Operations and Algebraic Thinking

Understand and apply properties of operations and the relationship between addition and subtraction.

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This 46-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 1 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 and 2-5. | Instructional Strategy, Reference Materials Grade Level: 1 | |

This problem with multiple solutions offers an opportunity for students to practice simple addition and subtraction, work with number sentences (equations), and develop systematic work habits. Given cards containing the addition, subtraction and equal signs along with the digits 2, 4, 6, and 8. solvers are challenged to find as many ways as possible to arrange some or all seven cards to create true statements. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, printable cards (pdf) and a link to an interactive Flash applet. | Activity, Interactive Media Grade Level: 1, 2 | |

This web site contains information and interactive applets related to our Hindu-Arabic number system. Users learn the history and structure of the system as well as how to count and write numbers. Users can learn and practice various algorithms for whole number computation and explore fractions, decimals and percents in our number system. The site explains various sets of numbers and how they relate to operations. | Activity, Interactive Media, Tutorial, Reference Materials Grade Level: 1, 2, 3, 4, 5 | |

This interactive Java game, similar to Connect Four, helps students develop game strategy and fluency with number facts. Two players each try to connect four game pieces in a row (vertically, horizontally or diagonally) before the opponent does by correctly answering problems. For each game players can choose whole numbers and/or integers as well as the operation(s) – addition, subtraction, multiplication, division. They can also select the difficulty level and the time limit for each problem. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5, 6+ | |

This problem, from the collection of Aunty Mathilda challenges, promotes algebraic thinking and problem solving strategies. Aunty Math must determine the individual weight of her two nephews and niece given clues about their combined weight. Included are links to an easier challenge and to a harder one, depending on the level of the solver, and a link to a page for parents and teachers with additional background support, alignment to the CCSS, explanations and extensions. | Activity Grade Level: 1, 2, 3 | |

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet. | Activity, Instructor Guide/Manual, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately). | Activity, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

This interactive 100 grid has a variety of open-ended uses. Users can "make" as many counters as they choose from among three different kinds, and then drag them onto the grid, allowing any number to be covered by up to 3 different markers at one time. An Ideas page offers possible tasks and games suited to the applet. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5 | |

With this flexible Flash applet students can explore a wide range of concepts, including addition and subtraction, factors and multiples, fractions, ratios, and combinations. Users place, move and rotate virtual Cuisenaire Rods on a grid which can be enlarged, reduced, moved or printed. It contains a link to page of challenges which can take advantage of this tool. | Activity, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This interactive Flash applet models the difference meaning of subtraction. A child or teacher can compare two rows of beads and analyze the calculation they represent. Once a user sets up the two rows of beads (up to 30 each), the applet provides a series of animations which represents the rows with two number lines and then as a single number line with the difference indicated by a "jump". This applet works well with an interactive white board. A teacher's guide to this series of applets is cataloged separately. | Activity, Interactive Media Grade Level: K, 1, 2 |