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 iOS app requires students to use a ten frame to fill in the remaining addend with contrasting chips and then count them to tell how many more to make ten. The app can be set to build sequentially or it can be set to give random values. Additionally, the app includes an option to show number sentences when the problem is complete. | Activity, Interactive Media, Mobile App Grade Level: K, 1 | |

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 | |

This 28-minute video contains a panel interview with three experts in the areas of math, cognition, and dyscalculia. The panel discusses the nature of dyscalculia, how to diagnose students with dyscalculia, and how to teach students with dyscalculia. | Events, Instructional Strategy, Community, Video Grade Level: K, 1, 2, 3, 4, 5, 6+ Resource is part of a PD collection | |

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 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 | |

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 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 |