Operations and Algebraic Thinking

Analyze patterns and relationships.

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This 68-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 5 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-4. | Instructional Strategy, Reference Materials Grade Level: 5 | |

This web page provides links to resources aligned to the CCSS that guide and support fifth grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS), Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks 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 5 standards and are also organized by progression for an alternate search route. | Instructional Strategy, Problem Set, Reference Materials, Video Grade Level: 5 | |

This page provides examples of 5th 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 5th Grade Number Activities listed are in PDF format. | Activity, Game Grade Level: 5 | |

This set of three interactive challenges from the Annenberg Teachers' Lab has learners investigate properties of squares and groups of squares. In Quilts learners construct quilt blocks exhibiting four types of symmetry. In Taxicab Treasure Hunt, they work with distance and direction on a grid of city streets. Finally, in From Corner to Corner learners measure the sides and diagonals of squares looking for an approximate relationship between the two measures. Background discussion and NCTM standards information is included. | Activity, Game, Interactive Media Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This problem, from the collection of Aunty Mathilda challenges, promotes algebraic thinking and problem solving strategies. When Mathilda was ten years old her rich aunties wanted to give her a gift of money for her birthday but she must first decide if she would rather have one more silver dollar then she received last year on her birthday or twice as many dimes then she received last year. Aunty Mathilda's nephew believes she made the wrong decision. Included are links to an easier challenge and to a harder one, and additional background support: alignment to the CCSS standards, explanations, literature connections and extensions regarding the challenge. | Activity Grade Level: 2, 3, 4, 5 | |

In this formative assessment lesson students identify patterns (both linear and exponential) in a realistic context. They may solve this problem through a variety of strategies, providing opportunities for groups of students to share and critique various problem solving approaches. | Activity, Lesson Plans Grade Level: 4, 5, 6+ | |

In this activity, learners decipher a page from the Dresden Codex, one of the few Mayan books still in existence. By thinking like an archaeologist, students combine their mathematical abilities with some basic logic and trial-and-error investigation to figure out what the codex means. In the course of this explorations, participants discover: How archaeologists have figured out what Mayan documents mean. How the Mayan system of counting is like ours, and how it is different. How Mayan beliefs were tied to their understanding of mathematics. | Activity, Instructor Guide/Manual, Project, Reference Materials, Article Grade Level: 4, 5, 6+ | |

This sample constructed response problem for grade 3-5 students provides an opportunity to analyze patterns and develop algebraic thinking in the context of a telephone chain. It includes suggestions for adjusting the challenge level and a task-specific rubric with annotated samples of student work at each level. Free registration allows users to download a 9-page print-friendly version (pdf). | Assessment, Activity Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This webpage features a STEM investigation developed by teachers Carrie Lewis and Kelly Steele to strengthen understanding of patterns with grade 5 students. After observing and analyzing dance videos, teams of students create their own routines based on numerical patterns. The page includes a downloadable (pdf) lesson plan, student handouts, and teacher tools, and features a 9-minute video describing the project and demonstrating students at work. | Activity, Lesson Plans, Unit of Instruction, Video Grade Level: 4, 5, 6+ | |

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 |