Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

Showing 11-20 of 47 results | Sort by: |

Resource | Resource Type Grade Level | Rating |
---|---|---|

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 | |

This interactive applet allows a student to visually explore the concept of factors by creating different rectangular arrays for a number. The user constructs the array by clicking and dragging on a grid. The length and width of the array are factors of the number. A student can elect an option of a randomly selected number or the student selects his own number between 2 and 50. Exploration questions are included to promote student discovery of mathematical concepts with factors. | Activity, Interactive Media Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This Sketchpad activity, which opens on Geometer's Sketchpad as well as on iOS with Sketchbook Explorer (cataloged separately), allows students to be informally introduced to a rectangular array model of multiplication in this series of three games. Learners subdivide a rectangular array into strips of size 1, 2, and 5 squares and then skip count to determine the total number of squares in the array. A three-minute movie provides detailed instructions and downloadable PDF of teacher notes and student worksheets are also included. | Activity, Instructor Guide/Manual, Tutorial, Video Grade Level: 2, 3, 4 | |

This virtual manipulative is a Java applet that allows students to explore concepts in whole number operations and fractions, just as they would with a physical manipulative such as Cuisinaire Rods. The user can add bars of length 1 to 10 to the workspace, change their color, and move, duplicate, or remove them. Instructions for using the applet and teaching ideas for parents/teachers are available through the links at the top of the page. | Activity Grade Level: K, 1, 2, 3, 4, 5, 6+ | |

In this 28-minute professional development video, teachers focus on geometry and spatial relations by having students explore shapes that tessellate and have the same area. Teachers from different grade levels collaborate on what they want their students to be able to understand and accomplish. Viewers can watch how a 3rd-grade teacher guides his students in understanding area through the application of tessellations. Support Materials includes a Sidewalk Capers Lesson Plan. | Activity, Lesson Plans, Video Grade Level: 3, 4, 5 | |

This activity tool for the interactive white board (free access with registration) displays all the factor pairs a number has in an organized list after users choose a number and then press 'set'. When the numerical expression is clicked, an array of dots is shown to the left. Learners can relate the arrays to the times table by looking at the multiplication expressions shown at the side. | Activity, Interactive Media Grade Level: 3, 4 | |

This brief article advocates the use of arrays to model the commutative and distributive properties as well as the inverse relationship between multiplication and division. The author explains how arrays also help children form mental pictures that support their memory and reasoning. | Instructional Strategy, Reference Materials, Article Grade Level: 2, 3, 4, 5 Resource is part of a PD collection | |

This 60-page research-based guide provides the best practices for teaching students with learning difficulties in math and reading. The highlighted interventions include supporting cognitive processing, intensifying instructional delivery, increasing learning time, and reducing group size. The article also provides suggestions for further reading and three examples of how lessons can be modified to include these recommendations. | Instructional Strategy, Lesson Plans, Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5, 6+ Resource is part of a PD collection | |

In this problem students practice addition and subtraction (and possibly multiplication) while developing systematic work strategies. Given two types of ladybirds, each with either 4 or 7 spots, learners explore ways of combining them to achieve different total numbers of spots. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and links to related games. | Activity Grade Level: 1, 2, 3 | |

This three-page article describes a teaching approach to prime numbers which helps students appreciate them and understand their properties, and does more than just define and identify them. It also develops composite number concepts. It is supported by a Flash application (see Related Resources). Register as a FREE Associate Member to access the article. | Activity, Instructional Strategy, Lesson Plans, Reference Materials, Article Grade Level: 3, 4, 5, 6+ |