Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

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This 75-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 4 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-3 and 5. | Instructional Strategy, Reference Materials Grade Level: 4 | |

This web page provides links to resources aligned to the CCSS that guide and support fourth grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) for the Noyce Foundation, Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks developed by the Noyce Foundation are also included. The performance tasks were originally designed to measure students' ability to solve non-routine problems and then to explain and justify their solutions. The task scoring rubric, student responses, and discussion of student understanding and misconceptions are provided to improve instruction. Resources are listed for specific grade 4 standards and are also organized by progression for an alternate search route. | Activity, Instructional Strategy, Problem Set, Reference Materials, Video Grade Level: 4 | |

This page provides examples of 4th Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for the 4th Grade Number Activities listed are in PDF format. | Activity, Game Grade Level: 4 | |

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 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 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 document provides descriptions and examples of what each Mathematics Common Core standard means a Grade Four 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: 4 | |

This applet demonstrates operations with whole numbers on a number line. The student selects an operation and the applet represents an example. It helps students understand the commutativity of multiplication, remainders in division, inverse operations, and the relationships between operations. | Activity, Interactive Media Grade Level: K, 1, 2, 3 | |

Teachers and students can use this interactive Java applet to model and carry out arithmetic operations on the number line. Users manipulate the size, position, and direction of color bars to represent addition, subtraction, multiplication and division with whole numbers, integers and fractions. Options include the ability to zoom in and out, change the colors of the bars, and adjust the step size of the bars and number line increments. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

In this series of videos (16 clips, 1-10 min each), math coach Becca Sherman works with a fourth grade class in developing concepts of equal groups, multiplication, division, and the relationships among them. She employs multiple models, including the "Singapore Bar Model," and facilitates student discussion, allowing her to assess students understanding of the language and the math involved. Included are teacher commentary, video transcripts, student work samples, and a video of debriefing among colleague observers. | Instructional Strategy, Video Grade Level: 3, 4, 5 Resource is part of a PD collection |