This collection of resources helps to guide students through the process of constructing viable arguments and critiquing the reasoning of others (CCSS Practice Standard 3). Students learn to use logical reasoning to solve problems and to explain their thinking, as well as to consider and reflect upon solutions offered by others. Initially teachers may need to model these practices but with experience, students eventually will be able to complete many of the activities independently. Additional resources for educators can be found in a companion Professional Development collection, "Incorporating CCSS Practice Standard 3."
The resources in this collection present students with problems, lessons, and activities in which they will create or use a model in order to understand and communicate the mathematical concept (CCSS Practice Standard 4). Students learn to apply math to everyday life by working with concrete, pictorial, and symbolic representations of the problems encountered in real situations. Additional resources for educators can be found in a companion Professional Development collection for CCSS Practice Standard 4.
The resources in this collection include problems, lessons, and activities that prompt students to consider the strengths and weaknesses of available tools when solving a problem and to make strategic choices about the tools that they will utilize (CCSS Practice Standard 5).
The tools that students may utilize in mathematics are wide in variety, but all contribute to their mathematical knowledge and understanding when used appropriately. Some of the tools students might use include calculators, paper and pencil, rulers and other measuring tools, connecting cubes, base ten blocks, spreadsheets and other dynamic software, online applets, and mobile apps.
Additional resources for educators can be found in a companion Professional Development collection for CCSS Practice Standard 5.
Common Core’s Mathematical Practice Standard 6, Attend to Precision, calls for students to be clear in their reasoning, calculation, and communication through the precise use of words, symbols, units of measure, mathematical expressions, and processes. They recognize various levels of precision and apply them appropriately; they calculate accurately and efficiently and label axes of graphs appropriately.
These resources have been selected to help teachers and math specialists implement MP 6 in the classroom. They include tools and references to be used by students themselves, mathematical tasks and problems that provide opportunities for children to attend to precision in a variety of ways, and lessons and techniques for teachers to use with students to foster these habits of mind.
A companion Professional Development collection includes resources to help teachers and math specialists understand the intent and scope of MP 6 and plan for successful implementation.
The resources in this collection present students with problems, lessons, and activities in which they must look for and make use of structure in order to determine the answer and/or develop the mathematical concept (CCSS Practice Standard 7). Students learn to identify the structure of patterns, data displays, numerical quantities, operations, and geometric figures. Additional resources for educators can be found in a companion Professional Development collection, "CCSS Practice Standard 7."
The resources in this collection provide activities in a variety of math content areas that offer students rich problem solving experiences and afford opportunities to develop the habits of looking for and expressing regularity in repeated reasoning. Some resources provide tasks that call for repeated calculations and lend themselves to generalizations; others encourage pattern recognition and shortcut calculations. Some tasks require students to evaluate different strategies and monitor their own solving process. Educators looking for ways advance their own expertise in these areas should draw upon the companion PD collection for Practice Standard 8.