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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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 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 | |

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 | |

In this iOS App students recognize numbers of dots on dominos and identify their value, compare their values, and use their values to complete addition or subtraction equations up to ten. The first four levels of this App are free for calculations with numbers to ten, there are more levels and tasks available for a fee. Within each level of the App there are two buttons in the upper right corner. One is a camera button that will take a picture of a finished sheet and the other is an activity button that opens up more complicated equations with multiple operations. | Activity, Interactive Media Grade Level: 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 | |

Students can use this interactive Flash applet to practice subitizing and counting groups of objects, to understand the importance of 5 in our base-10 number system, and to learn basic addition facts. In the four included games students construct groups of 5 objects, add groups of objects within 10, and identify and record numbers within 10. Auditory prompts support students with limited reading ability. | Activity, Interactive Media Grade Level: K, 1 | |

This intereactive Flash applet helps children learn grouping, tally marks, place value, addition, and subtraction. Students help the alien spaceship move cows into corrals by counting by 5s and 10s. They also can apply those grouping skills to practice adding and subtracting two-digit numbers with regrouping. Audio cues and prompts reinforce the user's actions and facilitate counting and the development of math language. | Activity, Interactive Media Grade Level: K, 1, 2 | |

This website, devoted to early numeracy skills, includes links to Happy Numbers teacher accounts, student accounts, and blog. A free teacher account provides access to applets that develop conceptual understanding and procedural fluency. The applets are compatible with interactive whiteboards and tablets. With a subscription teachers can create student accounts and individualize assignments. The blog posts further explain how to utilize these applets in the classroom. | Activity, Interactive Media, Community Grade Level: K, 1, 2 | |

The activities in this 6-lesson unit use fish-shaped crackers to help students develop their understanding of comparative subtraction by exploring five meanings of subtraction (counting, sets, number line, balance, and inverse of addition). Students investigate properties of subtraction, represent subtraction with objects and pictures, record subtraction with vertical notation and equations, create and solve problems, and carry out missing addend activities. Lessons include questions for student discussion and teacher reflection, extensions, printable student sheets, assessment options, and links to online applets. | Activity, Game, Instructional Strategy, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 |