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 unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus. | Activity, Instructional Strategy, Lesson Plans, Unit of Instruction Grade Level: 3, 4, 5 | |

This interactive Flash applet helps students develop the concept of equal groups as a foundation for multiplication and division. The applet displays an array of dots, some of which are covered by a card. Student use the visible number of rows and columns to determine the total number of dots. Clicking on the card reveals the full array, and a voice announces the total. | Activity, Interactive Media Grade Level: 2, 3, 4 Resource is part of a PD collection | |

This familiar game can be played by one or two players taking turns. Players choose to match equivalent representations of numbers, shapes, fractions, or multiplication facts. The game can be played in clear pane mode, or for added challenge, with the windows closed. | Game Grade Level: K, 1, 2, 3, 4, 5 | |

This is the NCTM Android app of their familiar on line Illuminations game, "Concentration" ( cataloged separately ) which challenges a user to match whole numbers, shapes, fractions, or multiplication facts to equivalent representations. This game can be played by one or two players taking turns and can be played in clear pane mode, or for added challenge, with the windows closed. | Game, Mobile App Grade Level: K, 1, 2, 3, 4, 5 | |

This NCTM iOS app of the familiar online Illuminations game, "Concentration" (cataloged separately) challenges a user to match whole numbers, shapes, fractions, or multiplication facts to equivalent representations. This game can be played by one or two players taking turns and can be played in clear pane mode, or for added challenge, with the windows closed. | Game, Mobile App Grade Level: K, 1, 2, 3, 4, 5 | |

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 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 Sketchpad activity, which opens on Geometer's Sketchpad as well as on iOS with Sketchbook Explorer (cataloged separately), allows students to be informally introduced to a rectangular array model of multiplication in this series of three games. Learners subdivide a rectangular array into strips of size 1, 2, and 5 squares and then skip count to determine the total number of squares in the array. A three-minute movie provides detailed instructions and downloadable PDF of teacher notes and student worksheets are also included. | Activity, Instructor Guide/Manual, Tutorial, Video Grade Level: 2, 3, 4 |