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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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 virtual manipulative is a Java applet that allows students to explore concepts in whole number operations and fractions, just as they would with a physical manipulative such as Cuisinaire Rods. The user can add bars of length 1 to 10 to the workspace, change their color, and move, duplicate, or remove them. Instructions for using the applet and teaching ideas for parents/teachers are available through the links at the top of the page. | Activity Grade Level: K, 1, 2, 3, 4, 5, 6+ | |

This interactive Flash applet provides a classroom display for demonstrating additions using the fingers on a pair of hands. It is useful for those just learning the sums from 5 and up. | Demonstration, Interactive Media Grade Level: Pre-K, K | |

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 | |

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 27-minute video demonstrates Hungary's approach to teaching primary math and compares it to practices in the UK. Hungarian pupils absorb concepts early on, manipulating objects, using visual models and learning mental math techniques. Teachers introduce written methods when pupils have a solid grasp of the mathematical processes they represent and stronger kinesthetic skills. Lessons through the first five years are lively and logically-structured and involve all children actively. The video describes how the training of Hungarian teachers provides thorough grounding in the math they need to know and the methods they should use to teach math effectively. A side bar includes reflection questions for viewers. | Instructional Strategy, Video Grade Level: K, 1, 2, 3, 4 | |

This 42-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 Kindergarten 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 1-5. | Instructional Strategy, Reference Materials Grade Level: K | |

This web page provides links to resources aligned to the CCSS that guide and support kindergarten mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) and Problems of the Month, (POM home page is cataloged separately) 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. Resources are listed for specific kindergarten standards and are also organized by progression for an alternate search route. | Instructional Strategy, Problem Set Grade Level: K |