Operations and Algebraic Thinking

Add and subtract within 20.

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This 46-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 1 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 and 2-5. | Instructional Strategy, Reference Materials Grade Level: 1 | |

This web page provides links to resources aligned to the CCSS that guide and support first 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 activities were designed to measure students' ability to solve non-routine problems, explain and justify their solutions, and promote high level thinking skills. Resources are listed for specific grade 1 standards and are also organized by progression for an alternate search route. | Instructional Strategy, Problem Set, Reference Materials Grade Level: 1 | |

This problem with multiple solutions offers an opportunity for students to practice simple addition and subtraction, work with number sentences (equations), and develop systematic work habits. Given cards containing the addition, subtraction and equal signs along with the digits 2, 4, 6, and 8. solvers are challenged to find as many ways as possible to arrange some or all seven cards to create true statements. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, printable cards (pdf) and a link to an interactive Flash applet. | Activity, Interactive Media Grade Level: 1, 2 | |

This interactive Java game, similar to Connect Four, helps students develop game strategy and fluency with number facts. Two players each try to connect four game pieces in a row (vertically, horizontally or diagonally) before the opponent does by correctly answering problems. For each game players can choose whole numbers and/or integers as well as the operation(s) – addition, subtraction, multiplication, division. They can also select the difficulty level and the time limit for each problem. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

This 8-page monograph explains bansho, a research-informed instructional strategy for mathematical communication and collective problem-solving. Following a brief overview, the article outlines how bansho can be used to plan and implement an effective three-part problem-solving lesson. Bansho can be incorporated into collaborative planning sessions, in which teachers work with partners or in groups within communities of practice to learn about mathematics for teaching. The author provides a sample grade 2 lesson on the development of multiplication concepts and a list of references. | Instructional Strategy, Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5 Resource is part of a PD collection | |

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet. | Activity, Instructor Guide/Manual, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

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 | |

In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately). | Activity, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

This interactive 100 grid has a variety of open-ended uses. Users can "make" as many counters as they choose from among three different kinds, and then drag them onto the grid, allowing any number to be covered by up to 3 different markers at one time. An Ideas page offers possible tasks and games suited to the applet. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5 | |

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 |