Counting and Cardinality

Count to tell the number of objects.

4. Understand the relationship between numbers and quantities; connect counting to cardinality.

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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 interactive Flash applet is a number matching activity for up to ten objects. Students develop mouse skills as they click on a given number of moving fish, which land in their fish bowl. When children decide they have caught the right number, they can check their accuracy. Users may also listen to a counting song. | Activity, Interactive Media Grade Level: K | |

Students can use this interactive Flash applet to practice subitizing and counting groups of objects, to understand the importance of 5 in our base-10 number system, and to learn basic addition facts. In the four included games students construct groups of 5 objects, add groups of objects within 10, and identify and record numbers within 10. Auditory prompts support students with limited reading ability. | Activity, Interactive Media Grade Level: K, 1 | |

This interactive Flash applet provides a classroom display for demonstrating additions using the fingers on a pair of hands. It is useful for those just learning the sums from 5 and up. | Demonstration, Interactive Media Grade Level: Pre-K, K | |

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 | |

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 | |

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 | |

In this Peg+Cat interactive game players navigate a treasure map by following directions and counting. Players are given a grid and directions on where to move Peg next on the treasure map, each direction includes a direction and a number of spaces. | Game Grade Level: Pre-K, K | |

This Flash-based game of chance helps young children learn to move along a track either side of a central point, as a precursor to working on a number line. Using the familiar nursery rhyme as a context, players roll a die to move either up or down a vertical waterspout. The game can be played with the applet or on paper (printable pdf included). A 2-dice variation introduces strategic thinking. The Teacher' Notes page suggests strategies for introducing the game, questions to facilitate students' thinking, support suggestions, and a link to a more advanced version of the game (Tug of War, cataloged separately). | Activity, Game, Interactive Media Grade Level: K, 1 | |

This 42-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 Kindergarten 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 1-5. | Instructional Strategy, Reference Materials Grade Level: K |