The Common Core’s Mathematical Practice 6, Attend to Precision, calls for students to be careful in their reasoning, calculation, and communication through the precise use of words, symbols, units of measure, mathematical expressions, and processes. Students recognize various levels of precision and apply them appropriately, for example, by determining when an estimate is sufficient or more appropriate than an exact answer. When an exact answer is called for, they calculate it accurately and efficiently.

The clarity fostered by these habits of mind is a hallmark of mathematical thinking. In addition to the obvious need to communicate clearly with others, being precise per se fosters greater conceptual development and higher order thinking. For example, the confusion many children have with regard to the equal sign has critical implications for their understanding of the larger concept of equivalence, on which much of mathematics is based. Specifying units of measure gives meaning to a calculation and helps a student judge its reasonableness. Labeling graphs helps a student analyze and interpret them. Once they understand the concepts behind computations, we want students to master procedures and algorithms that allow them to solve problems accurately and efficiently, so that more attention can be paid to problem solving and deeper thinking.

Like other Mathematical Practices, MP 6 is best addressed in the context of doing worthwhile mathematics. Rich problems and investigations provide authentic opportunities to apply and hone these dispositions. Students learn to be precise in their communication by hearing their teachers model correct math language and by explaining their thinking to their peers, first with math talk and then in writing, whether through pictures, diagrams, symbols, or words. Problem solving offers a meaningful context in which to develop vocabulary and address aspects of precision in a way that helps learners internalize them and appreciate their importance.

The resources in this collection are intended to help teachers and math specialists understand the intent and scope of MP 6 and plan for successful attainment in the classroom. They include resources that help us interpret the practice and appreciate its importance and videos that illustrate teachers fostering the practice with their students. Several resources offer suggestions for vocabulary development as well as general strategies that promote precision, including explicit modeling, formats for sharing student thinking, and problem solving approaches.

A companion classroom collection, Implementing MP 6: Attend to Precision, includes resources to help teachers foster this practice with their students.

This 17-minute Flash presentation explains CCSS Mathematical Practice 6 and illustrates how it applies in the K-5 classroom. It addresses implications such as understanding the need for precision and clarity in communication and pursuing accuracy in calculations and explanations. It offers strategies for modeling effective communication, introducing new content, developing vocabulary, and understanding units of measure and degree of precision. Sample problems are included. A transcript of the audio is available for download (pdf).

This series of nine articles interprets and illustrates each of the eight Mathematical Practices of the Common Core State Standards as they might be exemplified in grades K-5. The final article sheds light on how curriculum needs to connect the Practices with the Content Standards.

This 8-page monograph discusses the importance of developing student communication in mathematics, both oral and written, and the elements that make communication effective. It describes three approaches for organizing and facilitating students sharing their thinking about problem solving: Gallery Walk, Math Congress, and Bansho (Board Writing). The author provides tips for getting started with these strategies and a list of references.

This 8-page monograph explains bansho, a research-informed instructional strategy for mathematical communication and collective problem-solving. Following a brief overview, the article outlines how bansho can be used to plan and implement an effective three-part problem-solving lesson. Bansho can be incorporated into collaborative planning sessions, in which teachers work with partners or in groups within communities of practice to learn about mathematics for teaching. The author provides a sample grade 2 lesson on the development of multiplication concepts and a list of references.

In his 8-page article Dunston and Tyminski discuss the importance of directly teaching math vocabulary, why this may differ from vocabulary instruction in other content areas, and methods for math vocabulary instruction. The methods for math vocabulary instruction addressed in this article include: The Frayer Model, Four Square, and Feature Analysis. While the scenarios presented in this article deal with middle school students these strategies can be applied to upper elementary students.

In this 7-minute video mathematics education professor Doug Clements argues that some of the difficulty young math students have with geometry and measurement stems from classroom materials that are inexact and misleading. He proposes involving children in diverse exploratory activities that foster spatial reasoning and precision of thought about shapes and their properties.

As part of its NSF-funded research, the NGPM project is exploring the use of PD videos such as these, which focus on the role of math talk in preschool classrooms. The four brief clips (3-5 min. each) in this blog entry show teachers discussing the nature and importance of math talk and demonstrating how they promote it with their students.

This half-hour video includes 18 classroom excerpts from classroom lessons which show students representing, discussing, reading, writing, and listening as vital parts of learning and using mathematics. It shows how communication that arises naturally from rich tasks and experiences fosters understanding of mathematical concepts and development of mathematical language.

The authors of this 5-page article present anecdotal and research evidence that misinterpretation of the equal sign as an operator results in difficulty with the concept of equality. They describe one teacher's efforts to advance the notion that the symbol represents a relationship and several reasons why that is important for students' further mathematical development.

This article summarizes the research of Texas A&M faculty Robert M. Capraro and Mary Capraro comparing students' interpretation of the equal sign internationally and its relationship to achievement in mathematics. The page includes a 1-minute video of Robert Capraro discussing the importance of understanding the concept of equivalence and how misunderstandings arise.

This professional development video clip of students engaged in Common Core Practice Standard #6—attend to precision. The video clip shows two important instances of the idea of precision; that precision is important in their measurements of the circumference and diameter and in their use of vocabulary in context as they discover the relationship between circumference, diameter, circles, and pi. Additional resources include a video transcript, teaching tips, and a link to a professional development reflection activity based upon the video.

This article describes a teaching approach to help students solve word problems and develop the language skills necessary to translate between practical and mathematical statements and situations. The "Headline Stories" approach introduces a scenario and encourages students to produce questions and the language needed to express them. The open-ended problem situations can take many forms and pertain to almost any content. There is a link to two demo Headline stories videos (cataloged separately).

This blog entry provides links to resources and teaching strategies for implementing journal writing in the mathematics classroom. It includes a section entitled "How to Get Elementary Students Writing About Math." The author links to a follow-up page of additional resources.

This 5-minute video follows Carlos and Sara, students in Jennifer Saul's third grade class, as they explain different strategies, both mental and written, for adding multi-digit numbers. These children demonstrate effective presentations skills, while their classmates exhibit the established expectations for being a supportive audience. The page provides reflection questions for the viewer and downloadable supporting materials, including a transcript of the video (doc) and problem solving work samples from Carlos and Sara (pdf).

This professional development video ( video 1) from Minnesota Math and Science Teacher Academy Center in Region 11 presents an algebra training session on justification. Viewers watch Dr. Terry Wyberg, a methods professor at the University of Minnesota, discuss five statements after teachers have had an opportunity to decide if each statement is always, sometimes or never true and a reason why. Dr. Wyberg shares that in math a response of always or never mean you need justification. Justification is central to mathematics and even young children cannot learn mathematics without engaging in justification. He also presents information about the use of math conventions with the use of algebraic representation for his audience.

This 19-page draft document (pdf) offers guidance to K-5 educators in interpreting the CCSS Mathematical Practices for the elementary grades. The first section provides annotations to the original language. The second section integrates those annotations into coherent descriptions of how each practice standard applies in the K–5 classroom.

This 8-page article from Teaching Children Mathematics discusses how overgeneralizing commonly accepted practices, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students’ math careers. The authors provide a table of some "expired" mathematical language and suggest more appropriate alternatives.