Operations and Algebraic Thinking

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

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Resource | Resource Type Grade Level | Rating |
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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. | Instructional Strategy, Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5, 6+ Resource is part of a PD collection | |

This 60-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 3 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-2 and 4-5. | Instructional Strategy, Reference Materials Grade Level: 3 | |

This web page provides links to resources aligned to the CCSS that guide and support third grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) and Problems of the Month, (POM home page is cataloged separately) 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 3 standards and are also organized by progression for an alternate search route. | Instructional Strategy, Problem Set, Reference Materials Grade Level: 3 | |

In this problem learners practice addition, subtraction and multiplication while developing logical reasoning. Solvers apply the given clues along with their understanding of the domino numbering system to determine which dominoes are missing from a set. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, printable sheets of dominoes (pdf), and a link to an interactive Dominoes Environment (cataloged separately). | Activity Grade Level: 3, 4, 5 | |

This problems is an opportunity to explore triangular numbers in the familiar context of decorating a birthday cake with a number of candles corresponding to a child's age. The problem lends itself to systematic strategies and multiple representations. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support. | Activity Grade Level: 1, 2, 3 | |

This sample constructed response problem for grade 3-5 students provides an opportunity to analyze patterns and develop algebraic thinking in the context of a telephone chain. It includes suggestions for adjusting the challenge level and a task-specific rubric with annotated samples of student work at each level. Free registration allows users to download a 9-page print-friendly version (pdf). | Assessment, Activity Grade Level: 3, 4, 5 Resource is part of a PD collection | |

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). | Instructional Strategy, Video Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This financial literacy activity requires students to determine how to spend within a budget. The purpose of this task is to have students solve problems using all four operations and represent their solutions on a bar graph. | Activity Grade Level: 3, 4, 5 | |

This unit contains two lessons which help students develop number sense through activities involving collection, representation, and analysis of data. Students also practice reading and writing large numbers and develop estimation skills. In Lesson 1, Every Breath You Take, students estimate the number of breaths taken during a specified time, experiment, and display real-life data. In Lesson 2, Making Your First Millions, students develop the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition. They analyze situations and identify patterns that will enable them to develop the concept of large numbers. Each lesson includes student activity sheets, an instructional plan, and extensions. | Activity, Experiment/Lab Activity, Lesson Plans, Unit of Instruction Grade Level: 3, 4, 5, 6+ | |

In this 47-minute webinar Grant Wiggins discusses the difficulty students traditionally have in transferring their knowledge to problem solving, especially in standardized testing situations, and how standard math curriculum affects students' perception of mathematics. He describes how real problems differ from typical exercises, and advocates using them as the foundation of a math curriculum to ensure that Standards are met and that students develop into independent problem solvers. His slides are included as a pdf download. | Lecture/Presentation, Voice Recording Grade Level: 3, 4, 5, 6+ Resource is part of a PD collection |