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 interactive Flash applet includes single-step and multi-step whole number word problems at two levels: (1) addition and subtraction, and (2) multiplication and division. Students enter their answers to displayed problems and are either rewarded with a "home run" or given the option for a hint to help them correct an error. If, after asking for help, a student still answers incorrectly, the program provides a solution. The difficulty level gradually increases throughout any round of 15 (level 1) or 12 (level 2) problems. | Activity, Interactive Media Grade Level: 2, 3, 4, 5 | |

This problem from Figure This! helps students develop problem solving skills and algebraic thinking while practicing number operations. Students are challenged to use combinations of stamps of two different denominations to make a specific total. The "Try These" feature provides further challenges. The Answer page offers four different solution approaches. "Did You Know?" presents several related facts. The activity includes a page of print and Internet resources. Figure This! also provides information and support for families. | Activity Grade Level: 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 lesson plan uses the book Math Curse [Jon Scieszka and Lane Smith]. Students will use estimation, measurement and scaling skills to make predictions and solve problems involving length. | Lesson Plans Grade Level: 4, 5, 6+ | |

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 |