Operations and Algebraic Thinking

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

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This instructional guide (PDF) is for the mobile app Pick-a-Path (both iOS and Android platforms). The guide provides professional development by discussing the math in each level of the game, giving suggestions for classroom use, and recommending related resources from Illuminations. The Pick-a-Path app is cataloged separately and listed as a related resource. | Instructor Guide/Manual Grade Level: 3, 4, 5, 6+ | |

This article focuses on the role and techniques of effective ("distributed") practice that leads to full and fluent mastery of mental mathematics as well as conceptual growth around properties of arithmetic. It lists the essential mental math skills needed for fluent computation at grades 1, 2, and 3. The article describes a number of strategies for developing mental skills and links to pages with more details on others (some not yet complete). While this article refers to the Think Math! curriculum published by EDC, the methods generalize to any program. The Fact of the Day technique and a related video are cataloged separately. | Activity, Instructional Strategy, Reference Materials, Article Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection | |

In this online version of the popular card game, students combine five given number cards, using the four arithmetic operations (addition, subtraction, multiplication, division), to arrive at a target number. This version uses the numbers 1–10 only. Users may ask for a hint or view a possible solution, although there are often multiple solutions. | Activity, Game, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This 5 1/2-minute video explains how to create a factor tree to find the prime factorization of a number. It demonstrates the process for 6, 24, and 525. | Lecture/Presentation, Video Grade Level: 3, 4, 5 | |

This 4-minute video introduces the definition of a prime number and illustrates it through a discussion of factors and composite numbers. It makes use of the definition to explain why 1 is not a prime and ends with a question for the viewer to ponder. | Lecture/Presentation, Video Grade Level: 3, 4, 5 | |

This Flash applet helps students understand prime and composite numbers by visualizing them in terms of their prime factors. Numbers are presented as nested sets of small black dots. When a number has several different prime factors, the factors on the right can be rearranged (dragged) to offer different images of the same number. Click on Launch Primitives to start the applet. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This 7-minute video features Drew Crandall working with his third grade class to develop concepts involving properties of operations and the relationship between multiplication and division. His approach allows students to learn from each other, to construct and revise their own meaning, and to develop communication skills. A downloadable transcript of the video is available (doc). | Activity, Instructional Strategy, Video Grade Level: 3, 4 | |

This interactive Java applet use arrays and three different computational models (Grouping, Common, or Lattice) to help students visualize and understand the process of multiplication of whole numbers. In each method the user drags sliders to adjust the two factors and then observes the resulting changes in the rectangular array and in the respective algorithm and product. | Activity, Interactive Media Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This activity uses Cuisenaire Rods to develop conceptual understanding of factors and multiples and to encourage systematic thinking. Users are shown a train of four different rods and asked to find equivalent trains, each made from rods of just one color. An interactive Flash Cuisenaire applet is provided as an alternative to using real rods. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support. | Activity, Interactive Media Grade Level: 1, 2, 3 | |

In this lesson plan students develop an understanding of early proportionality by helping the Cyberchase kids save money to bid at an auction. Students use line graphs and tables to track their totals and discover the overall relationship between the amount of money needed and the number of days to earn the money. This lesson plan contains two student worksheets, two short video clips, two assessment options, and an answer key. | Assessment, Lesson Plans, Video Grade Level: 4, 5, 6+ |