Operations and Algebraic Thinking

Write and interpret numerical expressions.

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This article (pdf) describes a game for 2-5 players that develops fluency with whole number operations. The game is played on a non-standard 8 by 8 number grid with three dice. Players take turns rolling the dice and forming expressions that result in a target number on the grid. The name "Contig" refers to the fact that players score points by claiming a number adjacent to occupied squares. A Contig game board is provided as well as a game board (same numbers rearranged), rule sheet and scoring sheet for Number Neighborhood, an alternative name for the game. The author suggests game variations and discussion questions. | Activity, Game, Reference Materials, Article Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This 8-page article from Teaching Children Mathematics discusses how overgeneralizing commonly accepted practices, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students’ math careers. The authors provide a table of some "expired" mathematical language and suggest more appropriate alternatives. | Instructional Strategy, Reference Materials, Article Grade Level: K, 1, 2, 3, 4, 5, 6+ Resource is part of a PD collection | |

This Java applet game promotes mental math and strategic thinking skills using a card from Suntex's 24 Game. The player is presented with four numbers (1-9) on a card. The goal is to manipulate each of the four numbers only once so that the end result is 24. Addition, subtraction, multiplication, division and/or parentheses maybe used and the player must be able to enter the expression using the online calculator. | Activity, Game, Interactive Media Grade Level: 4, 5 | |

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 Flash game develops students' computational fluency and flexibility. It can be played alone or with others. Players choose 6 face-down number cards, and the applet provides a target number. Number cards include one each of 25, 50, 75, and 100, and multiple copies of 1 to 10. The goal is to use the selected numbers and the four basic operations (addition, subtraction, multiplication, division) to arrive at the target. Players can ask the applet to Show a Solution, although others may be possible. Several rule and scoring variations are suggested. A full screen option facilitates use on an interactive board. (This game is not self-checking.) | Activity, Game, Interactive Media Grade Level: 3, 4, 5 | |

This interactive Java learning tool allows a teacher to demonstrate and explore the distributive property with expressions in the factored form (a + b) (c + d) using a matrix multiplication method with students. Sliders determine the number values from 20 to -20 with increments of one-tenth. Check boxes show or hide the factored form, starting matrix values, matrix, products in the matrix, and solution. | Demonstration, Interactive Media Grade Level: 3, 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 | |

This interactive Java learning tool, constructed using GeoGebra, allows a teacher to demonstrate and students to explore the distributive property of multiplication over addition. Students see the relationship between two different algebraic expressions: a(l+w) and a(l) + w with side-by-side diagrams that allow for comparison. The models shown can be determined by checking boxes and the sliders change the values of each variable. | Activity, Interactive Media Grade Level: 4, 5 |