Operations and Algebraic Thinking

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

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Resource | Resource Type Grade Level | Rating |
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This interactive Flash book, one in Greg Tang's series that combines math with poems and pictures, challenge learners to calculate how many objects are in each scene by thinking quickly in groups rather than counting. This more advanced book focuses on smart grouping strategies that make computations faster, easier and more accurate by looking for patterns, symmetries and rearrangements. | Activity, Interactive Media, Illustration, Video Grade Level: 3, 4, 5 | |

This Technology Problem of the Week (tPoW) challenges students to explain how to use the distributive property to calculate a food purchase. It links to the Java applet "Demonstration of the Distributive Law." Solve and explain your solution; download hints and answer checks. Free registration is required. | Experiment/Lab Activity Grade Level: 3, 4, 5 | |

This document provides descriptions and examples of what each Mathematics Common Core standard means a Grade Three student will know, understand and be able to do. This "unpacking" of the standards provides instructional guidelines and was developed to assist North Carolina educators teach the Mathematics Common Core (Standard Course of Study). | Reference Materials Grade Level: 3 | |

This 7-minute video highlights patterns in the multiplication table and offers strategies for learning multiplication facts. The presenter makes effective use of color on a multiplication grid. | Lecture/Presentation, Video Grade Level: 3, 4, 5 | |

This one-page article describes and illustrates how arrays can be used to represent many number concepts, including building multiplication facts, commutativity, parity (odd/even), and exploring factors, prime numbers, and square numbers. | Instructional Strategy, Reference Materials, Article Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection | |

This interactive Flash version of the familiar Concentration game ("pelmanism" in the UK) helps a single user practice multiplication 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 pairs of factors with their products as efficiently as possible. A scoring feature discourages random guessing. Users can choose to work with factors in three ranges: 2x-10x, 2x-21x, or 11x-21x. Printable versions of the game cards are available to download. | Activity, Game, Interactive Media Grade Level: 3, 4, 5 | |

This 4-lesson unit assumes student understanding of multiplication; it uses patterns, properties of the operation, and games to develop fact fluency. The unit included student recording sheets, questions for students and teachers, links to online applets, and suggestions for assessment and extension. | Activity, Interactive Media, Lesson Plans, Unit of Instruction Grade Level: 3, 4, 5 | |

This lesson helps students develop conceptual understanding of 2-digit multiplication. Students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and carry out paper-and-pencil calculations from the arrays. Included are student activity sheets, a link to a supporting online applet, and extension suggestions. | Activity, Lesson Plans Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This open-ended interactive Flash applet helps students develop operation and number sense, facility with number facts, and understanding of equations. Users designate single-digit whole numbers or integers and operations on both sides of an equation and test for balance. Users can enter numbers by using the keyboard or arrow buttons or by dragging number tiles. Each element can be hidden and a seesaw may be toggled on/off. Teachers may use this applet to lead instruction, or students may use it independently to perform specific investigations or explore freely. Supplementary documents include Objectives, containing teaching suggestions, and a student recording sheet. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

This interactive game develops fluency and flexibility with whole number operations. Each round presents a card (flippo) with four single-digit whole numbers. The player uses each number exactly once with the interactive calculator to arrive as close as possible to the target number 24. | Activity, Game, Interactive Media Grade Level: 3, 4, 5 |