Common Core’s Mathematical Practice 2, Reason abstractly and quantitatively, calls for students to make sense of quantities and their relationships in problem situations. They are able to translate a problem context into models, numbers and symbols that they can manipulate; they can interpret the meaning of numbers, symbols and units in their work in terms of what they represent in the original problem. This collection includes mathematical tasks and problems that provide opportunities for children to develop reasoning in a variety of ways, and a tool for creating visual models of problem situations. A companion Professional Development collection includes resources to help teachers and math specialists understand the intent and scope of MP 2 and plan for successful implementation.
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.
The resources in this collection are challenging puzzles that can be solved offline, and that call for some assembling and/or manipulating by the learner. The collection houses numerical, spatial and logic puzzles. The numerical puzzles not only develop number and operation sense, but involve reasoning skills as well. Some spatial puzzles involve working with shapes and some with transformations. Several resources suggest strategies for introducing and implementing puzzles in the classroom. Mathlanding also hosts a classroom collection of online, Interactive Puzzles.
The resources in this collection are challenging interactive puzzles for use on the computer or interactive whiteboard. The collection houses numerical, spatial and logic puzzles. Several puzzles make connections with science and other STEM topics. Some spatial puzzles involve working with shapes and some with transformations. The numerical puzzles not only develop reasoning skills but also provide repeated practice in basic arithmetic. Several resources suggest reasons for teaching with puzzles and strategies for introducing them into the classroom.
This collection of resources helps to develop algebraic thinking skills for K-2 students. The interactive games and activities emphasize pattern recognition and logical thinking. One activity focuses attention on the patterns in a hundred chart while several others emphasize shape and/or color patterns. Several balance activities introduce basic ideas about equality. Use these resources to begin to build mathematical thinking skills in young students.
This collection of resources helps students develop skill and understanding with measuring. Content topics include length, area, perimeter, volume, weight, time, money, angle, and circle measures. Learning resources include lesson plans, activities, interactive media, investigations, and games. Additional resources are available in two professional development collections on measurement, one for K-2 and the other for 3-5.
The resources in this collection help students develop fluency with number facts. These resources strive to deepen mathematical thinking, develop problem solving, and encourage reasoning and strategic thinking. They take advantage of patterns and number sense. By employing a variety of strategies and representations, they help students make connections, thereby improving retention and transferability. Additional resources for educators can be found in a companion Professional Development collection, "Developing Fact Fluency."
This collection of resources helps students develop geometric thinking about shape and space in mathematical and real-world contexts. Students will gain knowledge and rich conceptual understandings of two- and three-dimensional shapes, patterns, transformations, symmetry, and visualization. Learning resources include interactive media, videos and games for both primary and upper elementary grades.
This collection has lesson plans and interactive whiteboard tools for teaching equivalent fractions. There are also games and interactive activities in which students create and use various models associated with fractions. Some resources provide students with practice in renaming and simplifying. After a few directions or demonstrations, students will be able to use many of these activities independently.
This collection of resources includes tools that teachers can use when introducing and modeling operations with fractions. These handy tools can be used for whiteboard demonstrations and some also provide students with opportunities to manipulate the models. Additional resources include solving word problems with fractions and estimation using benchmark fractions.
Use the resources in this collection to encourage your students to talk about the math they use to play the game or solve the problem. Encourage them to share their thoughts and describe their strategies to one another as they figure out the best moves or steps in a process. Provide students with opportunities to demonstrate their work and explain their reasoning using the language of mathematics. Listen carefully as your students interact with one another to exchange ideas, organize their thoughts, present their arguments and consider the suggestions of their classmates. These resources provide you with starting points that engage students in mathematical thinking and communication.
This collection has tools that teachers can use in the classroom, on individual computers or with an interactive white board. You'll find virtual Cuisenaire rods, base ten blocks, pattern blocks, and thinking blocks for whole numbers and for fractions, and an interactive hundreds chart. There are two virtual geoboards, a coordinate one and an isometric one. Two tools enable you or your students to create various types of graphs, and the dynamic paper tool allows you to custom create many types of graph paper for use in your classroom. There are also interactive coordinate graphs.
This collection of resources will help teachers to find interesting and challenging problems that engage students in learning new concepts and developing new stategies. Several teacher packets from the Math Forum @ Drexel University provide a sample problem and all of the information you need to use it with your classes. The other sources include access to a variety of problems appropriate for elementary level children and offer suggestions about how to use them with your students.
This collection of resources will help teachers to find real data and statistics about food, sports, animals, populations, jobs, and other subjects. Teachers will be able to choose real data that is interesting to their students and that connects to content being explored in other subjects.
This collection of resources provides students with practice on basic facts. Teachers may use these games and activities to help students build fluency while also developing logical thinking skills. Several of the games may be played online by two or more players. Some of the resources focus on just one operation while others include several operations. All provide students with engaging ways to practice basic facts.