and precision in mathematical language. See the idea that this efficiency makes their math work less time-consuming and more understandable when it is initially presented to classmates and teachers.  Teacher Tip:  Learning new words serves a purpose. Academic language has distinctive communicative capacities. It is well-defined, shared, and makes it possible to say precisely what you mean. Mastering this language makes communication more precise, readily understood and supports access.  You may want ot create a list on a poster of ways to say things that are more and less precise. You can add to the list as examples arise in class. If a student is imprecise, you might ask if there is a better way to say that. If they seem to be stuck, you can refer them to the poster, or add to the poster it nothing on it is helpful. 
MORE PRECISE: He earned $10 per lawn mowed. Her hits per game fluctuated.   It was twice as much 
Most frequently used: during the "last third" of a lesson. when the whole class is discussing the mathematics. after a classroom culture is established (advanced move).
OKAY: He got another $10 every time he mowed the lawn. The number of hits she got went up and down and up and down from one game to the next.  It was that much and that much again. 
Most frequently used: during the initial phases of a lesson. during the "last third" of a lesson. within small groups. when the whole class is discussing the mathematics. after a classroom culture is established (advanced move).
FORTIFY A STUDENT STATEMENT The problem:  Sometimes students don’t perceive the correspondence between their everyday speech and academic language. The move: Teachers can refer to student statements using some student language while strategically incorporating more precise academic language with the addition of a key word or phrase. Similarly, teachers can restate a student statement verbatim, then rephrase it for the class by replacing key words or phrases with more academic language while still crediting the student for offering the idea.   Teacher Tip:  The goal is to get the students to take up the student’s idea in their discussions with the additional academic language. It represents an additive approach in which students are supported in developing new linguistic capacities. Over time the burden of being precise should shift to the student. But it’s important not to discourage math talk by over-emphasizing precise language. 
Most frequently used: during the "last third" of a lesson. when the whole class is discussing the mathematics.
TERMS IN COMMON The problem:  Students are using a variety of invented terms instead of standard terms for math concepts.    The move: Teacher can note the terms in question and then and facilitate a whole class discussion to reach a consensus on which term the class should use.  In many cases there is established terminology from the discipline. In which case the move is to connect the diverse terminology to the conventional. Teacher Tip:  At first it is natural and useful for students to develop and use their own terminology. But at some point the multiplicity of terminology becomes an obstacle to understanding other students’ thinking and communicating. To move forward it is necessary to incorporate the conventional terminology.
Why are some moves considered advanced? In general, the teacher moves in the 5 x 8 resource do not have prerequisites.  Any teacher should be able to try them and be successful. However, moves marked “advanced” may require more groundwork or particular persistence on the part of teachers in order to be successful. 
Why are some moves better for the initial phases of a lesson? The goal of classroom activities is to have students understand a concept and master the related skills. The challenge for teachers is to help the students move from their initial way of thinking about the problem(s) in the lesson toward the grade level target. In the first phase of a lesson, teachers elicit students' divergent ways of thinking about a topic by allowing students to work in pairs and small groups. Students begin with their own way of understanding, and, by working together, the class creates examples of different ways of thinking about the mathematics. The students’ different ways of thinking are the " stepping stones" that take them from their starting point to grade-level ways of thinking.  Representations of these ways of thinking (students’ work and their talk about it) are the “stepping stones” that teachers use to help students get to the target.  During this first phase of the lesson, it is helpful,teachers circulate among the groups to: 1) ensure that they are struggling productively with the mathematics and intervene to re-engage struggle when needed, 2) select student work that is representative of diverse ways of thinking and will help students step up to the target ways of thinking, and 3) determine the order in which student work will be presented. The easiest way of making sense of the problem should be presented first (usually concrete thinking), and the closest-to-grade-level way of thinking should be presented last. 
Why are some moves recommended for Small Groups of Students? While some moves can be effective across multiple class structures (pairs, small groups, whole class, et cetera), other moves are particularly effective with small groups, or are only relevant to small groups.  By noting the class structure, the 5 x 8 resource supports users who want to think about how to promote vital actions within particular class structures. 
Why are some moves better to use toward the conclusion (or final third) or a lesson? The goal of a lesson is to have all students reach a shared understanding of the target mathematics. In the first phase of the lesson, students may create various representations of different ways of thinking.  In the second phase, teachers can organize presentations of these ways of thinking and a summary of the mathematics that help students "step up to the target." Presentations begin with the easiest-to-understand way of thinking and conclude with the way of thinking that represents the lesson target. Following student presentations, the teacher can give a summary of the mathematics that involves quoting from student presentations, highlighting correspondences between the various representations shared, and opportunities for students to ask questions. By helping students connect their way of thinking with increasingly more complex ways of thinking, students are able to "step up to the target mathematics". 
Why are some moves recommended for the Whole Class? While some moves can be effective across multiple class structures (pairs, small groups, whole class, et cetera), other moves are particularly effective with the whole class, or are only relevant to whole-class structures.  By noting the class structure, the 5 x 8 resource supports users who want to think about how to promote vital actions within particular class structures. 
ELLs produce language.
Tap on any of the Student Vital Actions to explore teaching moves!
Students say a second sentence.
Students revise their thinking.
Students talk about each other’s thinking.
What is a Teaching Move?
Students engage and persevere.
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All students participate.
First Steps:Creating a Classroom Culture
What is a Student Vital Action?
Students say a second sentence.
ELLs produce language.
Students talk about each other’s thinking.
Students engage and persevere.
The Common Core State Standards in mathematics are the first to articulate “practice standards:” expectations not only for what students should know, but for what they should be able to do. Teachers and administrators are now confronted with the questions: how would a classroom look if students were developing these practices? What would we expect to see students doing? A SERP team worked with Bay Area district partners to produce an answer to this question in the form of 7 “student vital actions” organized for simplicity and ease of use on a 5x8 Card. The vital actions are intended to be catalytic rather than comprehensive. There are many other things students do to learn, but these 7 are concrete, observable, and leverage related important learning actions. Learning is active; the vital actions attempt to capture the spirit of that action. They are intended as a productive starting point for shifting the focus from teacher actions to student actions–one that will be continuously improved as we learn more. We welcome your feedback! Please visit the 5x8 Card Website for additional information. 
What is a Student Vital Action?
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Student action is influenced by the classroom culture and leadership of the teacher. A teacher plans, assigns, prompts, spots trouble and responds, sees opportunities and seizes them, sees disengagement and re-engages. When a teacher acts to make a teaching episode productive, we refer to the teacher action as "a move.” Every teacher has a repertoire of moves that serve different purposes in different situations.  The 5x8 “deck" lists a selection of teacher moves that promote student vital actions. Teacher moves can make lessons flow toward the mathematics of the unit, and they keep students with a variety of dispositions and prior knowledge engaged in the discussion. Teacher moves also advance the discussion from initial ways of thinking toward grade-level ways of thinking. Which move should a teacher use? It depends on the purpose and the circumstance. Often, more than one move is worth trying. If one doesn’t work, try another. Good teaching entails paying attention to students’ ways of thinking and responding to it. When observing, work from student actions (good and bad) back to the presence or the absence of teacher moves.