Operations and Algebraic Thinking

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

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Resource | Resource Type Grade Level | Rating |
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This problem is an investigation into combinations of a number of cubes. It is a practical activity which involves working systematically, and visualizing and relating 3D shapes to their representation on paper. Children are asked how many different towers are possible using seven cubes on a base of two of them. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable handouts (word/pdf). | Activity Grade Level: K, 1, 2 | |

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 | |

This formative assessment lesson is intended to help teachers assess how well students are able to use addition and subtraction in a problem solving situation. In particular, this lesson aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data, examining the data and looking for patterns and lastly describing and explaining findings clearly and effectively. | Activity, Lesson Plans Grade Level: K, 1, 2, 3 | |

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 Flash applet supports the exploration of early number. A child or teacher can place a number of objects on the screen and then move the objects to group them, drag them onto a number line or track, into a hoop to create sets of objects, or into a 10 by 10 grid. This applet lends itself well to group work with a projector. Clicking on the info button allows the user to mouse over items to learn how to use them. | Activity, Interactive Media Grade Level: K, 1, 2 | |

This interactive Flash applet supports the exploration of numbers to 100 by simulating a 100-bead string. A teacher or child can move all or some beads to the left or right to add and subtract. The controls allow users to move beads individually or 10 at a time to model different counting and calculation strategies. Users can hide or show the numbers represented by the beads. This applet lends itself well to use on an interactive white board. A pdf guide to this collection of teaching applets is cataloged separately. | Activity, Interactive Media Grade Level: K, 1, 2 | |

In this 6-lesson unit, students use dominoes to explore four models of addition: counting, number line, sets, and balanced equations. They learn about the commutative property, the relation between addition and subtraction, the result of adding 0, and the concept of doubles. Students write story problems which involve the operation of addition and begin to memorize the addition facts. They represent addition in pictures. The various models of addition help students develop a rich conceptual schema for addition. Included are a Bibliography of Counting Books, student materials, questions for student and teacher reflection, assessment and extension ideas. [Suggestion: Use the alternate applet, Pan Balance - Numbers, listed as a Related Resource, rather than Pan Balance - Shapes, in Lesson 4.] | Activity, Game, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

This interactive Flash applet provides a customizable set of dominoes that users can manipulate to play games or solve puzzles. It can be used with an interactive whiteboard to facilitate group work. Users can determine the size of a set (up to double-9), remove individual dominoes, rotate and move them, and change their size. The Teachers' Notes page includes a link to page containing domino games and challenges (cataloged separately). | Interactive Media Grade Level: K, 1, 2, 3, 4, 5 | |

This 37-page pdf provides background information and teaching activities for developing young children's number sense. The document includes instructions and printable materials for using dot cards, five frames, and ten frames. | Activity, Game, Instructional Strategy, Lesson Plans Grade Level: Pre-K, K, 1 | |

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 |