Operations and Algebraic Thinking

Understand properties of multiplication and the relationship between multiplication and division.

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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 | |

This web site contains information and interactive applets related to our Hindu-Arabic number system. Users learn the history and structure of the system as well as how to count and write numbers. Users can learn and practice various algorithms for whole number computation and explore fractions, decimals and percents in our number system. The site explains various sets of numbers and how they relate to operations. | Activity, Interactive Media, Tutorial, Reference Materials Grade Level: 1, 2, 3, 4, 5 | |

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 interactive Flash applet offers three ways for students to practice basic fact skills related to multiplication and division. Users control the challenge level by choosing the size of the blank multiplication grid displayed by the applet. In Multiply mode users type in the product that completes a multiplication sentence. In Factor mode users click a grid cell that matches a given product. In Divide mode users type in a missing factor in the displayed multiplication sentence. A sound effect and timing feature are optional. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

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 | |

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 9-minute video teaches divisibility rules for the factors 2 through 10. The presenter explains each rule and provides examples. | Lecture/Presentation, Video Grade Level: 3, 4, 5 | |

This Flash applet allows the user to explore the concept of a function using an input-output machine with two operations and options to set and hide or reveal all operations and numbers. A notepad is available for recording inputs and outputs, and a loop function takes the current output as the next input. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

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 |