Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.

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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 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 | |

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 | |

With this flexible Flash applet students can explore a wide range of concepts, including addition and subtraction, factors and multiples, fractions, ratios, and combinations. Users place, move and rotate virtual Cuisenaire Rods on a grid which can be enlarged, reduced, moved or printed. It contains a link to page of challenges which can take advantage of this tool. | Activity, Interactive Media Grade Level: 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 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 page contains thirty-three problems involving algebraic thinking from the Port Angeles School District in Washington state. Links to state GLEs and revised standards are provided. Topics covered include patterns, and concepts of equality and inequality and applications of arithmetic. | Problem Set Grade Level: K, 1, 2 |