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 math app intended for upper elementary students using the addition and subtraction level and middle school students using all four operations helps players practice their order of operations. This interactive game encourages students to use higher order thinking to use the five numbers and given operations to solve the "target" number by working backwards given the answer but not the equation. The best feature about this math game is that teachers are able to receive immediate feedback of their students’ progress through email. Students do not have to provide an email address in order to play. | Activity, Interactive Media, Mobile App Grade Level: 4, 5, 6+ | |

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 Technology Problem of the Week (tPoW) challenges students to compile a spreadsheet that tracks different savings rates across different time spans, and to then use their accounting work to identify the calendar date when those contributions reach the goal of accumulating 1,000,000 pennies. Solve and explain your solution; download hints and answer checks. Also available in Spanish. Free registration is required. | Problem Set Grade Level: 4, 5 | |

This Java applet activity allows students to explore the various situations described in "The Chairs Around the Table" lesson (cataloged separately). The user can select Exploration mode, in which the number of chairs needed for a particular arrangement of tables is displayed; or Guess, in which the user is able to construct an arrangement and then predict the number of chairs. There are two types of tables to choose from and two different table arrangements. Instructions and exploration question are provide. | Activity, Interactive Media Grade Level: 3, 4, 5, 6+ | |

In this lesson from Illuminations, students explore and discover linear relationships. Linear patterns are identified, extended and described verbally, numerically and algebraically through three investigations. Using manipulatives and the linked applet, "Chairs", learners determine the number of chairs needed when the number of tables is known, and vice versa. Instructional plan, questions for the students, assessment options, extensions and teacher reflections are provided. | Activity, Interactive Media Grade Level: 3, 4, 5 Resource is part of a PD collection | |

This problem offers students an opportunity to analyze an interactive Flash game similar to "First Connect Three" (cataloged separately) which involves adding and subtracting positive and negative numbers. This advanced version includes a game board with the integers from -12 to 12. Each player rolls the dice, (one with the numbers 1, 2, 3, −4, −5, −6 and the other with the numbers −1, −2, −3, 4, 5, 6), chooses which number to begin with and whether to add or subtract the other number to produce either a negative or positive result shown on the board. The goal is to be first player to complete a row of three counters either horizontally, vertically or diagonally on the game board. There a link to a resource, "Playing Connect Three" (cataloged separately). | Activity, Game, Interactive Media Grade Level: 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 |