Operations and Algebraic Thinking

Understand and apply properties of operations and the relationship between addition and subtraction.

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Resource | Resource Type Grade Level | Rating |
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This interactive applet gives students practice with addition and subtraction of whole numbers and integers. Users drag the given number arrows onto a number line and choose whether to add or subtract them in order to arrive at the given target number. After all arrows are placed in a correct arrangement, a user drags numbers and operations signs to create a number sentence (equation) that represents the arrow sequence. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

This activity helps children become more familiar with horizontal and vertical number lines (0 through 10) and how to use them for addition. It can be used to introduce subtraction as the inverse of addition and the use of an unknown number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, printable number lines (pdf), and a link to a related game, Incey Wincey Spider (catalogued separately). | Activity Grade Level: K, 1 | |

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 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 | |

In this lesson, students will play the roles of banker and consumers as they learn how to use different combinations of coins to make money amounts up to 25 cents. Students will earn money and save it in their piggy banks until they have the exact amount to purchase an item of their choice. Suggestions for questions and assessment options are included. | Lesson Plans Grade Level: Pre-K, K, 1, 2 | |

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 | |

The characters in this free iOS app model effective strategies for learning addition facts (counting, counting on, near doubles, tens). During the tool round children develop conceptual understanding as they practice using these strategies. The speed round develops fact fluency and encourages memorization, providing hints as needed. Controls allow teachers to setup a class and adjust difficulty settings. | Interactive Media, Mobile App Grade Level: K, 1, 2 | |

This interactive Flash applet contains a progressive range of exercises to sharpen mental math and recall of number facts. Levels include one-digit addition and subtraction within 20, two-digit addition and subtraction within 100, and multiplication up to x5 and x10. The goal is to complete 10 correctly as quickly as possible. An incorrect answer deletes a point, discouraging guessing. At the end of each round the applet reports the time taken and the number of errors. | Activity, Interactive Media Grade Level: 1, 2, 3, 4 | |

This article discusses the importance of abstraction and generalization in being able to use models and diagrams effectively, whether children are creating their own models to represent a situation and explain their thinking, or interpreting a provided model. The resource offers examples to illustrate these ideas as well as teaching strategies and activities in the areas of parity, mental addition, equivalent fractions, and multi-digit multiplication. | Activity, Instructional Strategy, Instructor Guide/Manual Grade Level: 1, 2, 3, 4, 5 Resource is part of a PD collection |