Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

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Resource | Resource Type Grade Level | Rating |
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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 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 100 grid has a variety of open-ended uses. Users can "make" as many counters as they choose from among three different kinds, and then drag them onto the grid, allowing any number to be covered by up to 3 different markers at one time. An Ideas page offers possible tasks and games suited to the applet. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5 | |

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 flash applet supports student development of the concept of functions through the use of an input/output or function table. Students select from among three activities: "What is the Output?”, "What is the Input?" and "Find the Function!" For each activity, the user clicks on the empty box and fills in the missing answer. Feedback is provided with a check answer button and if the response is incorrect, a hint is displayed to help when the student tries again. | Activity, Interactive Media Grade Level: 3, 4, 5 | |

This open-ended interactive Flash applet can be used in many ways to develop numeracy concepts and skills. It provides three highlight colors, a hide or reveal feature, and the ability to vary the start number and the increment size. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5, 6+ | |

This versatile interactive applet helps students learn to skip count, practice multiplication facts, and discover number patterns. Users select the number to count by and the starting number. In Practice mode the user clicks on the respective numbers in order. In Show mode the applet displays all numbers in the chosen counting sequence immediately. In Animate mode numbers in the counting sequence are highlighted in order one at a time. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This activity for the interactive white board (free access with registration) provides an opportunity for learners to practice building the fact family sets to reinforce the inverse relationship between multiplication and division. A set of three numbers are displayed and the learner drags the numbers and the operation down into the spaces to create a number fact (equation). The goal is to find all four facts in the family. | Activity, Interactive Media Grade Level: 3, 4, 5 |