Operations and Algebraic Thinking

Add and subtract within 20.

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This interactive Flash applet provides a customizable set of dominoes that users can manipulate to play games or solve puzzles. It can be used with an interactive whiteboard to facilitate group work. Users can determine the size of a set (up to double-9), remove individual dominoes, rotate and move them, and change their size. The Teachers' Notes page includes a link to page containing domino games and challenges (cataloged separately). | Interactive Media 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 | |

In this problem students practice basic addition and subtraction skills along with logical reasoning to satisfy three interdependent conditions. Solvers use the clues provided to determine the number of eggs in each of three baskets. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, a PowerPoint presentation, and vocabulary cards (pdf). | Activity Grade Level: 1, 2 | |

This series of activities can be used to introduce number sequences and patterns and to reinforce parity (even and odd numbers) and its application in addition. The resources are intended for use on an interactive whiteboard but may also be used individually or in small groups. They can be accessed online or downloaded (zip) to a local computer. The pack includes teacher notes, background information on the content, and a student worksheet. | Activity, Interactive Media, Lesson Plans Grade Level: 1, 2, 3 | |

This article proposes a structured set of lively, brief, daily exercises designed to help children master number facts and mental math skills. Each day's practice focuses on a small, highly focused, manageable, and strategically selected set of facts or skills that builds directly on the previous days' learning. Related resources (Practice and videos) are cataloged separately. | Activity, Instructional Strategy, Reference Materials, Article Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection | |

This Tetris-like interactive game develops estimation fluency with addition and subtraction. Users choose either operation, or a combination of both, and a difficulty range (0-20, 0-200, 0-2000). Sums and/or differences drop from the top of the field, and players use arrow keys to indicate whether they belong below or above the center of the range, or exactly on it. Created in The Netherlands, the applet contains a few Dutch words, but students will quickly figure out their meanings. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This problem with multiple solutions provides an opportunity for students to practice subtraction while developing logical thinking and systematic record-keeping strategies. Given a pyramid of six circles, solvers are challenged to arrange the numbers 1 - 6 so that each number is the difference between the two numbers just below it. Children may use pencil and paper or the interactive Flash applet provided. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, work sheets (pdf), and a link to a more challenging version. | Activity, Interactive Media Grade Level: 1, 2, 3 | |

This page provides examples of First Grade Number (Operations and Algebraic Thinking, and Number and Operations in Base Ten) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files listed are in PDF format. | Activity, Game Grade Level: 1 | |

This interactive Flash version of the familiar game Concentration ("pelmanism" in the UK) helps a single user practice addition facts while developing memory and concentration skills. The player can choose an array of 16, 20, or 24 cards, which appear face down. The goal is to flip two cards at a time to match all the 2- or 3-addend expressions with their sums as efficiently as possible. A scoring feature discourages random guessing. Printable versions of the game cards are available to download. | Activity, Game, Interactive Media Grade Level: 1, 2, 3 | |

In this brief article NCTM President Linda Gojak encourages educators to reconsider the notion of fluency with regard to number facts, procedures, and other topics. She elaborates on the NCTM's position of broadening the definition to include conceptual understanding and flexible thinking. | Instructional Strategy, Reference Materials, Article Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection |