Operations and Algebraic Thinking

Work with equal groups of objects to gain foundations for multiplication.

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This 51-page pdf document demonstrates the connections between the CCSS content standards and the mathematical practice standards. It is a compilation of research, standards from several states, instructional strategies, common misconceptions, and examples for each standard at the grade 2 level. It is intended to help teachers understand what each standard means in terms of what students must know and be able to do. Additional flip books are cataloged separately for grades K-1 and 3-5. | Instructional Strategy, Reference Materials Grade Level: 2 | |

This web page provides links to resources aligned to the CCSS that guide and support second grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS), Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks developed by the Noyce Foundation are included. The tasks were designed to measure students’ ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. They include the scoring rubric, student responses, and discussion of student understanding and misconceptions. Resources are listed for specific grade 2 standards and are also organized by progression for an alternate search route. | Assessment, Instructional Strategy, Problem Set, Reference Materials, Video Grade Level: 2 | |

This web page contains links to a video and several downloadable pdf files documenting the efforts of a third grade class to prove a set of conjectures about even and odd numbers. Included are a 4-minute Blue Stream video segment in which students discuss a classmate's conjecture that the sum of two odd numbers always equals an even number, a document providing background information on the investigation that led to the discussion, a transcript of the video, and the teacher's journal entry reflecting on the discussion and its implications. | Activity, Demonstration, Video Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This interactive Flash applet supports the exploration of early number. A child or teacher can place a number of objects on the screen and then move the objects to group them, drag them onto a number line or track, into a hoop to create sets of objects, or into a 10 by 10 grid. This applet lends itself well to group work with a projector. Clicking on the info button allows the user to mouse over items to learn how to use them. | Activity, Interactive Media Grade Level: K, 1, 2 | |

This collection of videos allows viewers to observe students as they are learning and to examine their work on a three-part lesson involving emergent multiplication concepts. A grade 2 teacher and her mentor analyze different strategies and models that children use to solve problems as they develop big ideas in mathematics, as well as teaching techniques that foster that development. The resource includes relevant video clips of Doug Clements and Lucy West, a Viewer's Guide, and organizers. | Activity, Instructional Strategy, Video Grade Level: K, 1, 2, 3, 4, 5 | |

This problem helps learners become more familiar with odd and even numbers and addition facts within five. By challenging them to justify their findings, it also develops reasoning and communication skills. The problem displays 9 dominoes and asks the student to sort them according to parity, and then into pairs totaling 5 pips. It poses questions that stimulate thinking about basic number concepts. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to an interactive Dominoes Environment (cataloged separately). | Activity Grade Level: K, 1, 2 | |

This narrative document describes the progression of Counting and Cardinality and Operations and Algebraic Thinking across the K-5 grade band. It is informed both by research on children's cognitive development and by the logical structure of mathematics. The document discusses the most important goals for elementary students that of understanding and using numbers. The focus is on the basic operations—the kinds of quantitative relationships they model and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships. | Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5 | |

This virtual manipulative is a Java applet that allows students to explore concepts in whole number operations and fractions, just as they would with a physical manipulative such as Cuisinaire Rods. The user can add bars of length 1 to 10 to the workspace, change their color, and move, duplicate, or remove them. Instructions for using the applet and teaching ideas for parents/teachers are available through the links at the top of the page. | Activity Grade Level: K, 1, 2, 3, 4, 5, 6+ | |

In this 39-slide slideshare presentation students are guided through the process of using repeated reasoning to discover the number of apples in a specific number of bags. This slideshare presentation was developed by the Illustrative Mathematics Project to illustrate CCSS-SMP 8. Throughout the slideshare student and teacher dialogue is presented along with commentary by two observers. | Lecture/Presentation, Reference Materials Grade Level: 1, 2 Resource is part of a PD collection | |

This document provides descriptions and examples of what each Mathematics Common Core standard means a Grade Two student will know, understand and be able to do. This "unpacking" of the standards provides instructional guidelines and was developed to assist North Carolina educators teach the Mathematics Common Core (Standard Course of Study). | Reference Materials Grade Level: 2 |