Operations and Algebraic Thinking

Multiply and divide within 100.

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This article (pdf) describes a game for 2-5 players that develops fluency with whole number operations. The game is played on a non-standard 8 by 8 number grid with three dice. Players take turns rolling the dice and forming expressions that result in a target number on the grid. The name "Contig" refers to the fact that players score points by claiming a number adjacent to occupied squares. A Contig game board is provided as well as a game board (same numbers rearranged), rule sheet and scoring sheet for Number Neighborhood, an alternative name for the game. The author suggests game variations and discussion questions. | Activity, Game, Reference Materials, Article Grade Level: 3, 4, 5 Resource is part of a PD collection | |

In this 4-minute video teacher Jan Saul demonstrates how she incorporates music and kinesthetic activity in warm-up activities in her grade 3 class. The songs involve skip-counting, laying the foundation for memorization of multiplication facts. The page included a link to the vendor of the recordings and a transcript of the video (doc). | Activity, Instructional Strategy, Video Grade Level: 3, 4 | |

This free iOS app provides practice with multiplication facts in an arcade-like format. Students choose from among 10 levels (2 to 10 times tables and mixed times tables) and identify products of given factors in order to free trapped monkeys. Scoring rewards both accuracy and speed. | Activity, Interactive Media, Mobile App Grade Level: 3, 4, 5 | |

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 | |

In this 1.5-minute video, mathematician Dr Ria Symonds describes a characteristic of numbers such as 7, which after repeated squaring of digits and summing of the squares, result in the number 1, the first natural number. This introduction invites an investigation to find other "happy" numbers, and to find out what happens to "sad" numbers. | Activity, Video Grade Level: 3, 4, 5 Resource is part of a PD collection | |

In this problem students practice basic number facts while developing systematic thinking and understanding of properties of numbers and operations. Four calculations are presented in a square configuration; solvers arrange the numbers 1 through 8 to make the calculations correct. An interactive applet is provided. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a downloadable pdf of the puzzle. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus. | Activity, Instructional Strategy, Lesson Plans, Unit of Instruction Grade Level: 3, 4, 5 | |

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 |