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 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 | |

In this problem students practice addition and subtraction (and possibly multiplication) while developing systematic work strategies. Given two types of ladybirds, each with either 4 or 7 spots, learners explore ways of combining them to achieve different total numbers of spots. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and links to related games. | Activity Grade Level: 1, 2, 3 | |

This 5-lesson unit is intended to help children who already understand the meanings of addition to develop fluency with addition facts. The activities and games take advantage of commutativity, the additive identity, doubles, and number patterns to develop operation sense and foster retention. Lessons include student materials, questions for students and teachers, assessment ideas, and links to interactive applets. | Activity, Game, Instructional Strategy, Lesson Plans, Unit of Instruction Grade Level: 1, 2 Resource is part of a PD collection | |

In this unit plan, primary learners explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using concrete (links), pictorial, and verbal representations to develop an understanding of symbolic notations. Students also investigate fact families, including those where one addend is 0 and where the addends are alike and also learn that the order (commutative) property) does not hold for subtraction. A brief bibliography of related books for children is provided. Instead of using hands on manipulatives and balances, links to Java applets: Pan Balance-Shapes and Pan Balance-Numbers ( both cataloged separately) are included. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to down load all student resources. | Activity, Interactive Media, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

In this 6-lesson unit students use pasta shapes to explore the take away model of subtraction in several different contexts (counting, sets, number line, balanced equations, and inverse of addition). They decompose numbers, explore the zero property, act out subtraction situations with objects and pictures, record differences with vertical and in horizontal notation, create fact families, find differences with a calculator, and compose and solve problems involving subtraction. The lessons include student activity sheets (pdf), questions for student discussion and teacher reflection, assessment options, and links to online applets. | Activity, Game, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 | |

This interactive online game for one or two players provides practice with number facts and builds strategic thinking and pattern discovery. Players choose an operation (addition, subtraction or multiplication) and 100 problems appear in a 10 by 10 grid. They then select problems that match given target numbers while attempting to get 5 in a row in the grid. Users have the option of working for 3 in a row on a 5 by 5 board, and of turning the sound off. This game is a good balance of skill and luck. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

In this lesson students find and record addends that sum to ten in three different activities, using ten frames, linking cubes, two-sided counters, and a concentration game. The lesson includes suggestions for assessment and extension, reflection questions for students and teachers, links to related resources, and printable materials (pdf). | Activity, Game, Interactive Media, Lesson Plans Grade Level: K, 1, 2 |