Operations and Algebraic Thinking

Add and subtract within 20.

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Resource | Resource Type Grade Level | Rating |
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This interactive applet contains four puzzles which develop fluency with addition facts and foster logical reasoning. Each puzzle provides a shape with blanks along its sides and diagonals. The user must fill in the blanks with the numbers provided to reach the same target sum along each side/diagonal. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This flexible interactive applet helps students develop number sense and fluency as they explore number sequences and patterns. Users can select preset or random number lines, or create their own by entering starting numbers and increments. Colored blocks can be dragged to hide or reveal specific terms in any sequence. Starting numbers and increments may be positive or negative; they may also be decimals. An Ideas page suggests possible uses for this applet. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5, 6+ | |

This variation of Tic Tac Toe develops students' strategic thinking. Two players, one using 1s and the other using 0s, take turns entering their numbers into the cells of a 3 by 3 grid. The winner is the first to complete three in a row with an odd sum. The game can be played on paper with a friend or against the computer with the interactive applet. The interactive version allows a user to choose which number to play with and whether to go first or second, providing an opportunity to refine strategy by reflecting on how these choices affect the outcome. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This number puzzle helps children develop fluency with pairs of numbers that sum to 10 while applying logic and spatial-visualization skills. Users arrange 9 small triangles within a large one so that the numbers on the matching edges total 10. Students can use the interactive Flash applet or the printable (pdf) triangles provided. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to related games (cataloged separately). | Activity, Interactive Media Grade Level: 1, 2, 3 | |

This article focuses on the role and techniques of effective ("distributed") practice that leads to full and fluent mastery of mental mathematics as well as conceptual growth around properties of arithmetic. It lists the essential mental math skills needed for fluent computation at grades 1, 2, and 3. The article describes a number of strategies for developing mental skills and links to pages with more details on others (some not yet complete). While this article refers to the Think Math! curriculum published by EDC, the methods generalize to any program. The Fact of the Day technique and a related video are cataloged separately. | Activity, Instructional Strategy, Reference Materials, Article Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection | |

This pair of videos (8 min and 10 min) and accompanying text illustrate various strategies for providing mental skills practice that is brief, interesting, useful, and effective. They include examples of teachers working with their students in group settings as well as narrative elaboration by Paul Goldenburg. Two related articles (Practice and Fact of the day) are cataloged separately. | Activity, Instructional Strategy, Reference Materials, Article, Video Grade Level: 1, 2, 3, 4, 5, 6+ | |

This interactive Flash applet helps children understand the "take away" model of subtraction. Users choose starting numbers from within 10 or 20. A group of rabbits appears and the user is asked how many will remain if a certain number run away. Mousing over a clue button dims the number of runaways. After selecting the correct remainder, the rabbits run away, and the applet displays the number model and the word sentence that represent the problem. [Available for iPad & iPhone in the iTunes AppStore.] | Activity, Interactive Media Grade Level: K, 1, 2 | |

This is a collection of simple interactive activities to help young children practice early number skills. They use visual representations to develop counting and subitizing skills, number sense, place value concepts, and basic whole number operations (addition, subtraction, doubling). A teacher page summarizes the purpose and functions of each activity. | Activity, Interactive Media Grade Level: Pre-K, K, 1, 2 | |

This free iOS app provides activities for young children to develop skills in writing numerals, counting, addition, ordering, patterns, parity, algebraic thinking, and problem solving. | Activity, Interactive Media, Mobile App Grade Level: K, 1 | |

This interactive activity helps a user understand that one concept of subtraction is finding a missing addend. In each scenario, there is a given number of animals and some of them leave or hide, and the student must select the number from four choices that are missing based on knowing how many animals are still there. If a correct response is given, then the family of facts are provided and if an incorrect response is made, there is positive instructional feedback provided. | Activity, Interactive Media Grade Level: K, 1, 2 |