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 | |

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 Wolfram Demonstration helps students visualize the relationship between multiplication and the area of a rectangle. On a 10x10 multiplication table, with 1 in the lower left and 100 in the upper right, users adjust the size of a rectangle by dragging a vertex or sliders, or by choosing a product from a pulldown list. The resulting rectangle highlights the width, height and area (factors and product) as well as other equivalent areas (products) on the board, illustrating commutativity and multiple factor pairs. Wolfram CDF Player, a free download, is required to view this resource. | Activity, Interactive Media Grade Level: 3, 4, 5 Resource is part of a PD collection | |

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 applet helps students develop fluency and flexibility with numbers. At each of 6 difficulty levels the user is presented with 8 target numbers and a partial set of keys on a basic calculator (does not follow order of operations). The goal is to use the given keys to make as many of the target numbers as possible within the 3-minute time limit. Some levels include memory keys. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

This interactive Flash game helps students develop strategic thinking and number sense while practicing basic operations. It is based on the word game Hangman, but uses digits and operations instead of words. Players are presented with an equation missing most of its digits. They try to complete the blanks by guessing the missing digits (0 - 9) before making four incorrect guesses and thereby releasing the catapult. Difficulty increases over four rounds of equations. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

In this 4-minute video, educators can watch a teacher deliver a fourth grade lesson on using number sense, arrays, and simpler calculations to solve a more complex problem, called a cluster problem. Watch this teacher check for understanding of multiplicative distribution and the use of arrays. | Lesson Plans, Video Grade Level: 3, 4, 5 Resource is part of a PD collection |