Operations and Algebraic Thinking

Work with addition and subtraction equations.

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This 46-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 grade 1 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 K and 2-5. | Instructional Strategy, Reference Materials Grade Level: 1 | |

This web site contains information and interactive applets related to our Hindu-Arabic number system. Users learn the history and structure of the system as well as how to count and write numbers. Users can learn and practice various algorithms for whole number computation and explore fractions, decimals and percents in our number system. The site explains various sets of numbers and how they relate to operations. | Activity, Interactive Media, Tutorial, Reference Materials Grade Level: 1, 2, 3, 4, 5 | |

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 Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf). | Activity, Lesson Plans Grade Level: K, 1, 2 | |

This iOS app ($) is a collection of 18 activities providing practice with a wide range of early math skills involving number, shape, and measurement. | Activity, Interactive Media, Mobile App Grade Level: Pre-K, K, 1, 2 | |

This interactive Flash tool allows primary students to explore the concepts of equality and inequality with a balance. Learners receive cubes on both sides of a balance and must select from the given choices to determine the correct number of cubes to equalize the balance. | Activity, Interactive Media Grade Level: 1, 2 | |

This interactive 100 grid has a variety of open-ended uses. Users can "make" as many counters as they choose from among three different kinds, and then drag them onto the grid, allowing any number to be covered by up to 3 different markers at one time. An Ideas page offers possible tasks and games suited to the applet. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5 | |

This game from the BBC reinforces doubling and mental addition for a range of abilities. Students attempt to reach a target score by placing darts on the correct sections of a dartboard. The first level of the game provides practice doubling with a single number. Levels 2 and 3 increase the challenge level by involving two and three addends. Teachers and parents can control the starting level and the optional timing feature. | Game Grade Level: K, 1, 2, 3 | |

This interactive Java applet provides students with practice in subtraction and pattern recognition. Starting with four numbers in the corners of an outside square, students find the differences (larger minus the smaller) between the pair of numbers on each side of the square. After correctly completing each square, they repeat the process for the next inner square, until all squares are complete. Students can explore the patterns that emerge as they work toward the center square. Users can choose to work with whole numbers, integers, fractions, decimals, or money. They may also create their own problems by selecting the four starting numbers for the outside square. | Activity, Game, Interactive Media Grade Level: 1, 2, 3, 4, 5 | |

In this 6-lesson unit, students use dominoes to explore four models of addition: counting, number line, sets, and balanced equations. They learn about the commutative property, the relation between addition and subtraction, the result of adding 0, and the concept of doubles. Students write story problems which involve the operation of addition and begin to memorize the addition facts. They represent addition in pictures. The various models of addition help students develop a rich conceptual schema for addition. Included are a Bibliography of Counting Books, student materials, questions for student and teacher reflection, assessment and extension ideas. [Suggestion: Use the alternate applet, Pan Balance - Numbers, listed as a Related Resource, rather than Pan Balance - Shapes, in Lesson 4.] | Activity, Game, Lesson Plans, Unit of Instruction Grade Level: K, 1, 2 |