Operations and Algebraic Thinking

Work with addition and subtraction equations.

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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 | |

This page provides examples of First Grade Number (Operations and Algebraic Thinking, and Number and Operations in Base Ten) 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 listed are in PDF format. | Activity, Game Grade Level: 1 | |

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 activity promotes algebraic thinking of equivalency as well as giving children practice in addition and subtraction. Since there are many different solutions for the values of the unknowns, learners can focus on the idea of working systematically. Students see two weights on one side of an interactive balance, and are asked to find how many different ways they can hang three weights on the other side for it to be balanced. An easier problem, "Number Balance", (cataloged separately) is linked on the problem page. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support. | Activity, Interactive Media Grade Level: 1, 2, 3 | |

This page contains thirty-three problems involving algebraic thinking from the Port Angeles School District in Washington state. Links to state GLEs and revised standards are provided. Topics covered include patterns, and concepts of equality and inequality and applications of arithmetic. | Problem Set 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 | |

This interactive Flash applet helps students develop number sense and fluency with addition and subtraction facts within 10. Okta hides some bubbles under a shell, and then either adds more bubbles or takes some away. Students determine how many bubbles are left under the shell. Users can choose a specific one-digit starting number or let the applet choose randomly. Users can select addition, subtraction or both. | Activity, Interactive Media Grade Level: K, 1 | |

This open-ended interactive Flash applet can be used in many ways to develop numeracy concepts and skills. It provides three highlight colors, a hide or reveal feature, and the ability to vary the start number and the increment size. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5, 6+ |